TSTP Solution File: SWV665-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV665-1 : 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 16:27:36 EDT 2022
% Result : Timeout 300.05s 300.42s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SWV665-1 : TPTP v8.1.0. Released v4.1.0.
% 0.00/0.08 % Command : bliksem %s
% 0.07/0.27 % Computer : n032.cluster.edu
% 0.07/0.27 % Model : x86_64 x86_64
% 0.07/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27 % Memory : 8042.1875MB
% 0.07/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27 % CPULimit : 300
% 0.07/0.27 % DateTime : Thu Jun 16 04:39:59 EDT 2022
% 0.07/0.27 % CPUTime :
% 1.11/1.48 *** allocated 10000 integers for termspace/termends
% 1.11/1.48 *** allocated 10000 integers for clauses
% 1.11/1.48 *** allocated 10000 integers for justifications
% 1.11/1.48 *** allocated 15000 integers for termspace/termends
% 1.11/1.48 *** allocated 22500 integers for termspace/termends
% 1.11/1.48 *** allocated 33750 integers for termspace/termends
% 1.11/1.48 *** allocated 50625 integers for termspace/termends
% 1.11/1.48 Bliksem 1.12
% 1.11/1.48
% 1.11/1.48
% 1.11/1.48 Automatic Strategy Selection
% 1.11/1.48
% 1.11/1.48 Clauses:
% 1.11/1.48 [
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.11/1.48 ), =( Z, Y ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.11/1.48 ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.11/1.48 ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.11/1.48 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 1.11/1.48 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.11/1.48 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =( Y, Z ), ~(
% 1.11/1.48 'c_Deriv_Oderiv'( T, U, Z, X ) ), ~( 'c_Deriv_Oderiv'( T, U, Y, X ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), 'c_HOL_Oord__class_Oless'( Y, Z,
% 1.11/1.48 'tc_nat' ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.11/1.48 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.11/1.48 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.11/1.48 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), ~( =( hAPP(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), =( Y, Z ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), =( Y, Z ) ],
% 1.11/1.48 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.11/1.48 , hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), hAPP(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ],
% 1.11/1.48 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.11/1.48 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 1.11/1.48 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.11/1.48 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), hAPP(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ), ~( 'c_lessequals'( Z, Y, X
% 1.11/1.48 ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.11/1.48 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.11/1.48 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.11/1.48 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.11/1.48 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.11/1.48 [ =( hAPP( 'c_COMBC'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), Y ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.11/1.48 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.11/1.48 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Y, X ) )
% 1.11/1.48 , ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Y
% 1.11/1.48 , X ), 'c_lessequals'( Y, Y, X ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.11/1.48 , Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.11/1.48 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.11/1.48 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.11/1.48 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.11/1.48 'tc_nat' ) ), 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X,
% 1.11/1.48 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.48 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.11/1.48 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.11/1.48 'tc_nat' ) ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.11/1.48 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.11/1.48 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.11/1.48 , Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 1.11/1.48 , X ), X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 1.11/1.48 , X ), X ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.11/1.48 X ), Y ) ), Y ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y, hAPP(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.11/1.48 X ), Y ) ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y, hAPP(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.11/1.48 X ), Y ) ) ) ],
% 1.11/1.48 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =( hAPP(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.11/1.48 X ), Y ) ), Y ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.11/1.48 X ), Y ) ), Y ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.11/1.48 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.11/1.48 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.11/1.48 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.11/1.48 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.11/1.48 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.11/1.48 Z ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.11/1.48 Z ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ),
% 1.11/1.48 ~( 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), Y, X )
% 1.11/1.48 ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ),
% 1.11/1.48 ~( 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), Y, X )
% 1.11/1.48 ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ),
% 1.11/1.48 ~( 'c_lessequals'( Z, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X )
% 1.11/1.48 ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ),
% 1.11/1.48 ~( 'c_lessequals'( Z, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X )
% 1.11/1.48 ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), =( hAPP(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.11/1.48 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.48 ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.11/1.48 ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y ) ), =( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.48 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.11/1.48 ), Y ) ) ), =( 'c_HOL_Ozero__class_Ozero'( X ), Y ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.11/1.48 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.11/1.48 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.11/1.48 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.11/1.48 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.11/1.48 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.11/1.48 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.11/1.48 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.11/1.48 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.11/1.48 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.48 T, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.11/1.48 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.11/1.48 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.48 T, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.11/1.48 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.11/1.48 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.48 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.11/1.48 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.11/1.48 'c_lessequals'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.48 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.48 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.11/1.48 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.11/1.48 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.48 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.11/1.48 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.11/1.48 , Z ), T ), X ), ~( 'c_lessequals'( Y, T, X ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.11/1.48 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ),
% 1.11/1.48 ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z )
% 1.11/1.48 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, hAPP(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.11/1.48 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.48 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.11/1.48 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.11/1.48 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.11/1.48 'tc_nat' ) ), Y ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.11/1.48 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.11/1.48 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.11/1.48 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.11/1.48 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ),
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.48 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.11/1.48 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y,
% 1.11/1.48 'tc_nat' ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.11/1.48 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.11/1.48 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~( 'c_lessequals'( Y
% 1.11/1.48 , T, X ) ), 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.11/1.48 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.11/1.48 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.11/1.48 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Y, Z ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y
% 1.11/1.48 , Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.11/1.48 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Z, Y ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.11/1.48 ), =( Z, Y ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.11/1.48 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oone__class_Oone'(
% 1.11/1.48 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.48 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.11/1.48 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X,
% 1.11/1.48 Z, 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.11/1.48 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, Z, 'tc_nat' ) ),
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ), Z, 'tc_nat' ) ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.11/1.48 hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ),
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), Z, X ) ) ],
% 1.11/1.48 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, U ), T ) )
% 1.11/1.48 , hAPP( hAPP( Y, hAPP( hAPP( X, Z ), U ) ), T ) ), ~(
% 1.11/1.48 'c_Groebner__Basis_Ogb__semiring'( X, Y, W, V0, V1, V2 ) ) ],
% 1.11/1.48 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ), hAPP( hAPP( Y, hAPP(
% 1.11/1.48 hAPP( X, Z ), U ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Y, W
% 1.11/1.48 , V0, U, V1 ) ) ],
% 1.11/1.48 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ), hAPP( hAPP( Z, hAPP(
% 1.11/1.48 hAPP( X, T ), U ) ), Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, W
% 1.11/1.48 , V0, U, V1 ) ) ],
% 1.11/1.48 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, hAPP( hAPP( X, T ), T ) ),
% 1.11/1.48 Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, U, W, T, V0 ) ) ],
% 1.11/1.48 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.11/1.48 X, T, U, Y, W, V0 ) ) ],
% 1.11/1.48 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.11/1.48 X, T, U, Z, W, V0 ) ) ],
% 1.11/1.48 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.11/1.48 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.11/1.48 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.11/1.48 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.11/1.48 'c_Groebner__Basis_Ogb__semiring'( Y, X, W, V0, V1, V2 ) ) ],
% 1.11/1.48 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.11/1.48 T, X, U, Y, W, V0 ) ) ],
% 1.11/1.48 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.11/1.48 T, X, U, Z, W, V0 ) ) ],
% 1.11/1.48 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.11/1.48 T, X, U, W, Y, V0 ) ) ],
% 1.11/1.48 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.11/1.48 T, X, U, W, Z, V0 ) ) ],
% 1.11/1.48 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.11/1.48 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.11/1.48 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.11/1.48 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.11/1.48 , hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), hAPP( hAPP( X, T ), U ) ) ) ),
% 1.11/1.48 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.11/1.48 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.11/1.48 , hAPP( hAPP( X, T ), hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), U ) ) ),
% 1.11/1.48 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.11/1.48 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.11/1.48 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.11/1.48 , V0, V1, V2 ) ) ],
% 1.11/1.48 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.11/1.48 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.11/1.48 W, V0, V1, V2 ) ) ],
% 1.11/1.48 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.11/1.48 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.11/1.48 , V0, V1, V2 ) ) ],
% 1.11/1.48 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.11/1.48 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.11/1.48 W, V0, V1, V2 ) ) ],
% 1.11/1.48 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.11/1.48 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.11/1.48 ~( 'c_Groebner__Basis_Ogb__semiring'( X, W, V0, V1, V2, V3 ) ) ],
% 1.11/1.48 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.11/1.48 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.11/1.48 W, V0, V1, V2 ) ) ],
% 1.11/1.48 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.11/1.48 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.11/1.48 W, V0, V1, V2 ) ) ],
% 1.11/1.48 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.11/1.48 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.11/1.48 , V0, V1, V2 ) ) ],
% 1.11/1.48 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.11/1.48 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.11/1.48 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.11/1.48 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.11/1.48 , V0, V1, V2 ) ) ],
% 1.11/1.48 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.11/1.48 X, T, U, Y, W, V0 ) ) ],
% 1.11/1.48 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.11/1.48 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.11/1.48 , V0, V1, V2 ) ) ],
% 1.11/1.48 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.11/1.48 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.11/1.48 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.11/1.48 T, X, U, Y, W, V0 ) ) ],
% 1.11/1.48 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.11/1.48 T, X, U, W, Y, V0 ) ) ],
% 1.11/1.48 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.11/1.48 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.11/1.48 , V0, V1, V2 ) ) ],
% 1.11/1.48 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.11/1.48 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.11/1.48 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( Z, hAPP(
% 1.11/1.48 hAPP( X, Y ), T ) ), hAPP( hAPP( X, Y ), U ) ) ), ~(
% 1.11/1.48 'c_Groebner__Basis_Ogb__semiring'( Z, X, W, V0, V1, V2 ) ) ],
% 1.11/1.48 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.11/1.48 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.11/1.48 'c_Groebner__Basis_Ogb__semiring'( W, Y, X, V0, V1, V2 ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.11/1.48 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 1.11/1.48 ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.48 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), ~( 'c_lessequals'( Y,
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.11/1.48 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.11/1.48 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.48 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) )
% 1.11/1.48 ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ),
% 1.11/1.48 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.11/1.48 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y, X ) )
% 1.11/1.48 ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y, X ),
% 1.11/1.48 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.48 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) )
% 1.11/1.48 ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ),
% 1.11/1.48 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.11/1.48 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y, X ) )
% 1.11/1.48 ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y, X ),
% 1.11/1.48 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.48 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.11/1.48 X ), Y ) ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z
% 1.11/1.48 ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_Fun_Oinj__on'( 'c_COMBC'( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.11/1.48 , 'tc_nat', 'tc_nat', 'tc_nat' ), Y, 'tc_nat', 'tc_nat' ) ],
% 1.11/1.48 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( hAPP(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), X, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.11/1.48 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.11/1.48 , Z, X ) ) ), =( 'c_Divides_Odiv__class_Omod'( hAPP(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ),
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.11/1.48 T ), Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.11/1.48 'c_COMBB'( 'c_HOL_Ouminus__class_Ouminus'( X ), Y, X, X, X ), Z, hAPP(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( X ), T ), X ), ~( 'c_Deriv_Oderiv'( Y, Z
% 1.11/1.48 , T, X ) ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 1.11/1.48 , X ) ) ],
% 1.11/1.48 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.11/1.48 , Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.11/1.48 , Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.11/1.48 , X ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.11/1.48 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), Y ),
% 1.11/1.48 ~( 'c_Groebner__Basis_Ogb__semiring'( Z, T, X, U, W, V0 ) ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.11/1.48 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.11/1.48 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.11/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.11/1.48 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), Y,
% 1.11/1.48 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.11/1.48 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.48 , 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.48 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.11/1.48 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.11/1.48 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.11/1.48 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'(
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.11/1.48 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.11/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.48 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.11/1.48 X ), Y ) ), Z ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.11/1.48 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ),
% 1.11/1.48 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.11/1.48 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_lessequals'( Y, T
% 1.11/1.48 , X ) ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.11/1.48 , X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 1.11/1.48 , X ) ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.11/1.48 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.11/1.48 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X
% 1.11/1.48 ) ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.11/1.48 ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X
% 1.11/1.48 ) ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.11/1.48 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 1.11/1.48 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.11/1.48 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), ~(
% 1.11/1.48 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.11/1.48 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.11/1.48 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.11/1.48 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.11/1.48 Y ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.11/1.48 Y ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.48 ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.11/1.48 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.11/1.48 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.11/1.48 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), Z ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.11/1.48 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.11/1.48 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( Z, T, X ) ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.11/1.48 X ), Y ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.11/1.48 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.11/1.48 ), U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X ), W ), T ), Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.11/1.48 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.11/1.48 ) ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.11/1.48 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.11/1.48 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.11/1.48 X ), Y ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP( hAPP(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =( hAPP( hAPP(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.11/1.48 X ), Y ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), hAPP( hAPP(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ],
% 1.11/1.48 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ],
% 1.11/1.48 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ],
% 1.11/1.48 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.11/1.48 X ), Y ) ), Z ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ],
% 1.11/1.48 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.11/1.48 X ), Y ) ), Z ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.11/1.48 X ), Y ) ), Z ) ) ],
% 1.11/1.48 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =( hAPP( hAPP(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ), =( Y, hAPP(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), =( Y, Z ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.11/1.48 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.11/1.48 ), Y ), T ), Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.11/1.48 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z,
% 1.11/1.48 T, X ) ), T, X ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.11/1.48 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.11/1.48 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.11/1.48 ) ), Z ), T, X ) ) ],
% 1.11/1.48 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.11/1.48 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, Y, X ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X )
% 1.11/1.48 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.11/1.48 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ), Y ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.11/1.48 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ) ), 'c_Divides_Odiv__class_Omod'(
% 1.11/1.48 Z, Y, X ) ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 1.11/1.48 ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.48 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.11/1.48 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ), T ), hAPP( hAPP(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 X ), Y ), 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ) ),
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ), Z ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), Y ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( Y, hAPP( hAPP(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.48 X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.11/1.48 ), Y ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 1.11/1.48 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.11/1.48 ), Z ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.48 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 1.11/1.48 , X ), ~( 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ), X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.11/1.48 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.11/1.48 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.11/1.48 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ),
% 1.11/1.48 ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.11/1.48 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.11/1.48 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.11/1.48 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.11/1.48 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ),
% 1.11/1.48 ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.11/1.48 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.48 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.11/1.48 ), Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), Z ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.11/1.48 ), Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ), Z ) ]
% 1.11/1.48 ,
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.11/1.48 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.11/1.48 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.11/1.48 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.48 T, X ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.11/1.48 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.11/1.48 , U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.11/1.48 'c_HOL_Oplus__class_Oplus'( X ), W ), T ), Z, X ) ) ],
% 1.11/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.11/1.48 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.11/1.48 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.11/1.48 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.11/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.48 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.11/1.48 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.11/1.49 , Y ), T ), Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.11/1.49 , Y ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ),
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.11/1.49 , Y ), Z ), T, X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.11/1.49 ), Y ) ), Z ) ), Z ) ],
% 1.11/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.11/1.49 , Y ), Z ), Z, X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.11/1.49 , Y ), Z ), Y, X ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.11/1.49 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.11/1.49 'c_lessequals'( Y, T, X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.11/1.49 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.11/1.49 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.11/1.49 'c_lessequals'( Z, T, X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.11/1.49 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.11/1.49 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.11/1.49 'c_lessequals'( Y, T, X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.11/1.49 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.11/1.49 'c_lessequals'( Z, T, X ) ) ],
% 1.11/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.11/1.49 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.11/1.49 ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.11/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.11/1.49 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z, T
% 1.11/1.49 , X ) ), T, X ) ) ],
% 1.11/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.11/1.49 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.11/1.49 ), Z ), T, X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), Z ) ), =( Y, hAPP(
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( X ), T ) ) ],
% 1.11/1.49 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OMin', X ) ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.11/1.49 ) ],
% 1.11/1.49 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ) ), hAPP(
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ),
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), Z ), Y ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), 'c_lessequals'( Z,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.49 X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), =( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.11/1.49 Z, 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.11/1.49 Z, 'tc_nat' ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.49 X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.11/1.49 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.11/1.49 ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.11/1.49 'class_OrderedGroup_Omonoid__mult'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Ominus__class_Ominus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.11/1.49 X ), Y ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP(
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ) ) ],
% 1.11/1.49 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.11/1.49 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.11/1.49 ), U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Ominus__class_Ominus'( X ), W ), T ), Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), T, X ),
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.11/1.49 ), Y ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.11/1.49 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), T, X ),
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.11/1.49 ), 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), Z ), T, X ) ) ],
% 1.11/1.49 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), T, X ),
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.11/1.49 ), 'c_Divides_Odiv__class_Omod'( Y, T, X ) ),
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.11/1.49 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), 'c_lessequals'( U, T, X
% 1.11/1.49 ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.11/1.49 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), 'c_lessequals'( Z, Y, X
% 1.11/1.49 ), ~( 'c_lessequals'( U, T, X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.11/1.49 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( T, U, X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.11/1.49 , X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.11/1.49 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, U
% 1.11/1.49 , X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Ominus__class_Ominus'( X ), Z ), Y ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ), X ), ~( 'c_lessequals'( U
% 1.11/1.49 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.49 , U, X ) ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.49 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.11/1.49 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.11/1.49 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), U )
% 1.11/1.49 , X ), ~( 'c_lessequals'( U, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), U, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 Y, T, X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.11/1.49 ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.11/1.49 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), U )
% 1.11/1.49 , X ), ~( 'c_HOL_Oord__class_Oless'( U, Z, X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U, X ) ), ~(
% 1.11/1.49 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.11/1.49 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.11/1.49 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.11/1.49 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ), hAPP(
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP(
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.11/1.49 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Z ),
% 1.11/1.49 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.11/1.49 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.11/1.49 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.11/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.49 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.11/1.49 ],
% 1.11/1.49 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Omod'( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.11/1.49 , Y ) ) ],
% 1.11/1.49 [ ~( hBOOL( hAPP( X, Y ) ) ), hBOOL( hAPP( X,
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.11/1.49 'tc_nat' ) ) ) ],
% 1.11/1.49 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.11/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.11/1.49 'c_lessequals'( Z, Y, X ) ],
% 1.11/1.49 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.11/1.49 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.11/1.49 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.11/1.49 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OMin', X ) ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), ~(
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.11/1.49 , 'tc_nat' ), 'tc_nat' ), 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.49 X ), X ), ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.11/1.49 X ), Z ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.11/1.49 ), Y ), 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.11/1.49 , 'tc_nat' ), 'tc_nat' ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.11/1.49 , 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.49 X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), ~(
% 1.11/1.49 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.11/1.49 , 'tc_nat' ), 'tc_nat' ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.11/1.49 , 'tc_nat' ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), ~(
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.11/1.49 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.11/1.49 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.11/1.49 , 'tc_nat' ), 'tc_nat' ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), =( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OMin', X ) ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP(
% 1.11/1.49 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X )
% 1.11/1.49 ), Y ) ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.11/1.49 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.11/1.49 , Y, X ) ) ],
% 1.11/1.49 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X,
% 1.11/1.49 Y, 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc',
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ) ),
% 1.11/1.49 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.49 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ),
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.49 'tc_nat' ) ), Y, 'tc_nat' ) ), Y, 'tc_nat' ) ) ) ],
% 1.11/1.49 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.11/1.49 , hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ),
% 1.11/1.49 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ), X ), ~(
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.11/1.49 X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( 'c_Suc',
% 1.11/1.49 'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ) ) ), 'tc_nat' ) ],
% 1.11/1.49 [ =( hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.11/1.49 , hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.11/1.49 ) ), 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ) ), X ),
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.11/1.49 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), hAPP( 'c_Suc',
% 1.11/1.49 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.11/1.49 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'( X, Y
% 1.11/1.49 , 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.49 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.11/1.49 [ =( X, hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.11/1.49 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.11/1.49 'tc_nat' ) ) ],
% 1.11/1.49 [ =( hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' )
% 1.11/1.49 , X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.11/1.49 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.49 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ) ), T ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( T, X, 'tc_nat' ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.11/1.49 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), =( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.49 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T
% 1.11/1.49 ) ), X ), Y, 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, X ) ) ],
% 1.11/1.49 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), =( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 1.11/1.49 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.49 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T
% 1.11/1.49 ) ), X ), Y, 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, T ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.11/1.49 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.11/1.49 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.11/1.49 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( =( 'c_Divides_Odiv__class_Omod'( X,
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 1.11/1.49 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.49 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X,
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ],
% 1.11/1.49 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.11/1.49 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X,
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.49 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.11/1.49 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.11/1.49 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.11/1.49 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.11/1.49 , ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.11/1.49 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.11/1.49 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.11/1.49 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.11/1.49 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.11/1.49 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.11/1.49 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.11/1.49 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.11/1.49 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.11/1.49 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.11/1.49 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.11/1.49 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.11/1.49 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.11/1.49 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.11/1.49 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.11/1.49 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.11/1.49 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.11/1.49 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.11/1.49 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.11/1.49 , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.11/1.49 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.11/1.49 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.11/1.49 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.11/1.49 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.11/1.49 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.11/1.49 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.11/1.49 , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.11/1.49 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.11/1.49 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.11/1.49 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.49 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.11/1.49 ), Y ), Z ), Y, X ), Z ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.49 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.11/1.49 ), Y ), Z ), Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.49 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.11/1.49 ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z )
% 1.11/1.49 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.49 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.49 X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.49 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.49 X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.49 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.11/1.49 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.49 X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.49 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.11/1.49 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.49 X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.11/1.49 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.11/1.49 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.11/1.49 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), 'c_lessequals'( hAPP(
% 1.11/1.49 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.11/1.49 ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'( hAPP(
% 1.11/1.49 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.11/1.49 ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'( hAPP(
% 1.11/1.49 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.11/1.49 ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_lessequals'( Z,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 X ), Y ), Z ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.11/1.49 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.49 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.49 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.49 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), X ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.49 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.49 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'( Z,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.11/1.49 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.49 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 X ), Y ), Z ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.49 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 X ), Z ), Y ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.49 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 X ), Y ), Z ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.49 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 X ), Z ), Y ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.11/1.49 , ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.11/1.49 , ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.11/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.49 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.11/1.49 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.11/1.49 ), 'c_Divides_Odiv__class_Odiv'( Z, T, X ) ), =( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.49 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.11/1.49 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.11/1.49 ), 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ), =( Z,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.11/1.49 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.11/1.49 ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.11/1.49 , Z ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X )
% 1.11/1.49 ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.11/1.49 , Y ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.49 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.49 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.11/1.49 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.11/1.49 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.11/1.49 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.11/1.49 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.11/1.49 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.11/1.49 ), Y ), Z ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.11/1.49 ), Y ), Z ), Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.11/1.49 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.11/1.49 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.11/1.49 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.11/1.49 ), Y ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.49 ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.11/1.49 ), Y ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.11/1.49 ), Y ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~(
% 1.11/1.49 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.11/1.49 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.11/1.49 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.11/1.49 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.11/1.49 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.11/1.49 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.11/1.49 [ ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), hBOOL(
% 1.11/1.49 hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.49 'tc_nat' ), 'tc_nat' ) ) ) ],
% 1.11/1.49 [ hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ), ~( hBOOL( hAPP( X
% 1.11/1.49 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.11/1.49 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.49 'tc_nat' ), 'tc_nat' ) ],
% 1.11/1.49 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.11/1.49 ), 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.11/1.49 ), 'tc_nat' ) ) ],
% 1.11/1.49 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ),
% 1.11/1.49 ~( 'c_Groebner__Basis_Ogb__semiring'( T, U, X, W, Z, V0 ) ) ],
% 1.11/1.49 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.11/1.49 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( X ), Y, X,
% 1.11/1.49 'tc_fun'( X, X ), X ), Z, X, X, X ), T, hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), U ), Z ), X ), ~( 'c_Deriv_Oderiv'(
% 1.11/1.49 Y, T, U, X ) ) ],
% 1.11/1.49 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OMin', X ) ), Y ), 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OMin', X ) ), 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ) ), hAPP(
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.11/1.49 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.11/1.49 X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.11/1.49 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.11/1.49 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X )
% 1.11/1.49 ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.11/1.49 X ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ), hAPP(
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.11/1.49 X ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ), 'c_HOL_Oone__class_Oone'( X
% 1.11/1.49 ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.11/1.49 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc',
% 1.11/1.49 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.11/1.49 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ), ~(
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.11/1.49 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.11/1.49 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), ~(
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.11/1.49 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc',
% 1.11/1.49 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.11/1.49 hAPP( 'c_Suc', 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP(
% 1.11/1.49 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ) ),
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.11/1.49 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.11/1.49 [ =( 'c_Int_OBit1'( 'c_Int_OMin' ), 'c_Int_OMin' ) ],
% 1.11/1.49 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OMin' ) ), =( X, 'c_Int_OMin' ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( =( 'c_Int_OMin', 'c_Int_OBit1'( X ) ) ), =( 'c_Int_OMin', X ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ =( 'c_Int_OMin', 'c_Int_OBit1'( 'c_Int_OMin' ) ) ],
% 1.11/1.49 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'(
% 1.11/1.49 X, Y, 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.11/1.49 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ) ) ],
% 1.11/1.49 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_Suc', X ),
% 1.11/1.49 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.11/1.49 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ),
% 1.11/1.49 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 1.11/1.49 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), hAPP( 'c_Suc'
% 1.11/1.49 , U ) ), hAPP( hAPP( Y, T ), hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z
% 1.11/1.49 ), T ), U ) ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.11/1.49 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_Suc', X ), 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 X, hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.11/1.49 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', Z ) ), hAPP( hAPP( T, Y ), hAPP(
% 1.11/1.49 hAPP( X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W,
% 1.11/1.49 V0, V1 ) ) ],
% 1.11/1.49 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', Z ) ), hAPP( hAPP( T, Y ), hAPP(
% 1.11/1.49 hAPP( X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W,
% 1.11/1.49 V0, V1 ) ) ],
% 1.11/1.49 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ), hAPP( hAPP( Y, Z ),
% 1.11/1.49 hAPP( 'c_Suc', T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Y, W
% 1.11/1.49 , V0, V1 ) ) ],
% 1.11/1.49 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ), hAPP( hAPP( Z, Y ),
% 1.11/1.49 hAPP( 'c_Suc', T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Z, W
% 1.11/1.49 , V0, V1 ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_Fun_Oinj__on'( 'c_Suc', X, 'tc_nat', 'tc_nat' ) ],
% 1.11/1.49 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 1.11/1.49 hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ), =(
% 1.11/1.49 hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), =( hAPP(
% 1.11/1.49 'c_Suc', X ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', X ), 'tc_nat' ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', X ), 'tc_nat' ),
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ),
% 1.11/1.49 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ),
% 1.11/1.49 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ),
% 1.11/1.49 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( =( 'c_Int_OPls', 'c_Int_OMin' ) ) ],
% 1.11/1.49 [ ~( =( 'c_Int_OMin', 'c_Int_OPls' ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.11/1.49 'tc_nat' ) ), Y ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.11/1.49 'tc_nat' ) ), Y ) ],
% 1.11/1.49 [ ~( =( 'c_Int_OMin', 'c_Int_OBit0'( X ) ) ) ],
% 1.11/1.49 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OMin' ) ) ],
% 1.11/1.49 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ), Y ),
% 1.11/1.49 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.11/1.49 'tc_nat' ) ) ],
% 1.11/1.49 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Y, 'tc_nat' ), X ),
% 1.11/1.49 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.11/1.49 'tc_nat' ) ) ],
% 1.11/1.49 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.11/1.49 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.11/1.49 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP(
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), hAPP(
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), Z ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP(
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Y ), hAPP(
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), hAPP(
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), hAPP(
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ],
% 1.11/1.49 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), hAPP(
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), Z ), hAPP(
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.49 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.11/1.49 , X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) )
% 1.11/1.49 ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.49 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.11/1.49 , Z ), Y ), 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.49 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.11/1.49 , Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 1.11/1.49 ],
% 1.11/1.49 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.49 'tc_nat' ), X ), Y ), X, 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.49 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.49 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.11/1.49 , Z ), T ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) )
% 1.11/1.49 , ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.11/1.49 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, Z ), U ) )
% 1.11/1.49 , hAPP( hAPP( Y, Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.11/1.49 , T ), U ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, Y, V0, V1, V2
% 1.11/1.49 ) ) ],
% 1.11/1.49 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 X, T, 'tc_nat' ) ],
% 1.11/1.49 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ],
% 1.11/1.49 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ],
% 1.11/1.49 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ), ~(
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.11/1.49 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ),
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.11/1.49 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.49 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.11/1.49 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.49 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.11/1.49 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.49 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.49 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.11/1.49 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.49 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.11/1.49 'tc_nat' ) ) ],
% 1.11/1.49 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), hAPP(
% 1.11/1.49 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ),
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.11/1.49 'tc_nat' ), Z, 'tc_nat' ) ) ), 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.11/1.49 'tc_nat' ) ) ) ],
% 1.11/1.49 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.11/1.49 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.11/1.49 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.11/1.49 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'tc_nat' ), X ), 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ), Z,
% 1.11/1.49 'tc_nat' ) ) ) ],
% 1.11/1.49 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.11/1.49 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), =( Y,
% 1.11/1.49 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.11/1.49 [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), 'tc_nat' ),
% 1.11/1.49 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.11/1.49 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.11/1.49 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.11/1.49 'c_Groebner__Basis_Ogb__semiring'( U, W, X, V0, V1, V2 ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.11/1.49 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.11/1.49 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.11/1.49 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.11/1.49 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.11/1.49 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.11/1.49 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.11/1.49 ), Z ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.11/1.49 hAPP( 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.11/1.49 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.11/1.49 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.11/1.49 ), T ) ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Z
% 1.11/1.49 ), T ) ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.11/1.49 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.11/1.49 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.11/1.49 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.49 ) ) ), =( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.49 ) ) ), =( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.11/1.49 Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.11/1.49 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.49 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.11/1.49 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.11/1.49 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.11/1.49 'c_COMBB'( Y, Z, X, X, X ), T, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 X ), U ), W ), X ), ~( 'c_Deriv_Oderiv'( Z, T, W, X ) ), ~(
% 1.11/1.49 'c_Deriv_Oderiv'( Y, hAPP( Z, T ), U, X ) ) ],
% 1.11/1.49 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.11/1.49 'c_COMBB'( Y, Z, X, X, X ), T, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 X ), U ), W ), X ), ~( 'c_Deriv_Oderiv'( Y, hAPP( Z, T ), U, X ) ), ~(
% 1.11/1.49 'c_Deriv_Oderiv'( Z, T, W, X ) ) ],
% 1.11/1.49 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.11/1.49 'c_COMBB'( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, X, X, X ), T
% 1.11/1.49 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ), X ), ~(
% 1.11/1.49 'c_Deriv_Oderiv'( Z, T, U, X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Ominus__class_Ominus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.11/1.49 , hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.49 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.49 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.49 X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X )
% 1.11/1.49 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.11/1.49 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.49 'c_Divides_Odiv__class_Odiv'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.11/1.49 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.11/1.49 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.49 X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_HOL_Oone__class_Oone'( X ), X ) ],
% 1.11/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.11/1.49 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.11/1.49 , 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ],
% 1.11/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.11/1.49 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.11/1.49 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.11/1.49 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.49 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Ominus__class_Ominus'( X ), Y ), hAPP(
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.11/1.49 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.11/1.49 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.11/1.49 'c_COMBS'( 'c_COMBB'( 'c_HOL_Oplus__class_Oplus'( X ), Y, X, 'tc_fun'( X
% 1.11/1.49 , X ), X ), 'c_COMBB'( 'c_HOL_Ouminus__class_Ouminus'( X ), Z, X, X, X )
% 1.11/1.49 , X, X, X ), T, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), U ), hAPP(
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( X ), W ) ), X ), ~( 'c_Deriv_Oderiv'( Z,
% 1.11/1.49 T, W, X ) ), ~( 'c_Deriv_Oderiv'( Y, T, U, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP(
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.11/1.49 X ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'( Y,
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'( Y,
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.49 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.11/1.49 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.49 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.11/1.49 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.11/1.49 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.11/1.49 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.49 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.49 , X ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.49 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.49 ), X ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 X ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~( 'c_lessequals'( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.49 ), X ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.11/1.49 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.11/1.49 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.11/1.49 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~( 'c_lessequals'(
% 1.11/1.49 Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~( 'c_lessequals'(
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.49 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.11/1.49 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.11/1.49 ), X ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.49 X ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.11/1.49 ), X ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.49 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.11/1.49 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~( 'c_lessequals'( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.11/1.49 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.49 , X ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.11/1.49 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.11/1.49 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.11/1.49 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.11/1.49 , Y ), 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.49 X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.11/1.49 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.11/1.49 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.11/1.49 ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.11/1.49 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.11/1.49 ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.11/1.49 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.11/1.49 ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP(
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Y ), hAPP(
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), =( Z,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.11/1.49 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.11/1.49 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.11/1.49 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.11/1.49 ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.11/1.49 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ), ~( 'c_lessequals'( Z
% 1.11/1.49 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) )
% 1.11/1.49 ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.11/1.49 ), T ), Z ), Y, X ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.11/1.49 ), Z ), Y ), 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.11/1.49 ), Y ), Z ), 'tc_nat' ) ) ],
% 1.11/1.49 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 1.11/1.49 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 1.11/1.49 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.11/1.49 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ), X ) ],
% 1.11/1.49 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.11/1.49 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ],
% 1.11/1.49 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.11/1.49 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( X, 'c_HOL_Oone__class_Oone'(
% 1.11/1.49 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.11/1.49 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 1.11/1.49 'tc_nat' ) ) ],
% 1.11/1.49 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.11/1.49 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.11/1.49 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.11/1.49 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Z ),
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.11/1.49 ), Y ), Z ), 'tc_nat' ) ) ],
% 1.11/1.49 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ),
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.11/1.49 ), X ), Z ), 'tc_nat' ) ) ],
% 1.11/1.49 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.11/1.49 'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ) ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ),
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( Y, X, 'tc_nat' ) ) ) ],
% 1.11/1.49 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.11/1.49 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ) ), Y ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ),
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ) ],
% 1.11/1.49 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X
% 1.11/1.49 , Y, 'tc_nat' ) ), Y ) ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.11/1.49 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.11/1.49 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.11/1.49 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.11/1.49 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' )
% 1.11/1.49 ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.11/1.49 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.11/1.49 'c_COMBC'( 'c_COMBB'( 'c_Power_Opower__class_Opower'( X ), Y, X, 'tc_fun'(
% 1.11/1.49 'tc_nat', X ), X ), hAPP( 'c_Suc', Z ), X, 'tc_nat', X ), T, hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.49 X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.11/1.49 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), U ), hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), hAPP( Y, T ) ), Z ) ) ), X ), ~(
% 1.11/1.49 'c_Deriv_Oderiv'( Y, T, U, X ) ) ],
% 1.11/1.49 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.11/1.49 'c_COMBC'( 'c_COMBB'( 'c_Power_Opower__class_Opower'( X ), Y, X, 'tc_fun'(
% 1.11/1.49 'tc_nat', X ), X ), Z, X, 'tc_nat', X ), T, hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.11/1.49 Z, X ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), hAPP( Y, T ) ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), hAPP( 'c_Suc',
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ) ), X ), ~(
% 1.11/1.49 'c_Deriv_Oderiv'( Y, T, U, X ) ) ],
% 1.11/1.49 [ ~( =( 'c_Divides_Odiv__class_Omod'( X,
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.11/1.49 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.11/1.49 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.11/1.49 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( =( 'c_Divides_Odiv__class_Omod'( X,
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.11/1.49 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ),
% 1.11/1.49 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ),
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Odiv'( hAPP(
% 1.11/1.49 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ),
% 1.11/1.49 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ],
% 1.11/1.49 [ ~( =( 'c_Complex_Oii', 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex'
% 1.11/1.49 ) ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.49 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.11/1.49 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.11/1.49 , X ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~(
% 1.11/1.49 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y )
% 1.11/1.49 , T ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.11/1.49 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.49 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.11/1.49 Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.11/1.49 X ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.11/1.49 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.11/1.49 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z
% 1.11/1.49 ), Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.11/1.49 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.49 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ),
% 1.11/1.49 Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.11/1.49 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.49 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.11/1.49 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.11/1.49 , X ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.11/1.49 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.11/1.49 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.49 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z
% 1.11/1.49 ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.11/1.49 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.11/1.49 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.11/1.49 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.11/1.49 Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.11/1.49 X ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.49 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.11/1.49 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.11/1.49 ), Y ), T ), Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.11/1.49 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.49 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.11/1.49 Y, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 X ), T ), Z ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.11/1.49 , hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.11/1.49 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ),
% 1.11/1.49 Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 T, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.11/1.49 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z
% 1.11/1.49 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.49 , Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.11/1.49 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ),
% 1.11/1.49 Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.11/1.49 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.11/1.49 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T )
% 1.11/1.49 , Z ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.11/1.49 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.11/1.49 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z
% 1.11/1.49 ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.11/1.49 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T
% 1.11/1.49 ), Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.11/1.49 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~( 'c_lessequals'( Y
% 1.11/1.49 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.11/1.49 ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( T, Z, X ) )
% 1.11/1.49 ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.49 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.11/1.49 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.11/1.49 ~( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.49 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.49 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.11/1.49 ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~( 'c_lessequals'( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.49 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.49 X ), X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.11/1.49 ), X ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), T ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.49 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.49 ), Y, X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.11/1.49 ), X ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.49 X ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.49 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.11/1.49 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z
% 1.11/1.49 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.11/1.49 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.49 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.11/1.49 ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.11/1.49 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.11/1.49 X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X )
% 1.11/1.49 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.11/1.49 ), ~( 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.11/1.49 ), X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.11/1.49 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), =( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_lessequals'( hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.11/1.49 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), T ), Z ) ) ), =( Y, T ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.11/1.49 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.11/1.49 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.49 [ =( 'c_FFT__Mirabelle_Oroot'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ),
% 1.11/1.49 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ) ) ],
% 1.11/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.49 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.11/1.49 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.11/1.49 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ),
% 1.11/1.49 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ) ), =( Z,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.49 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.11/1.49 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.11/1.49 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ),
% 1.11/1.49 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ) ), =( T,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.11/1.49 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), X
% 1.11/1.49 ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.49 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.11/1.49 ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.49 X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.49 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.11/1.49 ), X ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 X ), Z ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y )
% 1.11/1.49 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.11/1.49 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.11/1.49 ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.11/1.49 ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), Y, X ), ~(
% 1.11/1.49 'c_lessequals'( Z, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.11/1.49 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.11/1.49 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), Z, X ), ~(
% 1.11/1.49 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.11/1.49 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.11/1.49 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.11/1.49 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 1.11/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.49 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.11/1.49 , Y ), Z ), Z, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.11/1.49 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 1.11/1.49 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.11/1.49 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.11/1.49 , Y ), Z ), Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.11/1.49 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 1.11/1.49 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.49 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP(
% 1.11/1.49 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( T, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.11/1.49 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Ominus__class_Ominus'( X ), U ), Y ) ), Z ) ), W ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.11/1.49 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), U ) ), W ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), Y ), hAPP(
% 1.11/1.49 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ), W ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP(
% 1.11/1.49 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T ), W, X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ) ), U ), W, X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), U ), hAPP(
% 1.11/1.49 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), W ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 X ), U ), Z ) ), W ), X ), ~( 'c_lessequals'( T, hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), U ), Y ) ), Z ) ), W
% 1.11/1.49 ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'( Y
% 1.11/1.49 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), U ) ), W ), X ), ~(
% 1.11/1.49 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), Y ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 X ), Z ), U ) ), W ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 X ), U ), Z ) ), W ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T
% 1.11/1.49 ), W, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ) ), U ), W, X ), ~(
% 1.11/1.49 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), U ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 X ), Z ), T ) ), W ), X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.11/1.49 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.11/1.49 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ), Y ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.11/1.49 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T )
% 1.11/1.49 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.11/1.49 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T )
% 1.11/1.49 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.49 X ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.11/1.49 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.49 X ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.49 X ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.11/1.49 ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z
% 1.11/1.49 , hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.11/1.49 ), Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.11/1.49 ), Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.11/1.49 ), Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.11/1.49 , Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), Y, X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.49 X ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.11/1.49 , Y ), T ), Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.49 X ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.11/1.49 , Y ), T ), Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.11/1.49 ), Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.11/1.49 ), T ), Z ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.11/1.49 ), Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.11/1.49 ), T ), Z ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.49 X ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.11/1.49 ), Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.49 X ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.11/1.49 , Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.11/1.49 ), Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.11/1.49 ), Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.49 X ), T ), Z ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.49 X ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), hAPP(
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), hAPP(
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), =( Z,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.11/1.49 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z )
% 1.11/1.49 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.11/1.49 X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.11/1.49 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z )
% 1.11/1.49 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( Z,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~( 'c_lessequals'( Z
% 1.11/1.49 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.11/1.49 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.11/1.49 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.11/1.49 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.11/1.49 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.11/1.49 , 'tc_nat' ), 'tc_nat' ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.11/1.49 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_lessequals'(
% 1.11/1.49 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.11/1.49 , 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.11/1.49 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.11/1.49 , 'tc_nat' ), 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Z,
% 1.11/1.49 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.11/1.49 , 'tc_nat' ), 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Z,
% 1.11/1.49 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ), ~(
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.11/1.49 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 1.11/1.49 'c_Finite__Set_Osetsum'( 'c_COMBB'( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.11/1.49 Y, X, X, Z ), Z, X ), T ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.11/1.49 hAPP( 'c_Finite__Set_Osetsum'( Y, Z, X ), T ) ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.11/1.49 X ), Y ), Z ), X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y,
% 1.11/1.49 X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Z
% 1.11/1.49 , T ) ],
% 1.11/1.49 [ ~( =( hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) )
% 1.11/1.49 , Y ) ), =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat'
% 1.11/1.49 ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.11/1.49 hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.11/1.49 hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.11/1.49 [ =( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X
% 1.11/1.49 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 X, hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.11/1.49 ), 'tc_nat' ) ) ],
% 1.11/1.49 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.49 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.11/1.49 [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc',
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), X ) ],
% 1.11/1.49 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.11/1.49 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc',
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.11/1.49 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 1.11/1.49 , X ) ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.11/1.49 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.11/1.49 Y, X ) ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ) ],
% 1.11/1.49 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', 'tc_nat' ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.11/1.49 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.49 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 1.11/1.49 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y
% 1.11/1.49 , 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 1.11/1.49 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 1.11/1.49 , 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.11/1.49 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.49 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.11/1.49 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Omod'( X,
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.11/1.49 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ),
% 1.11/1.49 ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.11/1.49 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Omod'( X,
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.11/1.49 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.11/1.49 ), Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 1.11/1.49 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.11/1.49 , Y, 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.11/1.49 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 1.11/1.49 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.11/1.49 , X, 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.11/1.49 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.11/1.49 ), Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.11/1.49 ), Z ), Y ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.11/1.49 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 1.11/1.49 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.11/1.49 , X, 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.11/1.49 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.49 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X
% 1.11/1.49 ), 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.11/1.49 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.49 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.11/1.49 ), 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.11/1.49 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.11/1.49 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.11/1.49 'tc_nat' ) ), =( Y, Z ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat'
% 1.11/1.49 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.11/1.49 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.11/1.49 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.49 'tc_nat' ) ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y ), 'tc_nat' ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.49 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.11/1.49 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), =( X,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( =( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.11/1.49 ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.11/1.49 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.11/1.49 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.49 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.11/1.49 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.11/1.49 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.11/1.49 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.11/1.49 ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.11/1.49 [ =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), hAPP( 'c_Suc',
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.11/1.49 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.49 [ =( hAPP( 'c_Suc', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.49 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 1.11/1.49 [ =( hAPP( 'c_Suc', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.49 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), 'tc_nat' ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'tc_nat' ), hAPP( 'c_Suc', X ) ), Y ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', X ) ), Z ),
% 1.11/1.49 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'tc_nat' ), hAPP( 'c_Suc', Z ) ), X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', Z ) ), Y ),
% 1.11/1.49 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat'
% 1.11/1.49 ), ~( 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP(
% 1.11/1.49 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~( hBOOL( hAPP( X, hAPP(
% 1.11/1.49 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.11/1.49 'tc_nat' ), X ), Y ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.11/1.49 'tc_nat' ) ) ],
% 1.11/1.49 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.11/1.49 , X ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ],
% 1.11/1.49 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP(
% 1.11/1.49 'c_Suc', Y ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ),
% 1.11/1.49 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), Y ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.11/1.49 'tc_nat' ), X ), Y ), hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.11/1.49 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), Y, 'tc_nat' )
% 1.11/1.49 , 'c_Divides_Odiv__class_Omod'( Z, Y, 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.11/1.49 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), U ) ) ) ), =(
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( T, Y, 'tc_nat' ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.11/1.49 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.11/1.49 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.49 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ), 'tc_nat'
% 1.11/1.49 ) ) ],
% 1.11/1.49 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ) ), Y ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.11/1.49 'v_m', 'tc_nat' ) ],
% 1.11/1.49 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.11/1.49 ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), =(
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.11/1.49 ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.11/1.49 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), =(
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.11/1.49 ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), =(
% 1.11/1.49 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.11/1.49 ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.49 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, Y ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( T
% 1.11/1.49 , X, Z, U, W, V0 ) ) ],
% 1.11/1.49 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP(
% 1.11/1.49 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.11/1.49 'tc_nat' ) ) ), Y ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.11/1.49 'tc_nat' ) ) ), Y ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 1.11/1.49 'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), hAPP(
% 1.11/1.49 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, 'tc_nat' ), hAPP(
% 1.11/1.49 'c_Suc', T ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 1.11/1.49 'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), hAPP(
% 1.11/1.49 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, 'tc_nat' ), hAPP(
% 1.11/1.49 'c_Suc', T ) ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.11/1.49 'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), hAPP(
% 1.11/1.49 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, 'tc_nat' ), T ) ) ),
% 1.11/1.49 hAPP( Y, T ) ) ), 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 1.11/1.49 'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), hAPP(
% 1.11/1.49 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, 'tc_nat' ), T ) ), hAPP(
% 1.11/1.49 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( Y, Z ) ), hAPP(
% 1.11/1.49 'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), hAPP(
% 1.11/1.49 'c_SetInterval_Oord__class_OatLeastLessThan'( hAPP( 'c_Suc', Z ),
% 1.11/1.49 'tc_nat' ), T ) ) ) ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 1.11/1.49 'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), hAPP(
% 1.11/1.49 'c_SetInterval_Oord__class_OatLeastLessThan'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ), 'tc_nat' ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), U ), T ) ) ), hAPP(
% 1.11/1.49 'c_Finite__Set_Osetsum'( 'c_COMBB'( Y, 'c_COMBC'(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T, 'tc_nat', 'tc_nat', 'tc_nat' )
% 1.11/1.49 , 'tc_nat', X, 'tc_nat' ), 'tc_nat', X ), hAPP(
% 1.11/1.49 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, 'tc_nat' ), U ) ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' )
% 1.11/1.49 , 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'tc_nat' ), X ), Y ) ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 'tc_nat' ), X ), Z ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.11/1.49 'tc_Complex_Ocomplex' ), 'c_FFT__Mirabelle_Oroot'( Y ) ), Z ) ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.11/1.49 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.11/1.49 'c_Groebner__Basis_Ogb__semiring'( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), 'c_Power_Opower__class_Opower'( X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.11/1.49 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ), Y ) ) ],
% 1.11/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ],
% 1.11/1.49 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X
% 1.11/1.49 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.49 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.11/1.49 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.49 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.11/1.49 ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.11/1.49 X ), Y ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.11/1.49 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.11/1.49 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.11/1.49 'c_Suc', X ) ) ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, 'tc_nat' ) ) ],
% 1.11/1.49 [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.11/1.49 'c_Suc', Y ) ) ), 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X, hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.11/1.49 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ), 'tc_nat' ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.11/1.49 ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), Z, X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.11/1.49 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.11/1.49 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.49 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.11/1.49 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.11/1.49 ), Y ), T ), Z, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.11/1.49 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.11/1.49 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.11/1.49 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.11/1.49 Y, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.49 X ), T ), Z ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.49 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.11/1.49 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.11/1.49 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.11/1.49 , hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.11/1.49 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.11/1.49 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.11/1.49 ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.49 X ), T ), Z ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.11/1.49 ), X ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.49 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.49 X ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.11/1.49 ), X ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.49 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.49 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.11/1.49 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.11/1.49 'c_COMBS'( 'c_COMBB'( 'c_HOL_Oplus__class_Oplus'( X ), Y, X, 'tc_fun'( X
% 1.11/1.49 , X ), X ), Z, X, X, X ), T, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.11/1.49 , U ), W ), X ), ~( 'c_Deriv_Oderiv'( Z, T, W, X ) ), ~( 'c_Deriv_Oderiv'(
% 1.11/1.49 Y, T, U, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 'c_lessequals'(
% 1.11/1.49 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.49 , X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.49 'tc_nat' ) ), X ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.11/1.49 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.11/1.49 ), Z ) ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.11/1.49 ), T ) ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.11/1.49 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.11/1.49 , X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.11/1.49 ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.11/1.49 ), 'c_HOL_Oone__class_Oone'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.49 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.11/1.49 ), 'c_HOL_Oone__class_Oone'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.49 , X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.11/1.49 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X )
% 1.11/1.49 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.11/1.49 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.11/1.49 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.11/1.49 ), X ) ) ],
% 1.11/1.49 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.11/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.11/1.49 ), Z ) ), T ) ) ],
% 1.11/1.49 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.11/1.49 'c_COMBS'( 'c_COMBB'( 'c_HOL_Ominus__class_Ominus'( X ), Y, X, 'tc_fun'(
% 1.11/1.49 X, X ), X ), Z, X, X, X ), T, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.11/1.49 ), U ), W ), X ), ~( 'c_Deriv_Oderiv'( Z, T, W, X ) ), ~(
% 1.11/1.49 'c_Deriv_Oderiv'( Y, T, U, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.11/1.49 X ), Y ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.11/1.49 hAPP( 'c_Power_Opower__class_Opower'( X ), hAPP(
% 1.11/1.49 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ), Z
% 1.11/1.49 ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ]
% 1.11/1.49 ,
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.11/1.49 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.11/1.49 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 1.11/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( X )
% 1.11/1.49 , 'c_Power_Opower_Opower'( 'c_HOL_Oone__class_Oone'( X ),
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.11/1.49 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( 'c_Suc', Y ), X ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.11/1.49 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), =( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_Finite__Set_Osetsum'( Y, Z, X
% 1.11/1.49 ), T ) ), U ), hAPP( 'c_Finite__Set_Osetsum'( 'c_COMBC'( 'c_COMBB'(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'( X, X ), Z ), U, Z, X,
% 1.11/1.49 X ), Z, X ), T ) ) ],
% 1.11/1.49 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_Finite__Set_Osetsum'( Y, Z, X
% 1.11/1.49 ), T ) ), U ), hAPP( 'c_Finite__Set_Osetsum'( 'c_COMBC'( 'c_COMBB'(
% 1.11/1.49 'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'( X, X ), Z ), U, Z, X,
% 1.11/1.49 X ), Z, X ), T ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.11/1.49 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.11/1.49 ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.11/1.49 hAPP( 'c_Suc', T ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Z
% 1.11/1.49 ), hAPP( 'c_Suc', T ) ), X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.11/1.49 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.11/1.49 hAPP( 'c_Power_Opower__class_Opower'( X ), T ), hAPP( 'c_Suc', Z ) ) ) )
% 1.11/1.49 , =( Y, T ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) )
% 1.11/1.49 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.11/1.49 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.49 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.11/1.49 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.11/1.49 'c_HOL_Oone__class_Oone'( X ) ) ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.50 Z, X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.11/1.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.11/1.50 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.11/1.50 'c_HOL_Oone__class_Oone'( X ) ) ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.50 Y, Z, X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.50 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.11/1.50 ), Y ), 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.50 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.50 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), X ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( 'c_Finite__Set_Osetsum'( Y, Z
% 1.11/1.50 , X ), T ) ), U ), hAPP( 'c_Finite__Set_Osetsum'( 'c_COMBC'( 'c_COMBB'(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Y, X, 'tc_fun'( X, X ), Z ), U, Z,
% 1.11/1.50 X, X ), Z, X ), T ) ) ],
% 1.11/1.50 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( 'c_Finite__Set_Osetsum'( Y, Z
% 1.11/1.50 , X ), T ) ), U ), hAPP( 'c_Finite__Set_Osetsum'( 'c_COMBC'( 'c_COMBB'(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Y, X, 'tc_fun'( X, X ), Z ), U, Z,
% 1.11/1.50 X, X ), Z, X ), T ) ) ],
% 1.11/1.50 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.50 'tc_nat' ), Y ), X ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.11/1.50 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 1.11/1.50 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.50 'tc_nat' ), X ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.11/1.50 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 1.11/1.50 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.11/1.50 Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc',
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.11/1.50 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ), 'tc_nat' ) ],
% 1.11/1.50 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ) ), 'tc_nat' ) ) ],
% 1.11/1.50 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.11/1.50 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.11/1.50 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.11/1.50 'tc_nat' ) ) ],
% 1.11/1.50 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.11/1.50 'tc_nat' ), X ), hAPP( 'c_Suc', Y ) ), X, 'tc_nat' ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.11/1.50 'tc_nat' ) ) ],
% 1.11/1.50 [ =( hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' )
% 1.11/1.50 , X ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ),
% 1.11/1.50 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.11/1.50 'tc_nat' ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), hAPP( 'c_Finite__Set_Osetsum'( Y,
% 1.11/1.50 'tc_nat', X ), hAPP( 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), Z ) ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.11/1.50 Z, X ) ), T ) ), hAPP( 'c_Finite__Set_Osetsum'( 'c_COMBC'( 'c_COMBB'(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), Y, X, 'tc_fun'( X, X ), 'tc_nat' ), T
% 1.11/1.50 , 'tc_nat', X, X ), 'tc_nat', X ), hAPP(
% 1.11/1.50 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 'tc_nat' ), 'tc_nat' ), Z ) ) ) ],
% 1.11/1.50 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ) ), Y, 'tc_nat'
% 1.11/1.50 ), 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', Z ), Y, 'tc_nat' ) ) ]
% 1.11/1.50 ,
% 1.11/1.50 [ =( 'c_FFT__Mirabelle_ODFT'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.50 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.11/1.50 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, Z ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_Complex_Ocomplex' ),
% 1.11/1.50 'c_FFT__Mirabelle_ODFT'( X, 'c_COMBB'( Y, hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat'
% 1.11/1.50 ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.50 'tc_Complex_Ocomplex' ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.11/1.50 'tc_Complex_Ocomplex' ), 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ), Z ) ), 'c_FFT__Mirabelle_ODFT'(
% 1.11/1.50 X, 'c_COMBB'( Y, 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.50 'tc_nat' ), hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_nat' )
% 1.11/1.50 , 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat', 'tc_nat',
% 1.11/1.50 'tc_nat' ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ), Z ) ) ) ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 1.11/1.50 'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), hAPP(
% 1.11/1.50 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 'tc_nat' ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.50 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.11/1.50 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_Finite__Set_Osetsum'( 'c_COMBB'(
% 1.11/1.50 Y, hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', X, 'tc_nat' ), 'tc_nat', X ),
% 1.11/1.50 hAPP( 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), Z ) ) ), hAPP(
% 1.11/1.50 'c_Finite__Set_Osetsum'( 'c_COMBB'( Y, 'c_COMBC'( 'c_COMBB'(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_nat' )
% 1.11/1.50 , 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat', 'tc_nat',
% 1.11/1.50 'tc_nat' ), 'tc_nat', X, 'tc_nat' ), 'tc_nat', X ), hAPP(
% 1.11/1.50 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 'tc_nat' ), 'tc_nat' ), Z ) ) ) ) ],
% 1.11/1.50 [ =( 'c_FFT__Mirabelle_OIDFT'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.50 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.11/1.50 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, Z ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_Complex_Ocomplex' ),
% 1.11/1.50 'c_FFT__Mirabelle_OIDFT'( X, 'c_COMBB'( Y, hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat'
% 1.11/1.50 ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.50 'tc_Complex_Ocomplex' ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.11/1.50 'tc_Complex_Ocomplex' ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.50 'tc_Complex_Ocomplex' ), 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex'
% 1.11/1.50 ) ), 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.50 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.11/1.50 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ) ), Z ) ),
% 1.11/1.50 'c_FFT__Mirabelle_OIDFT'( X, 'c_COMBB'( Y, 'c_COMBC'( 'c_COMBB'(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_nat' )
% 1.11/1.50 , 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat', 'tc_nat',
% 1.11/1.50 'tc_nat' ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ), Z ) ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~( 'c_lessequals'( Y,
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~( 'c_lessequals'(
% 1.11/1.50 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~( 'c_lessequals'(
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~( 'c_lessequals'(
% 1.11/1.50 Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( 'c_lessequals'(
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.50 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.50 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.11/1.50 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.11/1.50 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.11/1.50 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.11/1.50 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.11/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.11/1.50 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Z, X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.11/1.50 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.11/1.50 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.11/1.50 hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.11/1.50 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.11/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.11/1.50 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.11/1.50 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.11/1.50 ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.11/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.11/1.50 , T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.11/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.11/1.50 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.11/1.50 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.11/1.50 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.11/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.11/1.50 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.11/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.11/1.50 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.50 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.11/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.11/1.50 ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), T ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.11/1.50 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.11/1.50 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.50 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.11/1.50 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.11/1.50 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.11/1.50 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.11/1.50 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.11/1.50 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.11/1.50 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.11/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.11/1.50 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.50 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.11/1.50 ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.11/1.50 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.11/1.50 , T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.11/1.50 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.11/1.50 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.11/1.50 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.11/1.50 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.11/1.50 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ),
% 1.11/1.50 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.50 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.11/1.50 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.11/1.50 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.50 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.11/1.50 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.11/1.50 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.50 X ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.11/1.50 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.11/1.50 ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.11/1.50 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.11/1.50 'c_COMBS'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'(
% 1.11/1.50 X, X ), X ), Z, X, X, X ), T, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.11/1.50 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), hAPP( Z, T ) ) ),
% 1.11/1.50 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), W ), hAPP( Y, T ) ) ), X )
% 1.11/1.50 , ~( 'c_Deriv_Oderiv'( Z, T, W, X ) ), ~( 'c_Deriv_Oderiv'( Y, T, U, X )
% 1.11/1.50 ) ],
% 1.11/1.50 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.11/1.50 'c_COMBS'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'(
% 1.11/1.50 X, X ), X ), Z, X, X, X ), T, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.11/1.50 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( Y, T ) ), U ) ),
% 1.11/1.50 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), W ), hAPP( Z, T ) ) ), X )
% 1.11/1.50 , ~( 'c_Deriv_Oderiv'( Z, T, U, X ) ), ~( 'c_Deriv_Oderiv'( Y, T, W, X )
% 1.11/1.50 ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.11/1.50 , Y ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP(
% 1.11/1.50 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.11/1.50 ,
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.11/1.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.11/1.50 ), Y ), hAPP( 'c_Suc', Z ) ), 'c_HOL_Oone__class_Oone'( X ), X ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.11/1.50 ,
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ),
% 1.11/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.50 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.11/1.50 'c_Suc', X ) ) ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, 'tc_nat' ) ) ],
% 1.11/1.50 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.11/1.50 'c_Suc', Y ) ) ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ), 'tc_nat' ) ) ],
% 1.11/1.50 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.11/1.50 'c_Suc', X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.11/1.50 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.50 Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.50 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.11/1.50 'c_Suc', X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.11/1.50 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.50 Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.50 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.11/1.50 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.11/1.50 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.11/1.50 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.11/1.50 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), X ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.11/1.50 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'tc_nat' ) ],
% 1.11/1.50 [ 'c_Fun_Oinj__on'( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), X, 'tc_nat', 'tc_nat' ) ],
% 1.11/1.50 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.50 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.11/1.50 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP( T, hAPP(
% 1.11/1.50 hAPP( X, Y ), Z ) ), hAPP( hAPP( X, Y ), Z ) ) ), ~(
% 1.11/1.50 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1 ) ) ],
% 1.11/1.50 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.11/1.50 , X ) ), Y ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ),
% 1.11/1.50 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.11/1.50 'tc_nat' ) ) ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ), Y, 'tc_nat'
% 1.11/1.50 ) ) ],
% 1.11/1.50 [ =( 'c_FFT__Mirabelle_Oroot'( 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.50 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.11/1.50 ) ), 'c_Complex_Oii' ) ],
% 1.11/1.50 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.11/1.50 'c_COMBS'( 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( X ), Y, X,
% 1.11/1.50 'tc_fun'( X, X ), X ), Z, X, X, X ), T, hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), U ), hAPP( Z, T ) ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( Y, T ) ), W ) ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( Z, T ) ), hAPP( Z, T ) ) ), X )
% 1.11/1.50 , =( hAPP( Z, T ), 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Deriv_Oderiv'(
% 1.11/1.50 Z, T, W, X ) ), ~( 'c_Deriv_Oderiv'( Y, T, U, X ) ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.11/1.50 ), Y ), Y ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), X ) ), X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), X ) ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.50 [ ~( 'class_RealVector_Oreal__normed__algebra__1'( X ) ), =(
% 1.11/1.50 'c_Series_Osuminf'( 'c_COMBS'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X
% 1.11/1.50 ), Y, X, 'tc_fun'( X, X ), 'tc_nat' ), hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.11/1.50 'tc_nat', X, X ), X ), hAPP( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.11/1.50 ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.50 ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), =( Y, Z ), ~( 'c_lessequals'(
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.11/1.50 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.11/1.50 ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.11/1.50 ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.11/1.50 ,
% 1.11/1.50 [ =( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X
% 1.11/1.50 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.11/1.50 X, 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.11/1.50 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP( T, Y ), hAPP( hAPP(
% 1.11/1.50 T, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, Y ), Z ) ) ) ), ~(
% 1.11/1.50 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1 ) ) ],
% 1.11/1.50 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), 'tc_nat' ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.11/1.50 X ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ) ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), Z ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.11/1.50 T, X ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), hAPP(
% 1.11/1.50 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), hAPP( 'c_Suc',
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( 'c_Finite__Set_Osetsum'(
% 1.11/1.50 'c_COMBB'( 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_Power_Opower__class_Opower'(
% 1.11/1.50 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), X, 'tc_fun'(
% 1.11/1.50 X, X ), 'tc_nat' ), 'c_COMBB'( hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.11/1.50 , Y ), hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'tc_nat', X, 'tc_nat' ), 'tc_nat', X, X
% 1.11/1.50 ), 'tc_nat', X ), 'c_COMBB'(
% 1.11/1.50 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 'tc_nat' ), 'tc_nat' ), hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.11/1.50 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), hAPP( 'c_Suc'
% 1.11/1.50 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), 'tc_nat', 'tc_fun'(
% 1.11/1.50 'tc_nat', 'tc_bool' ), 'tc_nat' ), 'tc_fun'( 'tc_nat', 'tc_bool' ), X,
% 1.11/1.50 'tc_nat' ), 'tc_nat', X ), hAPP(
% 1.11/1.50 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 'tc_nat' ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.11/1.50 'tc_nat' ), T ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.11/1.50 ) ) ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 1.11/1.50 'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), hAPP(
% 1.11/1.50 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 'tc_nat' ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 1.11/1.50 ), Z ), T ) ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.11/1.50 'c_Finite__Set_Osetsum'( 'c_COMBB'( Y, 'c_COMBC'(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T, 'tc_nat', 'tc_nat', 'tc_nat' )
% 1.11/1.50 , 'tc_nat', X, 'tc_nat' ), 'tc_nat', X ), hAPP(
% 1.11/1.50 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 'tc_nat' ), 'tc_nat' ), Z ) ) ), hAPP( 'c_Finite__Set_Osetsum'( Y,
% 1.11/1.50 'tc_nat', X ), hAPP( 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), T ) ) ) ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 1.11/1.50 'c_Finite__Set_Osetsum'( 'c_COMBB'( Y, 'c_COMBC'(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z, 'tc_nat', 'tc_nat', 'tc_nat' )
% 1.11/1.50 , 'tc_nat', X, 'tc_nat' ), 'tc_nat', X ), hAPP(
% 1.11/1.50 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 'tc_nat' ), 'tc_nat' ), T ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.11/1.50 X ), hAPP( 'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), hAPP(
% 1.11/1.50 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 'tc_nat' ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 1.11/1.50 ), T ), Z ) ) ) ), hAPP( 'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), hAPP(
% 1.11/1.50 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 'tc_nat' ), 'tc_nat' ), Z ) ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), X ) ), X ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.11/1.50 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.11/1.50 ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.50 X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.11/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.11/1.50 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ]
% 1.11/1.50 ,
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.11/1.50 ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.11/1.50 ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.11/1.50 ), Z ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.11/1.50 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.11/1.50 ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), X ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.11/1.50 X ), 'c_HOL_Oone__class_Oone'( X ) ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ), 'c_HOL_Oone__class_Oone'( X ) ) ]
% 1.11/1.50 ,
% 1.11/1.50 [ 'c_Fun_Oinj__on'( 'c_COMBB'( 'c_Suc', hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_nat', 'tc_nat' ), X,
% 1.11/1.50 'tc_nat', 'tc_nat' ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ),
% 1.11/1.50 hAPP( hAPP( 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.11/1.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.11/1.50 ), Y ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.50 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.11/1.50 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.11/1.50 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.50 'c_Int_OMin', X ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.11/1.50 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ), 'c_HOL_Oone__class_Oone'( X ) ) ]
% 1.11/1.50 ,
% 1.11/1.50 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.50 'c_Int_OMin', X ) ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ) ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.11/1.50 X ), 'c_HOL_Oone__class_Oone'( X ) ) ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ) ), hAPP(
% 1.11/1.50 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ]
% 1.11/1.50 ,
% 1.11/1.50 [ =( hAPP( 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( 'tc_Complex_Ocomplex' ), 'v_a',
% 1.11/1.50 'tc_Complex_Ocomplex', 'tc_fun'( 'tc_Complex_Ocomplex',
% 1.11/1.50 'tc_Complex_Ocomplex' ), 'tc_nat' ), 'c_COMBB'( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.11/1.50 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.50 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.11/1.50 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_m' ) ) ), hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'v_i' ), 'tc_nat',
% 1.11/1.50 'tc_Complex_Ocomplex', 'tc_nat' ), 'tc_nat', 'tc_Complex_Ocomplex',
% 1.11/1.50 'tc_Complex_Ocomplex' ), 'tc_nat', 'tc_Complex_Ocomplex' ), hAPP(
% 1.11/1.50 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 'tc_nat' ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.50 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.11/1.50 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_m' ) ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_Complex_Ocomplex' ), hAPP(
% 1.11/1.50 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( 'tc_Complex_Ocomplex' ), 'c_COMBB'(
% 1.11/1.50 'v_a', hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat'
% 1.11/1.50 ), 'tc_Complex_Ocomplex', 'tc_fun'( 'tc_Complex_Ocomplex',
% 1.11/1.50 'tc_Complex_Ocomplex' ), 'tc_nat' ), 'c_COMBB'( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.11/1.50 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.50 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.11/1.50 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_m' ) ) ), 'c_COMBB'(
% 1.11/1.50 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'v_i' ), hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_nat', 'tc_nat' ), 'tc_nat'
% 1.11/1.50 , 'tc_Complex_Ocomplex', 'tc_nat' ), 'tc_nat', 'tc_Complex_Ocomplex',
% 1.11/1.50 'tc_Complex_Ocomplex' ), 'tc_nat', 'tc_Complex_Ocomplex' ), hAPP(
% 1.11/1.50 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 'tc_nat' ), 'tc_nat' ), 'v_m' ) ) ), hAPP( 'c_Finite__Set_Osetsum'(
% 1.11/1.50 'c_COMBS'( 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.50 'tc_Complex_Ocomplex' ), 'c_COMBB'( 'v_a', 'c_COMBC'( 'c_COMBB'(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_nat' )
% 1.11/1.50 , 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat', 'tc_nat',
% 1.11/1.50 'tc_nat' ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ),
% 1.11/1.50 'tc_Complex_Ocomplex', 'tc_fun'( 'tc_Complex_Ocomplex',
% 1.11/1.50 'tc_Complex_Ocomplex' ), 'tc_nat' ), 'c_COMBB'( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.11/1.50 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.50 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.11/1.50 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_m' ) ) ), 'c_COMBB'(
% 1.11/1.50 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'v_i' ), 'c_COMBC'(
% 1.11/1.50 'c_COMBB'( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_nat' )
% 1.11/1.50 , 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat', 'tc_nat',
% 1.11/1.50 'tc_nat' ), 'tc_nat', 'tc_nat', 'tc_nat' ), 'tc_nat',
% 1.11/1.50 'tc_Complex_Ocomplex', 'tc_nat' ), 'tc_nat', 'tc_Complex_Ocomplex',
% 1.11/1.50 'tc_Complex_Ocomplex' ), 'tc_nat', 'tc_Complex_Ocomplex' ), hAPP(
% 1.11/1.50 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 'tc_nat' ), 'tc_nat' ), 'v_m' ) ) ) ) ],
% 1.11/1.50 [ =( hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' )
% 1.11/1.50 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 1.11/1.50 ) ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), =( X, 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 'tc_nat' ) ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 1.11/1.50 'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), hAPP(
% 1.11/1.50 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 'tc_nat' ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.11/1.50 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ) ) ), hAPP(
% 1.11/1.50 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.50 X ), hAPP( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( Y,
% 1.11/1.50 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ), hAPP( Y,
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP( Y,
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.11/1.50 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.11/1.50 'c_COMBS'( 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( X ), Y, X,
% 1.11/1.50 'tc_fun'( X, X ), X ), Z, X, X, X ), T, hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), U ), hAPP( Z, T ) ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), W ), hAPP( Y, T ) ) ) ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), hAPP( Z, T ) ), hAPP( 'c_Suc', hAPP(
% 1.11/1.50 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ), X ), =( hAPP( Z
% 1.11/1.50 , T ), 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Deriv_Oderiv'( Z, T, W, X
% 1.11/1.50 ) ), ~( 'c_Deriv_Oderiv'( Y, T, U, X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ), ~(
% 1.11/1.50 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP(
% 1.11/1.50 'c_Finite__Set_Osetsum'( 'c_COMBC'( 'c_COMBB'(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), 'c_COMBS'( 'c_COMBB'(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), 'c_COMBB'( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), 'tc_nat', X, 'tc_nat' ), X
% 1.11/1.50 , 'tc_fun'( X, X ), 'tc_nat' ), hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.11/1.50 , Y ), 'tc_nat', X, X ), X, 'tc_fun'( X, X ), 'tc_nat' ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), T ), 'tc_nat', X, X ), 'tc_nat'
% 1.11/1.50 , X ), hAPP( 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), T ) ), hAPP(
% 1.11/1.50 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_Power_Opower__class_Opower'(
% 1.11/1.50 X ), Y ), X, 'tc_fun'( X, X ), 'tc_nat' ), 'c_COMBS'( 'c_COMBB'(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), 'c_COMBB'( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), 'tc_nat', X, 'tc_nat' ), X
% 1.11/1.50 , 'tc_fun'( X, X ), 'tc_nat' ), 'c_COMBB'( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), 'tc_nat', X, 'tc_nat' ),
% 1.11/1.50 'tc_nat', X, X ), 'tc_nat', X, X ), 'tc_nat', X ), hAPP(
% 1.11/1.50 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 'tc_nat' ), 'tc_nat' ), T ) ) ) ],
% 1.11/1.50 [ =( 'c_FFT__Mirabelle_ODFT'( X, Y, 'v_i' ), hAPP(
% 1.11/1.50 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_Complex_Ocomplex' ), 'c_COMBB'( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.11/1.50 'c_FFT__Mirabelle_Oroot'( X ) ), hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.50 'tc_nat' ), 'v_i' ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ),
% 1.11/1.50 'tc_Complex_Ocomplex', 'tc_fun'( 'tc_Complex_Ocomplex',
% 1.11/1.50 'tc_Complex_Ocomplex' ), 'tc_nat' ), Y, 'tc_nat', 'tc_Complex_Ocomplex',
% 1.11/1.50 'tc_Complex_Ocomplex' ), 'tc_nat', 'tc_Complex_Ocomplex' ), hAPP(
% 1.11/1.50 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 'tc_nat' ), 'tc_nat' ), X ) ) ) ],
% 1.11/1.50 [ =( 'c_FFT__Mirabelle_OIDFT'( X, Y, 'v_i' ), hAPP(
% 1.11/1.50 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( 'tc_Complex_Ocomplex' ), Y,
% 1.11/1.50 'tc_Complex_Ocomplex', 'tc_fun'( 'tc_Complex_Ocomplex',
% 1.11/1.50 'tc_Complex_Ocomplex' ), 'tc_nat' ), 'c_COMBB'( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.11/1.50 'c_FFT__Mirabelle_Oroot'( X ) ), hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.50 'tc_nat' ), 'v_i' ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ),
% 1.11/1.50 'tc_nat', 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ), 'tc_nat',
% 1.11/1.50 'tc_Complex_Ocomplex' ), hAPP(
% 1.11/1.50 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 'tc_nat' ), 'tc_nat' ), X ) ) ) ],
% 1.11/1.50 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.50 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.11/1.50 ) ) ],
% 1.11/1.50 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.50 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.11/1.50 ) ) ],
% 1.11/1.50 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.50 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.11/1.50 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.11/1.50 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.50 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.11/1.50 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.11/1.50 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.11/1.50 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.11/1.50 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.50 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.11/1.50 ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.50 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.11/1.50 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.11/1.50 X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), =(
% 1.11/1.50 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z ), =( T,
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.50 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.11/1.50 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.50 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ) ), Z ) ) ) ]
% 1.11/1.50 ,
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.50 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.11/1.50 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ), =( U,
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.50 ) ],
% 1.11/1.50 [ =( 'c_Int_OPls', 'c_Int_OBit0'( 'c_Int_OPls' ) ) ],
% 1.11/1.50 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.11/1.50 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.50 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.11/1.50 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.11/1.50 , X ) ), Z ) ), Z ) ) ],
% 1.11/1.50 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ) ) ) ],
% 1.11/1.50 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( Y ), X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.50 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.50 Y, X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.11/1.50 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ),
% 1.11/1.50 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.11/1.50 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.11/1.50 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.50 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ) ), Z ) ) ) ]
% 1.11/1.50 ,
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), Z ) ), =( Z,
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), T ) ), =( T,
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.50 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.11/1.50 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ],
% 1.11/1.50 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc', X ) ), Y ) ),
% 1.11/1.50 hAPP( 'c_Suc', Z ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.11/1.50 ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z )
% 1.11/1.50 ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.11/1.50 ), Y ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.11/1.50 ,
% 1.11/1.50 [ =( 'c_FFT__Mirabelle_Oroot'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.11/1.50 , 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ) ) ],
% 1.11/1.50 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.11/1.50 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), =( X, Z
% 1.11/1.50 ) ],
% 1.11/1.50 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.11/1.50 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.11/1.50 ) ],
% 1.11/1.50 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.11/1.50 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.11/1.50 ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.11/1.50 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 1.11/1.50 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =( hAPP(
% 1.11/1.50 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.11/1.50 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.11/1.50 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.11/1.50 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.11/1.50 , X ) ), Z ) ), Z ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.11/1.50 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ) ],
% 1.11/1.50 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ],
% 1.11/1.50 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( 'c_Finite__Set_Osetsum'( Z
% 1.11/1.50 , T, X ), U ) ), hAPP( 'c_Finite__Set_Osetsum'( 'c_COMBB'( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, X, X, T ), T, X ), U ) ) ]
% 1.11/1.50 ,
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( 'c_Finite__Set_Osetsum'( Z
% 1.11/1.50 , T, X ), U ) ), hAPP( 'c_Finite__Set_Osetsum'( 'c_COMBB'( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, X, X, T ), T, X ), U ) ) ]
% 1.11/1.50 ,
% 1.11/1.50 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.11/1.50 X ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.11/1.50 'c_Suc', Y ) ) ) ],
% 1.11/1.50 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.11/1.50 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, hAPP(
% 1.11/1.50 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.50 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.11/1.50 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, hAPP( 'c_Suc',
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.50 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.11/1.50 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.11/1.50 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.11/1.50 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oone__class_Oone'( X )
% 1.11/1.50 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X )
% 1.11/1.50 ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), 'c_HOL_Oone__class_Oone'(
% 1.11/1.50 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, Z ) ],
% 1.11/1.50 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), hAPP( 'c_Suc', hAPP( 'c_Suc', X ) )
% 1.11/1.50 ) ],
% 1.11/1.50 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ) ) ]
% 1.11/1.50 ,
% 1.11/1.50 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.11/1.50 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 1.11/1.50 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, hAPP( 'c_Suc'
% 1.11/1.50 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.11/1.50 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.11/1.50 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.50 X ), Y ), Y ) ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.11/1.50 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.50 'c_Int_OPls', X ) ), Y ), Y ) ],
% 1.11/1.50 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.50 'c_Int_OPls', X ) ), Y ) ],
% 1.11/1.50 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP(
% 1.11/1.50 'c_Suc', X ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.11/1.50 , hAPP( 'c_Suc', X ) ), Z ) ) ), =( Y, Z ) ],
% 1.11/1.50 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( 'c_Suc'
% 1.11/1.50 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.11/1.50 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), Y ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.11/1.50 'class_Power_Opower'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.11/1.50 , 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.11/1.50 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.11/1.50 [ ~( =( hAPP( 'c_Suc', X ), X ) ) ],
% 1.11/1.50 [ ~( =( X, hAPP( 'c_Suc', X ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.11/1.50 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.11/1.50 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.11/1.50 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ), =( T, U ), =( Z,
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.50 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.11/1.50 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ) ) ), =( Z, T ), =( Y
% 1.11/1.50 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.50 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 'tc_nat' ) ), Y ) ) ],
% 1.11/1.50 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 'tc_nat' ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.11/1.50 =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.11/1.50 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.11/1.50 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.11/1.50 ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 'tc_nat' ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.11/1.50 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.11/1.50 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.11/1.50 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), =( Y, hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =(
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.50 ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y ), =(
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.50 ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 1.11/1.50 =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.50 ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.11/1.50 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.50 ) ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.11/1.50 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.11/1.50 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.11/1.50 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ) ), X ) ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.11/1.50 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ) ), X ) ), =( X,
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ],
% 1.11/1.50 [ ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), Y ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), Y ), Z ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y, hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), Z ) ), =( Z,
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), Z ), Y ), =( Z,
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.50 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' )
% 1.11/1.50 , 'c_FFT__Mirabelle_Oroot'( X ) ), X ), 'c_HOL_Oone__class_Oone'(
% 1.11/1.50 'tc_Complex_Ocomplex' ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), ~( =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.50 ) ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =(
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.50 ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.11/1.50 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.50 ) ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), U ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ],
% 1.11/1.50 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.11/1.50 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.11/1.50 ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =( hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.11/1.50 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.11/1.50 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.11/1.50 'c_Suc', Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.11/1.50 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.11/1.50 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.11/1.50 , X ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ),
% 1.11/1.50 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 1.11/1.50 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.50 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.11/1.50 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.50 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.11/1.50 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.50 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.50 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ) ],
% 1.11/1.50 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ) ],
% 1.11/1.50 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.50 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.11/1.50 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.50 ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.11/1.50 X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), =(
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.50 ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.11/1.50 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.50 ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.11/1.50 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ), ~(
% 1.11/1.50 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ) ), hAPP(
% 1.11/1.50 hAPP( 'c_Power_Opower__class_Opower'( X ), T ), hAPP( 'c_Suc', Z ) ) ),
% 1.11/1.50 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ) ), hAPP(
% 1.11/1.50 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_Power_Opower__class_Opower'(
% 1.11/1.50 X ), Y ), X, 'tc_fun'( X, X ), 'tc_nat' ), 'c_COMBB'( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), T ), hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), 'tc_nat', X, 'tc_nat' ),
% 1.11/1.50 'tc_nat', X, X ), 'tc_nat', X ), hAPP(
% 1.11/1.50 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc', Z ) ) ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 X ) ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 X ) ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.11/1.50 , Y ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.11/1.50 X ) ), =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.50 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), X ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.50 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.11/1.50 X ) ), ~( =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) )
% 1.11/1.50 , =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.50 [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 1.11/1.50 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.50 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X
% 1.11/1.50 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.50 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.50 'c_Int_OBit1'( 'c_Int_OPls' ), X ) ), Y ), Y ) ],
% 1.11/1.50 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ) )
% 1.11/1.50 , Y ) ],
% 1.11/1.50 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.11/1.50 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, hAPP(
% 1.11/1.50 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.11/1.50 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.11/1.50 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 1.11/1.50 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.11/1.50 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.11/1.50 , X ) ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ) ) ) ],
% 1.11/1.50 [ ~( =( 'c_Int_OPls', 'c_Int_OBit0'( X ) ) ), =( 'c_Int_OPls', X ) ]
% 1.11/1.50 ,
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.50 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), T ), Y ) ), Z ) ), U ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.50 X ), T ), Z ) ), U ) ) ],
% 1.11/1.50 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ]
% 1.11/1.50 ,
% 1.11/1.50 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ]
% 1.11/1.50 ,
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), ~(
% 1.11/1.50 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP(
% 1.11/1.50 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_Power_Opower__class_Opower'(
% 1.11/1.50 X ), Y ), X, 'tc_fun'( X, X ), 'tc_nat' ), 'c_COMBB'( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Z ), hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc', T ) ), 'tc_nat'
% 1.11/1.50 , X, 'tc_nat' ), 'tc_nat', X, X ), 'tc_nat', X ), hAPP(
% 1.11/1.50 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc', T ) ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( 'c_Finite__Set_Osetsum'(
% 1.11/1.50 'c_COMBS'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), X, 'tc_fun'( X, X ), 'tc_nat' )
% 1.11/1.50 , 'c_COMBB'( hAPP( 'c_Power_Opower__class_Opower'( X ), Z ), hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), 'tc_nat', X, 'tc_nat' ),
% 1.11/1.50 'tc_nat', X, X ), 'tc_nat', X ), hAPP(
% 1.11/1.50 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc', T ) ) ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.11/1.50 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.11/1.50 hAPP( 'c_Suc', Y ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.50 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.50 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ) ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.11/1.50 Y ) ],
% 1.11/1.50 [ =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 'tc_nat' ) ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) )
% 1.11/1.50 ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ) ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.50 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.50 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP(
% 1.11/1.50 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), =( X, 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 'tc_nat' ) ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y )
% 1.11/1.50 , 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ) )
% 1.11/1.50 , Y ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ) )
% 1.11/1.50 , Y ) ],
% 1.11/1.50 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ) ) ), =( X, Y ) ],
% 1.11/1.50 [ ~( hBOOL( hAPP( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.11/1.50 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), Y ) )
% 1.11/1.50 ) ), hBOOL( hAPP( X, Z ) ) ],
% 1.11/1.50 [ ~( hBOOL( hAPP( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.11/1.50 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), Y ) )
% 1.11/1.50 ) ), hBOOL( hAPP( X, Z ) ) ],
% 1.11/1.50 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OPls' ) ), =( X, 'c_Int_OPls' ) ]
% 1.11/1.50 ,
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.11/1.50 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.11/1.50 ],
% 1.11/1.50 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OPls' ) ) ],
% 1.11/1.50 [ ~( 'class_RealVector_Oreal__field'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), W ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.50 X ), Y ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), Z ), U ) ), W ) ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ) ), W ) ), U ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.11/1.50 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( T, X ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 1.11/1.50 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), Y, X, 'tc_fun'( X, X ), Z ), T, Z, X,
% 1.11/1.50 X ), Z, X ), U ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), hAPP(
% 1.11/1.50 'c_Finite__Set_Osetsum'( Y, Z, X ), U ) ), hAPP( 'c_Finite__Set_Osetsum'(
% 1.11/1.50 T, Z, X ), U ) ) ) ],
% 1.11/1.50 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' )
% 1.11/1.50 , 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.50 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.11/1.50 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.11/1.50 'c_FFT__Mirabelle_Oroot'( X ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.50 'tc_nat' ), Y ), Z ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.50 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.11/1.50 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.50 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T
% 1.11/1.50 ) ) ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), ~( 'class_Int_Onumber'(
% 1.11/1.50 X ) ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.50 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.11/1.50 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.11/1.50 X ) ), Y ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.50 'tc_nat' ), X ), Y ) ) ) ],
% 1.11/1.50 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.11/1.50 'c_Suc', Y ) ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.50 'tc_nat' ), X ), Y ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.50 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.11/1.50 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( hAPP(
% 1.11/1.50 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T ), W ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.50 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.11/1.50 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( T, hAPP(
% 1.11/1.50 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), U ), Y ) ), Z ) ), W ) ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 1.11/1.50 'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), hAPP(
% 1.11/1.50 'c_SetInterval_Oord__class_OatLeastLessThan'( hAPP( 'c_Suc', Z ),
% 1.11/1.50 'tc_nat' ), hAPP( 'c_Suc', T ) ) ), hAPP( 'c_Finite__Set_Osetsum'(
% 1.11/1.50 'c_COMBB'( Y, 'c_Suc', 'tc_nat', X, 'tc_nat' ), 'tc_nat', X ), hAPP(
% 1.11/1.50 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, 'tc_nat' ), T ) ) ) ]
% 1.11/1.50 ,
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.11/1.50 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP(
% 1.11/1.50 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.11/1.50 [ ~( =( 'c_Int_OPls', 'c_Int_OBit1'( X ) ) ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.11/1.50 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.11/1.50 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), =( Y
% 1.11/1.50 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 1.11/1.50 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.11/1.50 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( X
% 1.11/1.50 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 1.11/1.50 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.11/1.50 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( Y
% 1.11/1.50 , Z ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.11/1.50 , hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.11/1.50 , X ) ), Z ) ), Z ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.50 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.11/1.50 Y ) ) ],
% 1.11/1.50 [ ~( =( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ) ) ), =( X, Y ) ],
% 1.11/1.50 [ ~( =( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ) ) ), =( X, Y ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), =( Y, hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =(
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.50 ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.50 X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y ), =(
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.50 ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.11/1.50 ), Y ) ) ],
% 1.11/1.50 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.11/1.50 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.50 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.11/1.50 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, hAPP(
% 1.11/1.50 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, hAPP( 'c_Suc'
% 1.11/1.50 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.11/1.50 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.50 Y, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.11/1.50 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.11/1.50 , 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ), =(
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.50 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.11/1.50 , Z ) ],
% 1.11/1.50 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.11/1.50 , Z ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.11/1.50 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.50 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.11/1.50 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.11/1.50 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.50 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.11/1.50 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ) ],
% 1.11/1.50 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.11/1.50 , X ) ), hAPP( 'c_Suc', Y ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.11/1.50 'tc_nat' ), X ), Y ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.11/1.50 , X ) ), Z ) ), Z ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), =( Z,
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.50 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.11/1.50 ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ), =( U,
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.50 ) ],
% 1.11/1.50 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.11/1.50 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y, hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), Z ) ), =( Z,
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), Z ), Y ), =( Z,
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.11/1.50 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.11/1.50 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.50 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.11/1.50 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.50 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.11/1.50 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.50 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 'tc_nat' ) ) ],
% 1.11/1.50 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 'tc_nat' ) ) ],
% 1.11/1.50 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.11/1.50 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.50 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.11/1.50 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.11/1.50 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.11/1.50 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.11/1.50 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.11/1.50 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.50 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.11/1.50 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.50 X ), Y ), Z ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.11/1.50 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.11/1.50 ) ), Z ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.50 X ), Z ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.11/1.50 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( T, X ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.50 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ],
% 1.11/1.50 [ =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 'tc_nat' ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y
% 1.11/1.50 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.50 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.50 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.50 [ ~( =( hAPP( 'c_Suc', X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.11/1.50 ,
% 1.11/1.50 [ ~( =( hAPP( 'c_Suc', X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.11/1.50 ,
% 1.11/1.50 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.11/1.50 'tc_nat' ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.11/1.50 ,
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 X ) ) ],
% 1.11/1.50 [ =( 'c_Int_OBit0'( 'c_Int_OPls' ), 'c_Int_OPls' ) ],
% 1.11/1.50 [ ~( 'class_Power_Opower'( X ) ), ~(
% 1.11/1.50 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 1.11/1.50 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_Power_Opower__class_Opower'(
% 1.11/1.50 X ), Y ), X, 'tc_fun'( X, X ), 'tc_nat' ), 'c_COMBB'( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Z ), hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), 'tc_nat', X, 'tc_nat' ),
% 1.11/1.50 'tc_nat', X, X ), 'tc_nat', X ), hAPP(
% 1.11/1.50 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc', T ) ) ), hAPP(
% 1.11/1.50 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), 'c_COMBB'( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), 'tc_nat', X, 'tc_nat' ), X
% 1.11/1.50 , 'tc_fun'( X, X ), 'tc_nat' ), hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.11/1.50 , Z ), 'tc_nat', X, X ), 'tc_nat', X ), hAPP(
% 1.11/1.50 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc', T ) ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.11/1.50 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.11/1.50 'class_Int_Onumber'( X ) ), ~( =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), =( Y, hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( T
% 1.11/1.50 , X ) ), Z ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ), =( Z,
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.50 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( 'c_Suc',
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.11/1.50 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( hAPP(
% 1.11/1.50 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.11/1.50 ,
% 1.11/1.50 [ =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ) ) ],
% 1.11/1.50 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.50 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.50 ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.11/1.50 ,
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ) ), =( U,
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.50 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ), hAPP(
% 1.11/1.50 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), =( Z,
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ) ), =( U, 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.50 ), =( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), U ), hAPP(
% 1.11/1.50 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.11/1.50 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.11/1.50 Y ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.11/1.50 Y ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.11/1.50 Y ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.11/1.50 Y ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.11/1.50 Y ) ],
% 1.11/1.50 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 'tc_nat' ) ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.11/1.50 ,
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.11/1.50 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.11/1.50 ) ), Z ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.11/1.50 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.50 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.11/1.50 ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.11/1.50 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.50 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.11/1.50 ) ) ],
% 1.11/1.50 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.11/1.50 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.11/1.50 X ), Y ), Z ) ), Z ), Y ) ],
% 1.11/1.50 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ) ) ), =( X, Y ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.11/1.50 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.11/1.50 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ) ) ],
% 1.11/1.50 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.11/1.50 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.11/1.50 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.11/1.50 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.11/1.50 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.11/1.50 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.11/1.50 ,
% 1.11/1.50 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.11/1.50 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.50 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.11/1.50 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.50 X ), Y ), Z ) ), T ) ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.11/1.50 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.11/1.50 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.50 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.11/1.50 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.50 X ), Y ), Z ) ), T ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.50 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.11/1.50 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.50 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.11/1.50 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.11/1.50 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.50 ) ) ],
% 1.11/1.50 [ =( hAPP( 'c_COMBB'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y, W ) ) ) ]
% 1.11/1.50 ,
% 1.11/1.50 [ =( hAPP( 'c_COMBS'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), hAPP( Y
% 1.11/1.50 , W ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.11/1.50 X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.11/1.50 X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.11/1.50 X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.50 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.11/1.50 ) ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.11/1.50 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP(
% 1.11/1.50 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.50 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ) ), =( Z, T ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), T ), T ) ) ), =( Y, Z ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.11/1.50 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.50 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.11/1.50 , X ) ), T ) ) ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), ~( =( hAPP( Y,
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.11/1.50 ) ), =( hAPP( 'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), hAPP(
% 1.11/1.50 'c_SetInterval_Oord__class_OatLeastLessThan'( hAPP( 'c_Suc',
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), Z ) ), hAPP(
% 1.11/1.50 'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), hAPP(
% 1.11/1.50 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 'tc_nat' ), 'tc_nat' ), Z ) ) ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.50 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), Y ) ) ]
% 1.11/1.50 ,
% 1.11/1.50 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.11/1.50 ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =( Y, Z ) ],
% 1.11/1.50 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 'tc_nat' ) ) ],
% 1.11/1.50 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.50 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), Z ), U ) ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ) ), U ) ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), Z ), U ) ) ) ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 1.11/1.50 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.50 X ), Y, X, 'tc_fun'( X, X ), Z ), T, Z, X, X ), Z, X ), U ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_Finite__Set_Osetsum'( Y, Z, X )
% 1.11/1.50 , U ) ), hAPP( 'c_Finite__Set_Osetsum'( T, Z, X ), U ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.50 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), U ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.50 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ), U )
% 1.11/1.50 ) ],
% 1.11/1.50 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ), T ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ), T ) ) ],
% 1.11/1.50 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.50 X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 X ) ) ), =( Y, Z ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 X ) ) ), =( Y, Z ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.11/1.50 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 1.11/1.50 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.11/1.50 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.11/1.50 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.11/1.50 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.11/1.50 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.11/1.50 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.11/1.50 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.50 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.11/1.50 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), Z ), U ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.11/1.50 Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.50 ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.50 ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.50 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.11/1.50 Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.50 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ), Y ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.11/1.50 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.11/1.50 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, hAPP( 'c_Suc',
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.11/1.50 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.11/1.50 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 1.11/1.50 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.11/1.50 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.50 'tc_nat' ), X ), X ) ) ],
% 1.11/1.50 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.11/1.50 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ],
% 1.11/1.50 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y )
% 1.11/1.50 , Y ) ) ],
% 1.11/1.50 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), =( Z,
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ), =( Y,
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.11/1.50 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP(
% 1.11/1.50 'c_Finite__Set_Osetsum'( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.11/1.50 'tc_nat', X ), hAPP( 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), Z ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), 'c_HOL_Oone__class_Oone'(
% 1.11/1.50 X ) ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ),
% 1.11/1.50 'c_HOL_Oone__class_Oone'( X ) ) ) ), =( Y, 'c_HOL_Oone__class_Oone'( X )
% 1.11/1.50 ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.11/1.50 Y ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.11/1.50 Y ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.11/1.50 Y ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.11/1.50 X ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.11/1.50 Y ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.11/1.50 Y ) ],
% 1.11/1.50 [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.11/1.50 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.11/1.50 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.11/1.50 Y ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.11/1.50 Y ) ],
% 1.11/1.50 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.11/1.50 X ), Y ), Z ) ), Z ), Y ) ],
% 1.11/1.50 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), X ), Y ) ],
% 1.11/1.50 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Y ), X ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.11/1.50 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.11/1.50 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.11/1.50 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.11/1.50 ) ) ],
% 1.11/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ) ],
% 1.11/1.50 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =( hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ) ],
% 1.11/1.50 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Complex_Ocomplex' )
% 1.11/1.50 , hAPP( 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( 'tc_Complex_Ocomplex' ), 'c_COMBB'(
% 1.11/1.50 'v_a', hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat'
% 1.11/1.50 ), 'tc_Complex_Ocomplex', 'tc_fun'( 'tc_Complex_Ocomplex',
% 1.11/1.50 'tc_Complex_Ocomplex' ), 'tc_nat' ), 'c_COMBB'( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.11/1.50 'c_FFT__Mirabelle_Oroot'( 'v_m' ) ), hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.50 'tc_nat' ), 'v_i' ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ),
% 1.11/1.50 'tc_nat', 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ), 'tc_nat',
% 1.11/1.50 'tc_Complex_Ocomplex' ), hAPP(
% 1.11/1.50 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 'tc_nat' ), 'tc_nat' ), 'v_m' ) ) ), hAPP( 'c_Finite__Set_Osetsum'(
% 1.11/1.50 'c_COMBS'( 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'(
% 1.11/1.50 'tc_Complex_Ocomplex' ), 'c_COMBB'( 'v_a', 'c_COMBB'( 'c_Suc', hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_nat', 'tc_nat' ), 'tc_nat'
% 1.11/1.50 , 'tc_Complex_Ocomplex', 'tc_nat' ), 'tc_Complex_Ocomplex', 'tc_fun'(
% 1.11/1.50 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ), 'tc_nat' ), 'c_COMBB'(
% 1.11/1.50 hAPP( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.11/1.50 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.50 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.11/1.50 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_m' ) ) ), 'c_COMBB'(
% 1.11/1.50 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'v_i' ), 'c_COMBB'( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'v_i' ), hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_nat', 'tc_nat' ), 'tc_nat'
% 1.11/1.50 , 'tc_nat', 'tc_nat' ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ),
% 1.11/1.50 'tc_nat', 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ), 'tc_nat',
% 1.11/1.50 'tc_Complex_Ocomplex' ), hAPP(
% 1.11/1.50 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 'tc_nat' ), 'tc_nat' ), 'v_m' ) ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( 'tc_Complex_Ocomplex' ), hAPP(
% 1.11/1.50 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( 'tc_Complex_Ocomplex' ), 'c_COMBB'(
% 1.11/1.50 'v_a', hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.11/1.50 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat'
% 1.11/1.50 ), 'tc_Complex_Ocomplex', 'tc_fun'( 'tc_Complex_Ocomplex',
% 1.11/1.50 'tc_Complex_Ocomplex' ), 'tc_nat' ), 'c_COMBB'( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.11/1.50 'c_FFT__Mirabelle_Oroot'( 'v_m' ) ), hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.50 'tc_nat' ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), 'v_i' )
% 1.11/1.50 , 'v_m' ) ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ), 'tc_nat',
% 1.11/1.50 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ), 'tc_nat',
% 1.11/1.50 'tc_Complex_Ocomplex' ), hAPP(
% 1.11/1.50 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 'tc_nat' ), 'tc_nat' ), 'v_m' ) ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Otimes__class_Otimes'( 'tc_Complex_Ocomplex' ), hAPP( hAPP(
% 1.11/1.50 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( 'tc_Complex_Ocomplex' ),
% 1.11/1.50 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ) ),
% 1.11/1.50 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.50 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.11/1.50 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_m' ) ) ) ), hAPP( hAPP(
% 1.11/1.50 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), 'v_i' ), 'v_m' ) ) ), hAPP(
% 1.11/1.50 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'(
% 1.11/1.50 'c_HOL_Oinverse__class_Odivide'( 'tc_Complex_Ocomplex' ), 'c_COMBB'(
% 1.11/1.50 'v_a', 'c_COMBB'( 'c_Suc', hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.11/1.50 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.11/1.50 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_nat', 'tc_nat' ), 'tc_nat'
% 1.11/1.50 , 'tc_Complex_Ocomplex', 'tc_nat' ), 'tc_Complex_Ocomplex', 'tc_fun'(
% 1.11/1.50 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ), 'tc_nat' ), 'c_COMBB'(
% 1.11/1.50 hAPP( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.11/1.50 'c_FFT__Mirabelle_Oroot'( 'v_m' ) ), hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.11/1.50 'tc_nat' ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), 'v_i' )
% 1.11/1.50 , 'v_m' ) ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ), 'tc_nat',
% 1.11/1.50 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ), 'tc_nat',
% 1.11/1.50 'tc_Complex_Ocomplex' ), hAPP(
% 1.11/1.50 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.11/1.50 'tc_nat' ), 'tc_nat' ), 'v_m' ) ) ) ) ) ) ],
% 1.11/1.50 [ 'class_Lattices_Oboolean__algebra'( 'tc_fun'( X, Y ) ), ~(
% 1.11/1.50 'class_Lattices_Oboolean__algebra'( Y ) ) ],
% 1.11/1.50 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 1.11/1.50 'class_Orderings_Opreorder'( Y ) ) ],
% 1.11/1.50 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 1.11/1.50 'class_Orderings_Oorder'( Y ) ) ],
% 1.11/1.50 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 1.11/1.50 ],
% 1.11/1.50 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 1.11/1.50 ) ],
% 1.11/1.50 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 1.11/1.50 ],
% 1.11/1.50 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 1.11/1.50 ,
% 1.11/1.50 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 1.11/1.50 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 1.11/1.50 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 1.11/1.50 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 1.11/1.50 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 1.11/1.50 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 1.11/1.50 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 1.11/1.50 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 1.11/1.50 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 1.11/1.50 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 1.11/1.50 [ 'class_Ring__and__Field_Ocomm__semiring__0'( 'tc_nat' ) ],
% 1.11/1.50 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 1.11/1.50 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 1.11/1.50 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 1.11/1.50 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 1.11/1.50 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 1.11/1.50 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 1.11/1.50 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 1.11/1.50 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 1.11/1.50 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 1.11/1.50 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 1.11/1.50 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 1.11/1.50 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 1.11/1.50 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 1.11/1.50 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 1.11/1.50 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 1.11/1.50 [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ],
% 1.11/1.50 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 1.11/1.50 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 1.11/1.50 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 1.11/1.50 [ 'class_Power_Opower'( 'tc_nat' ) ],
% 1.11/1.50 [ 'class_Int_Onumber'( 'tc_nat' ) ],
% 1.11/1.50 [ 'class_Lattices_Oboolean__algebra'( 'tc_bool' ) ],
% 1.11/1.50 [ 'class_Orderings_Opreorder'( 'tc_bool' ) ],
% 1.11/1.50 [ 'class_Orderings_Oorder'( 'tc_bool' ) ],
% 1.11/1.50 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 1.11/1.50 'tc_Int_Oint' ) ],
% 1.11/1.50 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 1.11/1.50 'tc_Int_Oint' ) ],
% 1.11/1.50 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 1.11/1.50 'tc_Int_Oint' ) ],
% 1.11/1.50 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_Int_Oint' )
% 1.11/1.50 ],
% 1.11/1.50 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'( 'tc_Int_Oint' )
% 1.11/1.50 ],
% 1.11/1.50 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_Int_Oint' ) ]
% 1.11/1.50 ,
% 1.11/1.50 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.11/1.50 ,
% 1.11/1.50 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_Int_Oint' ) ]
% 1.11/1.50 ,
% 1.11/1.50 [ 'class_Ring__and__Field_Oring__no__zero__divisors'( 'tc_Int_Oint' ) ]
% 1.11/1.50 ,
% 1.11/1.50 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.11/1.50 ,
% 1.11/1.50 [ 'class_Ring__and__Field_Oordered__ring__strict'( 'tc_Int_Oint' ) ]
% 1.11/1.50 ,
% 1.11/1.50 [ 'class_OrderedGroup_Opordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.11/1.50 [ 'class_OrderedGroup_Olordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.11/1.50 [ 'class_OrderedGroup_Oordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.11/1.50 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.11/1.50 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_Int_Oint' ) ],
% 1.11/1.50 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_Int_Oint' ) ],
% 1.11/1.50 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Int_Oint' ) ],
% 1.11/1.50 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_Int_Oint' ) ],
% 1.11/1.50 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Int_Oint' ) ],
% 1.11/1.50 [ 'class_Ring__and__Field_Ocomm__semiring__0'( 'tc_Int_Oint' ) ],
% 1.11/1.50 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Int_Oint' ) ],
% 1.11/1.50 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Int_Oint' ) ],
% 1.11/1.50 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.11/1.50 [ 'class_Ring__and__Field_Opordered__ring'( 'tc_Int_Oint' ) ],
% 1.11/1.50 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Int_Oint' ) ],
% 1.11/1.50 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Int_Oint' ) ],
% 1.11/1.50 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Int_Oint' ) ],
% 1.11/1.50 [ 'class_Ring__and__Field_Oordered__idom'( 'tc_Int_Oint' ) ],
% 1.11/1.50 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Int_Oint' ) ],
% 1.11/1.50 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Int_Oint' ) ],
% 1.11/1.50 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Int_Oint' ) ],
% 1.11/1.50 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_Int_Oint' ) ],
% 1.11/1.50 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Int_Oint' ) ],
% 1.11/1.50 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Int_Oint' ) ],
% 1.11/1.50 [ 'class_Ring__and__Field_Omult__mono'( 'tc_Int_Oint' ) ],
% 1.11/1.50 [ 'class_Ring__and__Field_Ocomm__ring'( 'tc_Int_Oint' ) ],
% 1.11/1.50 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Int_Oint' ) ],
% 1.11/1.50 [ 'class_Ring__and__Field_Osemiring'( 'tc_Int_Oint' ) ],
% 1.11/1.50 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Int_Oint' ) ],
% 1.11/1.50 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Int_Oint' ) ],
% 1.11/1.50 [ 'class_Ring__and__Field_Oring__1'( 'tc_Int_Oint' ) ],
% 1.11/1.50 [ 'class_Divides_Osemiring__div'( 'tc_Int_Oint' ) ],
% 1.11/1.50 [ 'class_Ring__and__Field_Oring'( 'tc_Int_Oint' ) ],
% 1.11/1.50 [ 'class_Ring__and__Field_Oidom'( 'tc_Int_Oint' ) ],
% 1.11/1.50 [ 'class_Nat_Osemiring__char__0'( 'tc_Int_Oint' ) ],
% 1.11/1.50 [ 'class_Orderings_Opreorder'( 'tc_Int_Oint' ) ],
% 1.11/1.50 [ 'class_Orderings_Olinorder'( 'tc_Int_Oint' ) ],
% 1.11/1.50 [ 'class_Divides_Oring__div'( 'tc_Int_Oint' ) ],
% 1.11/1.50 [ 'class_Orderings_Oorder'( 'tc_Int_Oint' ) ],
% 1.11/1.50 [ 'class_Int_Oring__char__0'( 'tc_Int_Oint' ) ],
% 1.11/1.50 [ 'class_Int_Onumber__ring'( 'tc_Int_Oint' ) ],
% 1.11/1.50 [ 'class_Power_Opower'( 'tc_Int_Oint' ) ],
% 1.11/1.50 [ 'class_Int_Onumber'( 'tc_Int_Oint' ) ],
% 1.11/1.50 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 1.11/1.50 'tc_Complex_Ocomplex' ) ],
% 1.11/1.50 [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 1.11/1.50 'tc_Complex_Ocomplex' ) ],
% 1.11/1.50 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 1.11/1.50 'tc_Complex_Ocomplex' ) ],
% 1.11/1.50 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Complex_Ocomplex' )
% 1.11/1.50 ],
% 1.11/1.50 [ 'class_RealVector_Oreal__normed__algebra__1'( 'tc_Complex_Ocomplex' )
% 1.11/1.50 ],
% 1.11/1.50 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Complex_Ocomplex' )
% 1.11/1.50 ],
% 1.11/1.50 [ 'class_Ring__and__Field_Odivision__by__zero'( 'tc_Complex_Ocomplex' )
% 1.11/1.50 ],
% 1.11/1.50 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Complex_Ocomplex' ) ]
% 1.11/1.50 ,
% 1.11/1.50 [ 'class_Ring__and__Field_Ocomm__semiring__0'( 'tc_Complex_Ocomplex' ) ]
% 1.11/1.50 ,
% 1.11/1.50 [ 'class_RealVector_Oreal__normed__algebra'( 'tc_Complex_Ocomplex' ) ]
% 1.11/1.50 ,
% 1.11/1.50 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Complex_Ocomplex' ) ]
% 1.11/1.50 ,
% 1.11/1.50 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Complex_Ocomplex' ) ]
% 1.11/1.50 ,
% 1.11/1.50 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Complex_Ocomplex' ) ]
% 1.11/1.50 ,
% 1.11/1.50 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Complex_Ocomplex' ) ]
% 1.11/1.50 ,
% 1.11/1.50 [ 'class_RealVector_Oreal__normed__field'( 'tc_Complex_Ocomplex' ) ]
% 1.11/1.50 ,
% 1.11/1.50 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Complex_Ocomplex' ) ]
% 1.11/1.50 ,
% 1.11/1.50 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Complex_Ocomplex' ) ]
% 1.11/1.50 ,
% 1.11/1.50 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Complex_Ocomplex' ) ]
% 1.11/1.50 ,
% 1.11/1.50 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Complex_Ocomplex' ) ],
% 1.11/1.50 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Complex_Ocomplex' ) ],
% 1.11/1.50 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Complex_Ocomplex' ) ],
% 1.11/1.50 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Complex_Ocomplex' ) ],
% 1.11/1.50 [ 'class_Ring__and__Field_Ocomm__ring'( 'tc_Complex_Ocomplex' ) ],
% 1.11/1.50 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Complex_Ocomplex' ) ],
% 1.11/1.50 [ 'class_Ring__and__Field_Osemiring'( 'tc_Complex_Ocomplex' ) ],
% 1.11/1.51 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Complex_Ocomplex' ) ],
% 1.11/1.51 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Complex_Ocomplex' ) ],
% 1.11/1.51 [ 'class_Ring__and__Field_Oring__1'( 'tc_Complex_Ocomplex' ) ],
% 1.11/1.51 [ 'class_RealVector_Oreal__field'( 'tc_Complex_Ocomplex' ) ],
% 1.11/1.51 [ 'class_Ring__and__Field_Ofield'( 'tc_Complex_Ocomplex' ) ],
% 1.11/1.51 [ 'class_Ring__and__Field_Oring'( 'tc_Complex_Ocomplex' ) ],
% 1.11/1.51 [ 'class_Ring__and__Field_Oidom'( 'tc_Complex_Ocomplex' ) ],
% 1.11/1.51 [ 'class_Nat_Osemiring__char__0'( 'tc_Complex_Ocomplex' ) ],
% 1.11/1.51 [ 'class_Int_Oring__char__0'( 'tc_Complex_Ocomplex' ) ],
% 1.11/1.51 [ 'class_Int_Onumber__ring'( 'tc_Complex_Ocomplex' ) ],
% 1.11/1.51 [ 'class_Power_Opower'( 'tc_Complex_Ocomplex' ) ],
% 1.11/1.51 [ 'class_Int_Onumber'( 'tc_Complex_Ocomplex' ) ],
% 1.11/1.51 [ =( hAPP( 'c_COMBS'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), hAPP( Y
% 1.11/1.51 , W ) ) ) ],
% 1.11/1.51 [ =( hAPP( 'c_COMBC'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), Y ) ) ]
% 1.11/1.51 ,
% 1.11/1.51 [ =( hAPP( 'c_COMBB'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y, W ) ) ) ]
% 1.11/1.51 ,
% 1.11/1.51 [ 'c_fequal'( X, X, Y ) ],
% 1.11/1.51 [ =( X, Y ), ~( 'c_fequal'( X, Y, Z ) ) ]
% 1.11/1.51 ] .
% 1.11/1.51
% 1.11/1.51
% 1.11/1.51 percentage equality = 0.249311, percentage horn = 0.842623
% 1.11/1.51 This is a problem with some equality
% 1.11/1.51
% 1.11/1.51
% 1.11/1.51
% 1.11/1.51 Options Used:
% 1.11/1.51
% 1.11/1.51 useres = 1
% 1.11/1.51 useparamod = 1
% 1.11/1.51 useeqrefl = 1
% 1.11/1.51 useeqfact = 1
% 1.11/1.51 usefactor = 1
% 1.11/1.51 usesimpsplitting = 0
% 1.11/1.51 usesimpdemod = 5
% 1.11/1.51 usesimpres = 3
% 1.11/1.51
% 1.11/1.51 resimpinuse = 1000
% 1.11/1.51 resimpclauses = 20000
% 1.11/1.51 substype = eqrewr
% 1.11/1.51 backwardsubs = 1
% 1.11/1.51 selectoldest = 5
% 1.11/1.51
% 1.11/1.51 litorderings [0] = split
% 1.11/1.51 litorderings [1] = extend the termordering, first sorting on arguments
% 1.11/1.51
% 1.11/1.51 termordering = kbo
% 1.11/1.51
% 1.11/1.51 litapriori = 0
% 1.11/1.51 termapriori = 1
% 1.11/1.51 litaposteriori = 0
% 1.11/1.51 termaposteriori = 0
% 1.11/1.51 demodaposteriori = 0
% 1.11/1.51 ordereqreflfact = 0
% 1.11/1.51
% 1.11/1.51 litselect = negord
% 1.11/1.51
% 1.11/1.51 maxweight = 15
% 1.11/1.51 maxdepth = 30000
% 1.11/1.51 maxlength = 115
% 1.11/1.51 maxnrvars = 195
% 1.11/1.51 excuselevel = 1
% 1.11/1.51 increasemaxweight = 1
% 1.11/1.51
% 1.11/1.51 maxselected = 10000000
% 1.11/1.51 maxnrclauses = 10000000
% 1.11/1.51
% 1.11/1.51 showgenerated = 0
% 1.11/1.51 showkept = 0
% 1.11/1.51 showselected = 0
% 1.11/1.51 showdeleted = 0
% 1.11/1.51 showresimp = 1
% 1.11/1.51 showstatus = 2000
% 1.11/1.51
% 1.11/1.51 prologoutput = 1
% 1.11/1.51 nrgoals = 5000000
% 1.11/1.51 totalproof = 1
% 1.11/1.51
% 1.11/1.51 Symbols occurring in the translation:
% 1.11/1.51
% 1.11/1.51 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.11/1.51 . [1, 2] (w:1, o:159, a:1, s:1, b:0),
% 1.11/1.51 ! [4, 1] (w:0, o:79, a:1, s:1, b:0),
% 1.11/1.51 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.11/1.51 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.11/1.51 'class_Ring__and__Field_Oordered__idom' [40, 1] (w:1, o:86, a:1, s:1
% 1.11/1.51 , b:0),
% 1.11/1.51 'c_HOL_Oord__class_Oless' [43, 3] (w:1, o:191, a:1, s:1, b:0),
% 1.11/1.51 'class_Orderings_Olinorder' [44, 1] (w:1, o:88, a:1, s:1, b:0),
% 1.11/1.51 'class_Orderings_Oorder' [45, 1] (w:1, o:89, a:1, s:1, b:0),
% 1.11/1.51 'c_lessequals' [46, 3] (w:1, o:192, a:1, s:1, b:0),
% 1.11/1.51 'tc_nat' [49, 0] (w:1, o:28, a:1, s:1, b:0),
% 1.11/1.51 'class_RealVector_Oreal__normed__field' [50, 1] (w:1, o:90, a:1, s:1
% 1.11/1.51 , b:0),
% 1.11/1.51 'c_Deriv_Oderiv' [54, 4] (w:1, o:200, a:1, s:1, b:0),
% 1.11/1.51 hAPP [56, 2] (w:1, o:184, a:1, s:1, b:0),
% 1.11/1.51 hBOOL [57, 1] (w:1, o:91, a:1, s:1, b:0),
% 1.11/1.51 'class_Lattices_Oboolean__algebra' [58, 1] (w:1, o:92, a:1, s:1, b:0)
% 1.11/1.51 ,
% 1.11/1.51 'c_HOL_Ouminus__class_Ouminus' [59, 1] (w:1, o:94, a:1, s:1, b:0),
% 1.11/1.51 'class_OrderedGroup_Ogroup__add' [60, 1] (w:1, o:95, a:1, s:1, b:0),
% 1.11/1.51
% 1.11/1.51 'c_Divides_Odiv__class_Omod' [63, 3] (w:1, o:193, a:1, s:1, b:0),
% 1.11/1.51 'class_OrderedGroup_Opordered__ab__group__add' [64, 1] (w:1, o:97, a:
% 1.11/1.51 1, s:1, b:0),
% 1.11/1.51 'c_Divides_Odiv__class_Odiv' [65, 3] (w:1, o:194, a:1, s:1, b:0),
% 1.11/1.51 'c_HOL_Ozero__class_Ozero' [66, 1] (w:1, o:98, a:1, s:1, b:0),
% 1.11/1.51 'class_Nat_Osemiring__char__0' [67, 1] (w:1, o:87, a:1, s:1, b:0),
% 1.11/1.51 'c_Nat_Osemiring__1__class_Oof__nat' [68, 2] (w:1, o:185, a:1, s:1
% 1.11/1.51 , b:0),
% 1.11/1.51 'class_Orderings_Opreorder' [70, 1] (w:1, o:99, a:1, s:1, b:0),
% 1.11/1.51 'c_COMBC' [74, 5] (w:1, o:203, a:1, s:1, b:0),
% 1.11/1.51 'c_HOL_Ominus__class_Ominus' [76, 1] (w:1, o:100, a:1, s:1, b:0),
% 1.11/1.51 'c_HOL_Oone__class_Oone' [77, 1] (w:1, o:101, a:1, s:1, b:0),
% 2.06/2.45 'c_Parity_Oeven__odd__class_Oeven' [78, 2] (w:1, o:186, a:1, s:1, b:0
% 2.06/2.45 ),
% 2.06/2.45 'class_Ring__and__Field_Oordered__semidom' [79, 1] (w:1, o:103, a:1
% 2.06/2.45 , s:1, b:0),
% 2.06/2.45 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [80, 1]
% 2.06/2.45 (w:1, o:104, a:1, s:1, b:0),
% 2.06/2.45 'c_HOL_Oplus__class_Oplus' [81, 1] (w:1, o:105, a:1, s:1, b:0),
% 2.06/2.45 'class_OrderedGroup_Oordered__ab__group__add' [84, 1] (w:1, o:96, a:1
% 2.06/2.45 , s:1, b:0),
% 2.06/2.45 'class_Divides_Osemiring__div' [85, 1] (w:1, o:107, a:1, s:1, b:0),
% 2.06/2.45 'class_Ring__and__Field_Oordered__semiring__strict' [86, 1] (w:1, o:
% 2.06/2.45 108, a:1, s:1, b:0),
% 2.06/2.45 'c_HOL_Otimes__class_Otimes' [87, 1] (w:1, o:93, a:1, s:1, b:0),
% 2.06/2.45 'class_Ring__and__Field_Oordered__semiring' [88, 1] (w:1, o:109, a:1
% 2.06/2.45 , s:1, b:0),
% 2.06/2.45 'class_Ring__and__Field_Oordered__ring__strict' [89, 1] (w:1, o:102
% 2.06/2.45 , a:1, s:1, b:0),
% 2.06/2.45 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [90, 1]
% 2.06/2.45 (w:1, o:110, a:1, s:1, b:0),
% 2.06/2.45 'class_OrderedGroup_Ocomm__monoid__add' [91, 1] (w:1, o:111, a:1, s:1
% 2.06/2.45 , b:0),
% 2.06/2.45 'class_OrderedGroup_Opordered__comm__monoid__add' [92, 1] (w:1, o:112
% 2.06/2.45 , a:1, s:1, b:0),
% 2.06/2.45 'class_OrderedGroup_Olordered__ab__group__add' [93, 1] (w:1, o:113
% 2.06/2.45 , a:1, s:1, b:0),
% 2.06/2.45 'c_Power_Opower_Opower' [94, 3] (w:1, o:195, a:1, s:1, b:0),
% 2.06/2.45 'c_Power_Opower__class_Opower' [95, 1] (w:1, o:114, a:1, s:1, b:0),
% 2.06/2.45 'class_Divides_Oring__div' [96, 1] (w:1, o:106, a:1, s:1, b:0),
% 2.06/2.45 'c_Groebner__Basis_Ogb__semiring' [102, 6] (w:1, o:205, a:1, s:1, b:0
% 2.06/2.45 ),
% 2.06/2.45 'class_Ring__and__Field_Osemiring__1' [108, 1] (w:1, o:120, a:1, s:1
% 2.06/2.45 , b:0),
% 2.06/2.45 'class_Ring__and__Field_Ocomm__ring__1' [109, 1] (w:1, o:121, a:1, s:
% 2.06/2.45 1, b:0),
% 2.06/2.45 'c_Fun_Oinj__on' [112, 4] (w:1, o:201, a:1, s:1, b:0),
% 2.06/2.45 'c_Suc' [113, 0] (w:1, o:61, a:1, s:1, b:0),
% 2.06/2.45 'c_COMBB' [115, 5] (w:1, o:202, a:1, s:1, b:0),
% 2.06/2.45 'class_Int_Onumber' [116, 1] (w:1, o:122, a:1, s:1, b:0),
% 2.06/2.45 'c_Int_Onumber__class_Onumber__of' [118, 2] (w:1, o:187, a:1, s:1, b:
% 2.06/2.45 0),
% 2.06/2.45 'class_Ring__and__Field_Oring' [120, 1] (w:1, o:115, a:1, s:1, b:0),
% 2.06/2.45
% 2.06/2.45 'class_Ring__and__Field_Oidom' [122, 1] (w:1, o:123, a:1, s:1, b:0),
% 2.06/2.45
% 2.06/2.45 'class_RealVector_Oreal__normed__algebra' [123, 1] (w:1, o:124, a:1
% 2.06/2.45 , s:1, b:0),
% 2.06/2.45 'class_OrderedGroup_Oab__group__add' [125, 1] (w:1, o:125, a:1, s:1
% 2.06/2.45 , b:0),
% 2.06/2.45 'class_OrderedGroup_Opordered__ab__semigroup__add' [126, 1] (w:1, o:
% 2.06/2.45 126, a:1, s:1, b:0),
% 2.06/2.45 'class_Int_Onumber__ring' [127, 1] (w:1, o:127, a:1, s:1, b:0),
% 2.06/2.45 'c_Int_OMin' [128, 0] (w:1, o:62, a:1, s:1, b:0),
% 2.06/2.45 'class_OrderedGroup_Omonoid__mult' [129, 1] (w:1, o:128, a:1, s:1, b:
% 2.06/2.45 0),
% 2.06/2.45 'class_Ring__and__Field_Oordered__field' [132, 1] (w:1, o:129, a:1
% 2.06/2.45 , s:1, b:0),
% 2.06/2.45 'c_HOL_Oinverse__class_Odivide' [133, 1] (w:1, o:130, a:1, s:1, b:0)
% 2.06/2.45 ,
% 2.06/2.45 'class_Ring__and__Field_Odivision__by__zero' [134, 1] (w:1, o:135, a:
% 2.06/2.45 1, s:1, b:0),
% 2.06/2.45 'class_Ring__and__Field_Ofield' [137, 1] (w:1, o:136, a:1, s:1, b:0)
% 2.06/2.45 ,
% 2.06/2.45 'c_Int_OPls' [141, 0] (w:1, o:65, a:1, s:1, b:0),
% 2.06/2.45 'c_Int_OBit1' [142, 1] (w:1, o:138, a:1, s:1, b:0),
% 2.06/2.45 'c_Int_OBit0' [143, 1] (w:1, o:137, a:1, s:1, b:0),
% 2.06/2.45 'class_Ring__and__Field_Oordered__comm__semiring__strict' [144, 1]
% 2.06/2.45 (w:1, o:139, a:1, s:1, b:0),
% 2.06/2.45 'class_Ring__and__Field_Omult__mono1' [145, 1] (w:1, o:140, a:1, s:1
% 2.06/2.45 , b:0),
% 2.06/2.45 'class_Ring__and__Field_Omult__mono' [146, 1] (w:1, o:141, a:1, s:1
% 2.06/2.45 , b:0),
% 2.06/2.45 'class_Ring__and__Field_Opordered__ring' [147, 1] (w:1, o:142, a:1
% 2.06/2.45 , s:1, b:0),
% 2.06/2.45 'class_Ring__and__Field_Opordered__cancel__semiring' [148, 1] (w:1
% 2.06/2.45 , o:143, a:1, s:1, b:0),
% 2.06/2.45 'class_Ring__and__Field_Opordered__semiring' [149, 1] (w:1, o:144, a:
% 2.06/2.45 1, s:1, b:0),
% 2.06/2.45 'tc_fun' [150, 2] (w:1, o:188, a:1, s:1, b:0),
% 2.06/2.45 'class_Ring__and__Field_Ocomm__semiring__1' [152, 1] (w:1, o:133, a:1
% 2.06/2.45 , s:1, b:0),
% 2.06/2.45 'c_COMBS' [157, 5] (w:1, o:204, a:1, s:1, b:0),
% 2.06/2.45 'c_Complex_Oii' [158, 0] (w:1, o:67, a:1, s:1, b:0),
% 2.06/2.45 'tc_Complex_Ocomplex' [159, 0] (w:1, o:68, a:1, s:1, b:0),
% 11.78/12.20 'c_FFT__Mirabelle_Oroot' [160, 1] (w:1, o:145, a:1, s:1, b:0),
% 11.78/12.20 'c_Finite__Set_Osetsum' [162, 3] (w:1, o:196, a:1, s:1, b:0),
% 11.78/12.20 'v_m' [165, 0] (w:1, o:70, a:1, s:1, b:0),
% 11.78/12.20 'c_SetInterval_Oord__class_OatLeastLessThan' [166, 2] (w:1, o:189, a:
% 11.78/12.20 1, s:1, b:0),
% 11.78/12.20 'class_Ring__and__Field_Oring__1' [167, 1] (w:1, o:116, a:1, s:1, b:0
% 11.78/12.20 ),
% 11.78/12.20 'class_Power_Opower' [168, 1] (w:1, o:153, a:1, s:1, b:0),
% 11.78/12.20 'class_Ring__and__Field_Osemiring__0' [169, 1] (w:1, o:119, a:1, s:1
% 11.78/12.20 , b:0),
% 11.78/12.20 'c_FFT__Mirabelle_ODFT' [170, 3] (w:1, o:197, a:1, s:1, b:0),
% 11.78/12.20 'c_FFT__Mirabelle_OIDFT' [171, 3] (w:1, o:198, a:1, s:1, b:0),
% 11.78/12.20 'class_RealVector_Oreal__normed__algebra__1' [172, 1] (w:1, o:154, a:
% 11.78/12.20 1, s:1, b:0),
% 11.78/12.20 'c_Series_Osuminf' [173, 2] (w:1, o:190, a:1, s:1, b:0),
% 11.78/12.20 'tc_bool' [175, 0] (w:1, o:71, a:1, s:1, b:0),
% 11.78/12.20 'v_a' [176, 0] (w:1, o:72, a:1, s:1, b:0),
% 11.78/12.20 'v_i' [177, 0] (w:1, o:73, a:1, s:1, b:0),
% 11.78/12.20 'class_Ring__and__Field_Ocomm__ring' [178, 1] (w:1, o:131, a:1, s:1
% 11.78/12.20 , b:0),
% 11.78/12.20 'class_Ring__and__Field_Ocomm__semiring' [180, 1] (w:1, o:134, a:1
% 11.78/12.20 , s:1, b:0),
% 11.78/12.20 'class_OrderedGroup_Ocancel__ab__semigroup__add' [181, 1] (w:1, o:146
% 11.78/12.20 , a:1, s:1, b:0),
% 11.78/12.20 'class_OrderedGroup_Ocancel__semigroup__add' [182, 1] (w:1, o:147, a:
% 11.78/12.20 1, s:1, b:0),
% 11.78/12.20 'class_Ring__and__Field_Ozero__neq__one' [183, 1] (w:1, o:155, a:1
% 11.78/12.20 , s:1, b:0),
% 11.78/12.20 'class_OrderedGroup_Oab__semigroup__mult' [184, 1] (w:1, o:148, a:1
% 11.78/12.20 , s:1, b:0),
% 11.78/12.20 'class_OrderedGroup_Ocomm__monoid__mult' [185, 1] (w:1, o:149, a:1
% 11.78/12.20 , s:1, b:0),
% 11.78/12.20 'class_OrderedGroup_Oab__semigroup__idem__mult' [186, 1] (w:1, o:150
% 11.78/12.20 , a:1, s:1, b:0),
% 11.78/12.20 'class_Ring__and__Field_Ono__zero__divisors' [187, 1] (w:1, o:85, a:1
% 11.78/12.20 , s:1, b:0),
% 11.78/12.20 'class_Ring__and__Field_Omult__zero' [188, 1] (w:1, o:84, a:1, s:1
% 11.78/12.20 , b:0),
% 11.78/12.20 'class_Ring__and__Field_Oring__1__no__zero__divisors' [189, 1] (w:1
% 11.78/12.20 , o:117, a:1, s:1, b:0),
% 11.78/12.20 'class_Ring__and__Field_Oring__no__zero__divisors' [190, 1] (w:1, o:
% 11.78/12.20 118, a:1, s:1, b:0),
% 11.78/12.20 'class_Ring__and__Field_Ocomm__semiring__0' [192, 1] (w:1, o:132, a:1
% 11.78/12.20 , s:1, b:0),
% 11.78/12.20 'class_RealVector_Oreal__field' [194, 1] (w:1, o:156, a:1, s:1, b:0)
% 11.78/12.20 ,
% 11.78/12.20 'class_Ring__and__Field_Osemiring' [196, 1] (w:1, o:157, a:1, s:1, b:
% 11.78/12.20 0),
% 11.78/12.20 'class_OrderedGroup_Oab__semigroup__add' [197, 1] (w:1, o:151, a:1
% 11.78/12.20 , s:1, b:0),
% 11.78/12.20 'class_Int_Oring__char__0' [198, 1] (w:1, o:158, a:1, s:1, b:0),
% 11.78/12.20 'class_OrderedGroup_Omonoid__add' [199, 1] (w:1, o:152, a:1, s:1, b:0
% 11.78/12.20 ),
% 11.78/12.20 'tc_Int_Oint' [202, 0] (w:1, o:76, a:1, s:1, b:0),
% 11.78/12.20 'c_fequal' [203, 3] (w:1, o:199, a:1, s:1, b:0).
% 11.78/12.20
% 11.78/12.20
% 11.78/12.20 Starting Search:
% 11.78/12.20
% 11.78/12.20 Resimplifying inuse:
% 11.78/12.20 Done
% 11.78/12.20
% 11.78/12.20
% 11.78/12.20 Intermediate Status:
% 11.78/12.20 Generated: 4349
% 11.78/12.20 Kept: 2002
% 11.78/12.20 Inuse: 74
% 11.78/12.20 Deleted: 1
% 11.78/12.20 Deletedinuse: 0
% 11.78/12.20
% 11.78/12.20 Resimplifying inuse:
% 11.78/12.20 Done
% 11.78/12.20
% 11.78/12.20 Resimplifying inuse:
% 11.78/12.20 Done
% 11.78/12.20
% 11.78/12.20
% 11.78/12.20 Intermediate Status:
% 11.78/12.20 Generated: 11575
% 11.78/12.20 Kept: 4155
% 11.78/12.20 Inuse: 213
% 11.78/12.20 Deleted: 4
% 11.78/12.20 Deletedinuse: 1
% 11.78/12.20
% 11.78/12.20 Resimplifying inuse:
% 11.78/12.20 Done
% 11.78/12.20
% 11.78/12.20 Resimplifying inuse:
% 11.78/12.20 Done
% 11.78/12.20
% 11.78/12.20
% 11.78/12.20 Intermediate Status:
% 11.78/12.20 Generated: 19488
% 11.78/12.20 Kept: 6160
% 11.78/12.20 Inuse: 289
% 11.78/12.20 Deleted: 4
% 11.78/12.20 Deletedinuse: 1
% 11.78/12.20
% 11.78/12.20 Resimplifying inuse:
% 11.78/12.20 Done
% 11.78/12.20
% 11.78/12.20 Resimplifying inuse:
% 11.78/12.20 Done
% 11.78/12.20
% 11.78/12.20
% 11.78/12.20 Intermediate Status:
% 11.78/12.20 Generated: 28716
% 11.78/12.20 Kept: 9232
% 11.78/12.20 Inuse: 373
% 11.78/12.20 Deleted: 4
% 11.78/12.20 Deletedinuse: 1
% 11.78/12.20
% 11.78/12.20 Resimplifying inuse:
% 11.78/12.20 Done
% 11.78/12.20
% 11.78/12.20 Resimplifying inuse:
% 11.78/12.20 Done
% 11.78/12.20
% 11.78/12.20
% 11.78/12.20 Intermediate Status:
% 11.78/12.20 Generated: 34006
% 11.78/12.20 Kept: 11309
% 11.78/12.20 Inuse: 398
% 11.78/12.20 Deleted: 4
% 11.78/12.20 Deletedinuse: 1
% 11.78/12.20
% 11.78/12.20 Resimplifying inuse:
% 11.78/12.20 Done
% 11.78/12.20
% 11.78/12.20 Resimplifying inuse:
% 11.78/12.20 Done
% 11.78/12.20
% 11.78/12.20
% 11.78/12.20 Intermediate Status:
% 11.78/12.20 Generated: 37876
% 11.78/12.20 Kept: 13325
% 11.78/12.20 Inuse: 411
% 11.78/12.20 Deleted: 4
% 11.78/12.20 Deletedinuse: 1
% 11.78/12.20
% 11.78/12.20 Resimplifying inuse:
% 11.78/12.20 Done
% 11.78/12.20
% 11.78/12.20
% 11.78/12.20 Intermediate Status:
% 11.78/12.20 Generated: 44239
% 11.78/12.20 Kept: 15503
% 11.78/12.20 Inuse: 471
% 11.78/12.20 Deleted: 6
% 11.78/12.20 Deletedinuse: 1
% 11.78/12.20
% 11.78/12.20 Resimplifying inuse:
% 11.78/12.20 Done
% 11.78/12.20
% 11.78/12.20 Resimplifying inuse:
% 11.78/12.20 Done
% 11.78/12.20
% 11.78/12.20
% 11.78/12.20 Intermediate Status:
% 11.78/12.20 Generated: 51008
% 11.78/12.20 Kept: 17503
% 11.78/12.20 Inuse: 519
% 11.78/12.20 Deleted: 6
% 11.78/12.20 Deletedinuse: 1
% 11.78/12.20
% 11.78/12.20 Resimplifying inuse:
% 11.78/12.20 Done
% 11.78/12.20
% 11.78/12.20 Resimplifying inuse:
% 11.78/12.20 Done
% 11.78/12.20
% 11.78/12.20
% 11.78/12.20 Intermediate Status:
% 11.78/12.20 Generated: 57769
% 34.93/35.36 Kept: 19679
% 34.93/35.36 Inuse: 611
% 34.93/35.36 Deleted: 6
% 34.93/35.36 Deletedinuse: 1
% 34.93/35.36
% 34.93/35.36 Resimplifying inuse:
% 34.93/35.36 Done
% 34.93/35.36
% 34.93/35.36 Resimplifying clauses:
% 34.93/35.36 Done
% 34.93/35.36
% 34.93/35.36 Resimplifying inuse:
% 34.93/35.36 Done
% 34.93/35.36
% 34.93/35.36
% 34.93/35.36 Intermediate Status:
% 34.93/35.36 Generated: 63994
% 34.93/35.36 Kept: 21727
% 34.93/35.36 Inuse: 686
% 34.93/35.36 Deleted: 450
% 34.93/35.36 Deletedinuse: 1
% 34.93/35.36
% 34.93/35.36 Resimplifying inuse:
% 34.93/35.36 Done
% 34.93/35.36
% 34.93/35.36 Resimplifying inuse:
% 34.93/35.36 Done
% 34.93/35.36
% 34.93/35.36
% 34.93/35.36 Intermediate Status:
% 34.93/35.36 Generated: 70642
% 34.93/35.36 Kept: 23767
% 34.93/35.36 Inuse: 746
% 34.93/35.36 Deleted: 450
% 34.93/35.36 Deletedinuse: 1
% 34.93/35.36
% 34.93/35.36 Resimplifying inuse:
% 34.93/35.36 Done
% 34.93/35.36
% 34.93/35.36
% 34.93/35.36 Intermediate Status:
% 34.93/35.36 Generated: 83773
% 34.93/35.36 Kept: 26233
% 34.93/35.36 Inuse: 771
% 34.93/35.36 Deleted: 450
% 34.93/35.36 Deletedinuse: 1
% 34.93/35.36
% 34.93/35.36 Resimplifying inuse:
% 34.93/35.36 Done
% 34.93/35.36
% 34.93/35.36 Resimplifying inuse:
% 34.93/35.36 Done
% 34.93/35.36
% 34.93/35.36
% 34.93/35.36 Intermediate Status:
% 34.93/35.36 Generated: 91928
% 34.93/35.36 Kept: 28346
% 34.93/35.36 Inuse: 816
% 34.93/35.36 Deleted: 450
% 34.93/35.36 Deletedinuse: 1
% 34.93/35.36
% 34.93/35.36 Resimplifying inuse:
% 34.93/35.36 Done
% 34.93/35.36
% 34.93/35.36 Resimplifying inuse:
% 34.93/35.36 Done
% 34.93/35.36
% 34.93/35.36
% 34.93/35.36 Intermediate Status:
% 34.93/35.36 Generated: 96296
% 34.93/35.36 Kept: 30348
% 34.93/35.36 Inuse: 830
% 34.93/35.36 Deleted: 450
% 34.93/35.36 Deletedinuse: 1
% 34.93/35.36
% 34.93/35.36 Resimplifying inuse:
% 34.93/35.36 Done
% 34.93/35.36
% 34.93/35.36 Resimplifying inuse:
% 34.93/35.36 Done
% 34.93/35.36
% 34.93/35.36
% 34.93/35.36 Intermediate Status:
% 34.93/35.36 Generated: 103166
% 34.93/35.36 Kept: 32370
% 34.93/35.36 Inuse: 859
% 34.93/35.36 Deleted: 450
% 34.93/35.36 Deletedinuse: 1
% 34.93/35.36
% 34.93/35.36 Resimplifying inuse:
% 34.93/35.36 Done
% 34.93/35.36
% 34.93/35.36
% 34.93/35.36 Intermediate Status:
% 34.93/35.36 Generated: 109793
% 34.93/35.36 Kept: 34482
% 34.93/35.36 Inuse: 896
% 34.93/35.36 Deleted: 450
% 34.93/35.36 Deletedinuse: 1
% 34.93/35.36
% 34.93/35.36 Resimplifying inuse:
% 34.93/35.36 Done
% 34.93/35.36
% 34.93/35.36 Resimplifying inuse:
% 34.93/35.36 Done
% 34.93/35.36
% 34.93/35.36
% 34.93/35.36 Intermediate Status:
% 34.93/35.36 Generated: 116702
% 34.93/35.36 Kept: 36914
% 34.93/35.36 Inuse: 921
% 34.93/35.36 Deleted: 450
% 34.93/35.36 Deletedinuse: 1
% 34.93/35.36
% 34.93/35.36 Resimplifying inuse:
% 34.93/35.36 Done
% 34.93/35.36
% 34.93/35.36 Resimplifying inuse:
% 34.93/35.36 Done
% 34.93/35.36
% 34.93/35.36
% 34.93/35.36 Intermediate Status:
% 34.93/35.36 Generated: 123555
% 34.93/35.36 Kept: 39222
% 34.93/35.36 Inuse: 946
% 34.93/35.36 Deleted: 450
% 34.93/35.36 Deletedinuse: 1
% 34.93/35.36
% 34.93/35.36 Resimplifying inuse:
% 34.93/35.36 Done
% 34.93/35.36
% 34.93/35.36 Resimplifying inuse:
% 34.93/35.36 Done
% 34.93/35.36
% 34.93/35.36 Resimplifying clauses:
% 34.93/35.36 Done
% 34.93/35.36
% 34.93/35.36
% 34.93/35.36 Intermediate Status:
% 34.93/35.36 Generated: 130144
% 34.93/35.36 Kept: 41460
% 34.93/35.36 Inuse: 966
% 34.93/35.36 Deleted: 695
% 34.93/35.36 Deletedinuse: 1
% 34.93/35.36
% 34.93/35.36 Resimplifying inuse:
% 34.93/35.36 Done
% 34.93/35.36
% 34.93/35.36 Resimplifying inuse:
% 34.93/35.36 Done
% 34.93/35.36
% 34.93/35.36
% 34.93/35.36 Intermediate Status:
% 34.93/35.36 Generated: 137724
% 34.93/35.36 Kept: 43546
% 34.93/35.36 Inuse: 1001
% 34.93/35.36 Deleted: 697
% 34.93/35.36 Deletedinuse: 3
% 34.93/35.36
% 34.93/35.36 Resimplifying inuse:
% 34.93/35.36 Done
% 34.93/35.36
% 34.93/35.36 Resimplifying inuse:
% 34.93/35.36 Done
% 34.93/35.36
% 34.93/35.36
% 34.93/35.36 Intermediate Status:
% 34.93/35.36 Generated: 147049
% 34.93/35.36 Kept: 45641
% 34.93/35.36 Inuse: 1031
% 34.93/35.36 Deleted: 697
% 34.93/35.36 Deletedinuse: 3
% 34.93/35.36
% 34.93/35.36 Resimplifying inuse:
% 34.93/35.36 Done
% 34.93/35.36
% 34.93/35.36 Resimplifying inuse:
% 34.93/35.36 Done
% 34.93/35.36
% 34.93/35.36
% 34.93/35.36 Intermediate Status:
% 34.93/35.36 Generated: 156409
% 34.93/35.36 Kept: 47730
% 34.93/35.36 Inuse: 1061
% 34.93/35.36 Deleted: 697
% 34.93/35.36 Deletedinuse: 3
% 34.93/35.36
% 34.93/35.36 Resimplifying inuse:
% 34.93/35.36 Done
% 34.93/35.36
% 34.93/35.36 Resimplifying inuse:
% 34.93/35.36 Done
% 34.93/35.36
% 34.93/35.36
% 34.93/35.36 Intermediate Status:
% 34.93/35.36 Generated: 166874
% 34.93/35.36 Kept: 49953
% 34.93/35.36 Inuse: 1111
% 34.93/35.36 Deleted: 697
% 34.93/35.36 Deletedinuse: 3
% 34.93/35.36
% 34.93/35.36 Resimplifying inuse:
% 34.93/35.36 Done
% 34.93/35.36
% 34.93/35.36 Resimplifying inuse:
% 34.93/35.36 Done
% 34.93/35.36
% 34.93/35.36
% 34.93/35.36 Intermediate Status:
% 34.93/35.36 Generated: 177893
% 34.93/35.36 Kept: 52720
% 34.93/35.36 Inuse: 1136
% 34.93/35.36 Deleted: 697
% 34.93/35.36 Deletedinuse: 3
% 34.93/35.36
% 34.93/35.36 Resimplifying inuse:
% 34.93/35.36 Done
% 34.93/35.36
% 34.93/35.36 Resimplifying inuse:
% 34.93/35.36 Done
% 34.93/35.36
% 34.93/35.36
% 34.93/35.36 Intermediate Status:
% 34.93/35.36 Generated: 185872
% 34.93/35.36 Kept: 54845
% 34.93/35.36 Inuse: 1151
% 34.93/35.36 Deleted: 699
% 34.93/35.36 Deletedinuse: 5
% 34.93/35.36
% 34.93/35.36 Resimplifying inuse:
% 34.93/35.36 Done
% 34.93/35.36
% 34.93/35.36 Resimplifying inuse:
% 34.93/35.36 Done
% 34.93/35.36
% 34.93/35.36
% 34.93/35.36 Intermediate Status:
% 34.93/35.36 Generated: 194013
% 34.93/35.36 Kept: 56856
% 34.93/35.36 Inuse: 1180
% 34.93/35.36 Deleted: 699
% 34.93/35.36 Deletedinuse: 5
% 34.93/35.36
% 34.93/35.36 Resimplifying inuse:
% 34.93/35.36 Done
% 34.93/35.36
% 34.93/35.36 Resimplifying inuse:
% 34.93/35.36 Done
% 34.93/35.36
% 34.93/35.36
% 34.93/35.36 Intermediate Status:
% 34.93/35.36 Generated: 201783
% 34.93/35.36 Kept: 58865
% 34.93/35.36 Inuse: 1206
% 34.93/35.36 Deleted: 699
% 34.93/35.36 Deletedinuse: 5
% 34.93/35.36
% 34.93/35.36 Resimplifying inuse:
% 34.93/35.36 Done
% 34.93/35.36
% 34.93/35.36
% 34.93/35.36 Intermediate Status:
% 34.93/35.36 Generated: 211874
% 34.93/35.36 Kept: 61527
% 34.93/35.36 Inuse: 1216
% 34.93/35.36 Deleted: 699
% 34.93/35.36 Deletedinuse: 5
% 34.93/35.36
% 34.93/35.36 Resimplifying inuse:
% 34.93/35.36 Done
% 34.93/35.36
% 34.93/35.36 Resimplifying clauses:
% 34.93/35.36 Done
% 34.93/35.36
% 34.93/35.36 Resimplifying inuse:
% 34.93/35.36 Done
% 34.93/35.36
% 34.93/35.36
% 34.93/35.36 Intermediate Status:
% 34.93/35.36 Generated: 222272
% 34.93/35.36 Kept: 63857
% 34.93/35.36 Inuse: 1251
% 34.93/35.36 Deleted: 2869
% 34.93/35.36 Deletedinuse: 6
% 34.93/35.36
% 34.93/35.36 Resimplifying inuse:
% 34.93/35.36 Done
% 34.93/35.36
% 34.93/35.36 Resimplifying inuse:
% 34.93/35.36 Done
% 34.93/35.36
% 34.93/35.36
% 34.93/35.36 Intermediate Status:
% 34.93/35.36 Generated: 231521
% 34.93/35.36 Kept: 66087
% 34.93/35.36 Inuse: 1281
% 34.93/35.36 Deleted: 2869
% 34.93/35.36 Deletedinuse: 6
% 34.93/35.36
% 34.93/35.36 Resimplifying inuse:
% 34.93/35.36 Done
% 34.93/35.36
% 34.93/35.36 Resimplifying inuse:
% 34.93/35.36 Done
% 34.93/35.36
% 34.93/35.36
% 34.93/35.36 Intermediate Status:
% 34.93/35.36 Generated: 240764
% 34.93/35.36 Kept: 68183
% 34.93/35.36 Inuse: 1316
% 34.93/35.36 Deleted: 2869
% 34.93/35.36 Deletedinuse: 6
% 34.93/35.36
% 34.93/35.36 Resimplifying inuse:
% 34.93/35.36 Done
% 34.93/35.36
% 34.93/35.36 Resimplifying inuse:
% 34.93/35.36 Done
% 34.93/35.36
% 34.93/35.36
% 34.93/35.36 Intermediate Status:
% 34.93/35.36 Generated: 255985
% 34.93/35.36 Kept: 70789
% 34.93/35.36 Inuse: 1335
% 34.93/35.36 Deleted: 2873
% 34.93/35.36 Deletedinuse: 9
% 34.93/35.36
% 34.93/35.36 Resimplifying inuse:
% 34.93/35.36 Done
% 34.93/35.36
% 34.93/35.36 Resimplifying inuse:
% 34.93/35.36 Done
% 34.93/35.36
% 34.93/35.36
% 34.93/35.36 Intermediate Status:
% 34.93/35.36 Generated: 263883
% 79.62/80.05 Kept: 72791
% 79.62/80.05 Inuse: 1346
% 79.62/80.05 Deleted: 2873
% 79.62/80.05 Deletedinuse: 9
% 79.62/80.05
% 79.62/80.05 Resimplifying inuse:
% 79.62/80.05 Done
% 79.62/80.05
% 79.62/80.05
% 79.62/80.05 Intermediate Status:
% 79.62/80.05 Generated: 273149
% 79.62/80.05 Kept: 75786
% 79.62/80.05 Inuse: 1364
% 79.62/80.05 Deleted: 2873
% 79.62/80.05 Deletedinuse: 9
% 79.62/80.05
% 79.62/80.05 Resimplifying inuse:
% 79.62/80.05 Done
% 79.62/80.05
% 79.62/80.05 Resimplifying inuse:
% 79.62/80.05 Done
% 79.62/80.05
% 79.62/80.05
% 79.62/80.05 Intermediate Status:
% 79.62/80.05 Generated: 280433
% 79.62/80.05 Kept: 77800
% 79.62/80.05 Inuse: 1391
% 79.62/80.05 Deleted: 2873
% 79.62/80.05 Deletedinuse: 9
% 79.62/80.05
% 79.62/80.05 Resimplifying inuse:
% 79.62/80.05 Done
% 79.62/80.05
% 79.62/80.05 Resimplifying inuse:
% 79.62/80.05 Done
% 79.62/80.05
% 79.62/80.05
% 79.62/80.05 Intermediate Status:
% 79.62/80.05 Generated: 287123
% 79.62/80.05 Kept: 79827
% 79.62/80.05 Inuse: 1410
% 79.62/80.05 Deleted: 2873
% 79.62/80.05 Deletedinuse: 9
% 79.62/80.05
% 79.62/80.05 Resimplifying inuse:
% 79.62/80.05 Done
% 79.62/80.05
% 79.62/80.05 Resimplifying inuse:
% 79.62/80.05 Done
% 79.62/80.05
% 79.62/80.05
% 79.62/80.05 Intermediate Status:
% 79.62/80.05 Generated: 298227
% 79.62/80.05 Kept: 84699
% 79.62/80.05 Inuse: 1435
% 79.62/80.05 Deleted: 2873
% 79.62/80.05 Deletedinuse: 9
% 79.62/80.05
% 79.62/80.05 Resimplifying inuse:
% 79.62/80.05 Done
% 79.62/80.05
% 79.62/80.05 Resimplifying clauses:
% 79.62/80.05 Done
% 79.62/80.05
% 79.62/80.05 Resimplifying inuse:
% 79.62/80.05 Done
% 79.62/80.05
% 79.62/80.05
% 79.62/80.05 Intermediate Status:
% 79.62/80.05 Generated: 305989
% 79.62/80.05 Kept: 86841
% 79.62/80.05 Inuse: 1445
% 79.62/80.05 Deleted: 3427
% 79.62/80.05 Deletedinuse: 9
% 79.62/80.05
% 79.62/80.05 Resimplifying inuse:
% 79.62/80.05 Done
% 79.62/80.05
% 79.62/80.05 Resimplifying inuse:
% 79.62/80.05 Done
% 79.62/80.05
% 79.62/80.05
% 79.62/80.05 Intermediate Status:
% 79.62/80.05 Generated: 312399
% 79.62/80.05 Kept: 88937
% 79.62/80.05 Inuse: 1470
% 79.62/80.05 Deleted: 3427
% 79.62/80.05 Deletedinuse: 9
% 79.62/80.05
% 79.62/80.05
% 79.62/80.05 Intermediate Status:
% 79.62/80.05 Generated: 326470
% 79.62/80.05 Kept: 92530
% 79.62/80.05 Inuse: 1485
% 79.62/80.05 Deleted: 3427
% 79.62/80.05 Deletedinuse: 9
% 79.62/80.05
% 79.62/80.05 Resimplifying inuse:
% 79.62/80.05 Done
% 79.62/80.05
% 79.62/80.05 Resimplifying inuse:
% 79.62/80.05 Done
% 79.62/80.05
% 79.62/80.05
% 79.62/80.05 Intermediate Status:
% 79.62/80.05 Generated: 334041
% 79.62/80.05 Kept: 95109
% 79.62/80.05 Inuse: 1515
% 79.62/80.05 Deleted: 3429
% 79.62/80.05 Deletedinuse: 11
% 79.62/80.05
% 79.62/80.05 Resimplifying inuse:
% 79.62/80.05 Done
% 79.62/80.05
% 79.62/80.05 Resimplifying inuse:
% 79.62/80.05 Done
% 79.62/80.05
% 79.62/80.05
% 79.62/80.05 Intermediate Status:
% 79.62/80.05 Generated: 345527
% 79.62/80.05 Kept: 98070
% 79.62/80.05 Inuse: 1535
% 79.62/80.05 Deleted: 3429
% 79.62/80.05 Deletedinuse: 11
% 79.62/80.05
% 79.62/80.05 Resimplifying inuse:
% 79.62/80.05 Done
% 79.62/80.05
% 79.62/80.05 Resimplifying inuse:
% 79.62/80.05 Done
% 79.62/80.05
% 79.62/80.05
% 79.62/80.05 Intermediate Status:
% 79.62/80.05 Generated: 354474
% 79.62/80.05 Kept: 100133
% 79.62/80.05 Inuse: 1570
% 79.62/80.05 Deleted: 3429
% 79.62/80.05 Deletedinuse: 11
% 79.62/80.05
% 79.62/80.05 Resimplifying inuse:
% 79.62/80.05 Done
% 79.62/80.05
% 79.62/80.05 Resimplifying inuse:
% 79.62/80.05 Done
% 79.62/80.05
% 79.62/80.05
% 79.62/80.05 Intermediate Status:
% 79.62/80.05 Generated: 363018
% 79.62/80.05 Kept: 102144
% 79.62/80.05 Inuse: 1607
% 79.62/80.05 Deleted: 3430
% 79.62/80.05 Deletedinuse: 12
% 79.62/80.05
% 79.62/80.05 Resimplifying inuse:
% 79.62/80.05 Done
% 79.62/80.05
% 79.62/80.05 Resimplifying inuse:
% 79.62/80.05 Done
% 79.62/80.05
% 79.62/80.05
% 79.62/80.05 Intermediate Status:
% 79.62/80.05 Generated: 371604
% 79.62/80.05 Kept: 104276
% 79.62/80.05 Inuse: 1629
% 79.62/80.05 Deleted: 3432
% 79.62/80.05 Deletedinuse: 13
% 79.62/80.05
% 79.62/80.05 Resimplifying inuse:
% 79.62/80.05 Done
% 79.62/80.05
% 79.62/80.05 Resimplifying clauses:
% 79.62/80.05 Done
% 79.62/80.05
% 79.62/80.05 Resimplifying inuse:
% 79.62/80.05 Done
% 79.62/80.05
% 79.62/80.05
% 79.62/80.05 Intermediate Status:
% 79.62/80.05 Generated: 380643
% 79.62/80.05 Kept: 106303
% 79.62/80.05 Inuse: 1659
% 79.62/80.05 Deleted: 4232
% 79.62/80.05 Deletedinuse: 20
% 79.62/80.05
% 79.62/80.05 Resimplifying inuse:
% 79.62/80.05 Done
% 79.62/80.05
% 79.62/80.05
% 79.62/80.05 Intermediate Status:
% 79.62/80.05 Generated: 389339
% 79.62/80.05 Kept: 108677
% 79.62/80.05 Inuse: 1669
% 79.62/80.05 Deleted: 4232
% 79.62/80.05 Deletedinuse: 20
% 79.62/80.05
% 79.62/80.05 Resimplifying inuse:
% 79.62/80.05 Done
% 79.62/80.05
% 79.62/80.05 Resimplifying inuse:
% 79.62/80.05 Done
% 79.62/80.05
% 79.62/80.05
% 79.62/80.05 Intermediate Status:
% 79.62/80.05 Generated: 397531
% 79.62/80.05 Kept: 110899
% 79.62/80.05 Inuse: 1679
% 79.62/80.05 Deleted: 4232
% 79.62/80.05 Deletedinuse: 20
% 79.62/80.05
% 79.62/80.05 Resimplifying inuse:
% 79.62/80.05 Done
% 79.62/80.05
% 79.62/80.05 Resimplifying inuse:
% 79.62/80.05 Done
% 79.62/80.05
% 79.62/80.05
% 79.62/80.05 Intermediate Status:
% 79.62/80.05 Generated: 404740
% 79.62/80.05 Kept: 112911
% 79.62/80.05 Inuse: 1702
% 79.62/80.05 Deleted: 4232
% 79.62/80.05 Deletedinuse: 20
% 79.62/80.05
% 79.62/80.05
% 79.62/80.05 Intermediate Status:
% 79.62/80.05 Generated: 416204
% 79.62/80.05 Kept: 115107
% 79.62/80.05 Inuse: 1709
% 79.62/80.05 Deleted: 4232
% 79.62/80.05 Deletedinuse: 20
% 79.62/80.05
% 79.62/80.05 Resimplifying inuse:
% 79.62/80.05 Done
% 79.62/80.05
% 79.62/80.05 Resimplifying inuse:
% 79.62/80.05 Done
% 79.62/80.05
% 79.62/80.05
% 79.62/80.05 Intermediate Status:
% 79.62/80.05 Generated: 427984
% 79.62/80.05 Kept: 117343
% 79.62/80.05 Inuse: 1719
% 79.62/80.05 Deleted: 4232
% 79.62/80.05 Deletedinuse: 20
% 79.62/80.05
% 79.62/80.05 Resimplifying inuse:
% 79.62/80.05 Done
% 79.62/80.05
% 79.62/80.05 Resimplifying inuse:
% 79.62/80.05 Done
% 79.62/80.05
% 79.62/80.05
% 79.62/80.05 Intermediate Status:
% 79.62/80.05 Generated: 437780
% 79.62/80.05 Kept: 119354
% 79.62/80.05 Inuse: 1752
% 79.62/80.05 Deleted: 4232
% 79.62/80.05 Deletedinuse: 20
% 79.62/80.05
% 79.62/80.05 Resimplifying inuse:
% 79.62/80.05 Done
% 79.62/80.05
% 79.62/80.05
% 79.62/80.05 Intermediate Status:
% 79.62/80.05 Generated: 445438
% 79.62/80.05 Kept: 121434
% 79.62/80.05 Inuse: 1774
% 79.62/80.05 Deleted: 4232
% 79.62/80.05 Deletedinuse: 20
% 79.62/80.05
% 79.62/80.05 Resimplifying inuse:
% 79.62/80.05 Done
% 79.62/80.05
% 79.62/80.05
% 79.62/80.05 Intermediate Status:
% 79.62/80.05 Generated: 460689
% 79.62/80.05 Kept: 125055
% 79.62/80.05 Inuse: 1784
% 79.62/80.05 Deleted: 4232
% 79.62/80.05 Deletedinuse: 20
% 79.62/80.05
% 79.62/80.05 Resimplifying inuse:
% 79.62/80.05 Done
% 79.62/80.05
% 79.62/80.05 Resimplifying clauses:
% 79.62/80.05 Done
% 79.62/80.05
% 79.62/80.05 Resimplifying inuse:
% 79.62/80.05 Done
% 79.62/80.05
% 79.62/80.05
% 79.62/80.05 Intermediate Status:
% 79.62/80.05 Generated: 470535
% 79.62/80.05 Kept: 127262
% 79.62/80.05 Inuse: 1814
% 79.62/80.05 Deleted: 4763
% 79.62/80.05 Deletedinuse: 20
% 79.62/80.05
% 79.62/80.05 Resimplifying inuse:
% 79.62/80.05 Done
% 79.62/80.05
% 79.62/80.05 Resimplifying inuse:
% 79.62/80.05 Done
% 79.62/80.05
% 79.62/80.05
% 79.62/80.05 Intermediate Status:
% 79.62/80.05 Generated: 478998
% 79.62/80.05 Kept: 129543
% 79.62/80.05 Inuse: 1844
% 79.62/80.05 Deleted: 4763
% 79.62/80.05 Deletedinuse: 20
% 79.62/80.05
% 79.62/80.05 Resimplifying inuse:
% 79.62/80.05 Done
% 79.62/80.05
% 79.62/80.05
% 79.62/80.05 Intermediate Status:
% 79.62/80.05 Generated: 487187
% 79.62/80.05 Kept: 131570
% 79.62/80.05 Inuse: 1849
% 79.62/80.05 Deleted: 4763
% 79.62/80.05 Deletedinuse: 20
% 79.62/80.05
% 79.62/80.05 Resimplifying inuse:
% 153.34/153.77 Done
% 153.34/153.77
% 153.34/153.77 Resimplifying inuse:
% 153.34/153.77 Done
% 153.34/153.77
% 153.34/153.77
% 153.34/153.77 Intermediate Status:
% 153.34/153.77 Generated: 498038
% 153.34/153.77 Kept: 133768
% 153.34/153.77 Inuse: 1894
% 153.34/153.77 Deleted: 4763
% 153.34/153.77 Deletedinuse: 20
% 153.34/153.77
% 153.34/153.77 Resimplifying inuse:
% 153.34/153.77 Done
% 153.34/153.77
% 153.34/153.77 Resimplifying inuse:
% 153.34/153.77 Done
% 153.34/153.77
% 153.34/153.77
% 153.34/153.77 Intermediate Status:
% 153.34/153.77 Generated: 506452
% 153.34/153.77 Kept: 135771
% 153.34/153.77 Inuse: 1920
% 153.34/153.77 Deleted: 4763
% 153.34/153.77 Deletedinuse: 20
% 153.34/153.77
% 153.34/153.77 Resimplifying inuse:
% 153.34/153.77 Done
% 153.34/153.77
% 153.34/153.77
% 153.34/153.77 Intermediate Status:
% 153.34/153.77 Generated: 516559
% 153.34/153.77 Kept: 138201
% 153.34/153.77 Inuse: 1929
% 153.34/153.77 Deleted: 4763
% 153.34/153.77 Deletedinuse: 20
% 153.34/153.77
% 153.34/153.77 Resimplifying inuse:
% 153.34/153.77 Done
% 153.34/153.77
% 153.34/153.77 Resimplifying inuse:
% 153.34/153.77 Done
% 153.34/153.77
% 153.34/153.77
% 153.34/153.77 Intermediate Status:
% 153.34/153.77 Generated: 524622
% 153.34/153.77 Kept: 140487
% 153.34/153.77 Inuse: 1954
% 153.34/153.77 Deleted: 4763
% 153.34/153.77 Deletedinuse: 20
% 153.34/153.77
% 153.34/153.77 Resimplifying inuse:
% 153.34/153.77 Done
% 153.34/153.77
% 153.34/153.77 Resimplifying inuse:
% 153.34/153.77 Done
% 153.34/153.77
% 153.34/153.77
% 153.34/153.77 Intermediate Status:
% 153.34/153.77 Generated: 533699
% 153.34/153.77 Kept: 142606
% 153.34/153.77 Inuse: 1975
% 153.34/153.77 Deleted: 4763
% 153.34/153.77 Deletedinuse: 20
% 153.34/153.77
% 153.34/153.77 Resimplifying inuse:
% 153.34/153.77 Done
% 153.34/153.77
% 153.34/153.77 Resimplifying inuse:
% 153.34/153.77 Done
% 153.34/153.77
% 153.34/153.77
% 153.34/153.77 Intermediate Status:
% 153.34/153.77 Generated: 542050
% 153.34/153.77 Kept: 144920
% 153.34/153.77 Inuse: 1994
% 153.34/153.77 Deleted: 4763
% 153.34/153.77 Deletedinuse: 20
% 153.34/153.77
% 153.34/153.77 Resimplifying inuse:
% 153.34/153.77 Done
% 153.34/153.77
% 153.34/153.77 Resimplifying clauses:
% 153.34/153.77 Done
% 153.34/153.77
% 153.34/153.77 Resimplifying inuse:
% 153.34/153.77 Done
% 153.34/153.77
% 153.34/153.77
% 153.34/153.77 Intermediate Status:
% 153.34/153.77 Generated: 558787
% 153.34/153.77 Kept: 147139
% 153.34/153.77 Inuse: 2019
% 153.34/153.77 Deleted: 5054
% 153.34/153.77 Deletedinuse: 20
% 153.34/153.77
% 153.34/153.77 Resimplifying inuse:
% 153.34/153.77 Done
% 153.34/153.77
% 153.34/153.77 Resimplifying inuse:
% 153.34/153.77 Done
% 153.34/153.77
% 153.34/153.77
% 153.34/153.77 Intermediate Status:
% 153.34/153.77 Generated: 568217
% 153.34/153.77 Kept: 149545
% 153.34/153.77 Inuse: 2039
% 153.34/153.77 Deleted: 5054
% 153.34/153.77 Deletedinuse: 20
% 153.34/153.77
% 153.34/153.77 Resimplifying inuse:
% 153.34/153.77 Done
% 153.34/153.77
% 153.34/153.77 Resimplifying inuse:
% 153.34/153.77 Done
% 153.34/153.77
% 153.34/153.77
% 153.34/153.77 Intermediate Status:
% 153.34/153.77 Generated: 577686
% 153.34/153.77 Kept: 151569
% 153.34/153.77 Inuse: 2062
% 153.34/153.77 Deleted: 5054
% 153.34/153.77 Deletedinuse: 20
% 153.34/153.77
% 153.34/153.77 Resimplifying inuse:
% 153.34/153.77 Done
% 153.34/153.77
% 153.34/153.77 Resimplifying inuse:
% 153.34/153.77 Done
% 153.34/153.77
% 153.34/153.77
% 153.34/153.77 Intermediate Status:
% 153.34/153.77 Generated: 586451
% 153.34/153.77 Kept: 154081
% 153.34/153.77 Inuse: 2084
% 153.34/153.77 Deleted: 5054
% 153.34/153.77 Deletedinuse: 20
% 153.34/153.77
% 153.34/153.77 Resimplifying inuse:
% 153.34/153.77 Done
% 153.34/153.77
% 153.34/153.77 Resimplifying inuse:
% 153.34/153.77 Done
% 153.34/153.77
% 153.34/153.77
% 153.34/153.77 Intermediate Status:
% 153.34/153.77 Generated: 596012
% 153.34/153.77 Kept: 156285
% 153.34/153.77 Inuse: 2109
% 153.34/153.77 Deleted: 5054
% 153.34/153.77 Deletedinuse: 20
% 153.34/153.77
% 153.34/153.77 Resimplifying inuse:
% 153.34/153.77 Done
% 153.34/153.77
% 153.34/153.77
% 153.34/153.77 Intermediate Status:
% 153.34/153.77 Generated: 603390
% 153.34/153.77 Kept: 158932
% 153.34/153.77 Inuse: 2124
% 153.34/153.77 Deleted: 5054
% 153.34/153.77 Deletedinuse: 20
% 153.34/153.77
% 153.34/153.77 Resimplifying inuse:
% 153.34/153.77 Done
% 153.34/153.77
% 153.34/153.77 Resimplifying inuse:
% 153.34/153.77 Done
% 153.34/153.77
% 153.34/153.77
% 153.34/153.77 Intermediate Status:
% 153.34/153.77 Generated: 610447
% 153.34/153.77 Kept: 161230
% 153.34/153.77 Inuse: 2139
% 153.34/153.77 Deleted: 5054
% 153.34/153.77 Deletedinuse: 20
% 153.34/153.77
% 153.34/153.77 Resimplifying inuse:
% 153.34/153.77 Done
% 153.34/153.77
% 153.34/153.77
% 153.34/153.77 Intermediate Status:
% 153.34/153.77 Generated: 617977
% 153.34/153.77 Kept: 163598
% 153.34/153.77 Inuse: 2154
% 153.34/153.77 Deleted: 5054
% 153.34/153.77 Deletedinuse: 20
% 153.34/153.77
% 153.34/153.77 Resimplifying inuse:
% 153.34/153.77 Done
% 153.34/153.77
% 153.34/153.77 Resimplifying inuse:
% 153.34/153.77 Done
% 153.34/153.77
% 153.34/153.77 Resimplifying clauses:
% 153.34/153.77 Done
% 153.34/153.77
% 153.34/153.77
% 153.34/153.77 Intermediate Status:
% 153.34/153.77 Generated: 625859
% 153.34/153.77 Kept: 165797
% 153.34/153.77 Inuse: 2169
% 153.34/153.77 Deleted: 5595
% 153.34/153.77 Deletedinuse: 20
% 153.34/153.77
% 153.34/153.77 Resimplifying inuse:
% 153.34/153.77 Done
% 153.34/153.77
% 153.34/153.77
% 153.34/153.77 Intermediate Status:
% 153.34/153.77 Generated: 631807
% 153.34/153.77 Kept: 168001
% 153.34/153.77 Inuse: 2184
% 153.34/153.77 Deleted: 5595
% 153.34/153.77 Deletedinuse: 20
% 153.34/153.77
% 153.34/153.77 Resimplifying inuse:
% 153.34/153.77 Done
% 153.34/153.77
% 153.34/153.77 Resimplifying inuse:
% 153.34/153.77 Done
% 153.34/153.77
% 153.34/153.77
% 153.34/153.77 Intermediate Status:
% 153.34/153.77 Generated: 641777
% 153.34/153.77 Kept: 170500
% 153.34/153.77 Inuse: 2199
% 153.34/153.77 Deleted: 5595
% 153.34/153.77 Deletedinuse: 20
% 153.34/153.77
% 153.34/153.77
% 153.34/153.77 Intermediate Status:
% 153.34/153.77 Generated: 652528
% 153.34/153.77 Kept: 172852
% 153.34/153.77 Inuse: 2204
% 153.34/153.77 Deleted: 5595
% 153.34/153.77 Deletedinuse: 20
% 153.34/153.77
% 153.34/153.77 Resimplifying inuse:
% 153.34/153.77 Done
% 153.34/153.77
% 153.34/153.77
% 153.34/153.77 Intermediate Status:
% 153.34/153.77 Generated: 677965
% 153.34/153.77 Kept: 175343
% 153.34/153.77 Inuse: 2213
% 153.34/153.77 Deleted: 5597
% 153.34/153.77 Deletedinuse: 21
% 153.34/153.77
% 153.34/153.77 Resimplifying inuse:
% 153.34/153.77 Done
% 153.34/153.77
% 153.34/153.77
% 153.34/153.77 Intermediate Status:
% 153.34/153.77 Generated: 688733
% 153.34/153.77 Kept: 177905
% 153.34/153.77 Inuse: 2218
% 153.34/153.77 Deleted: 5598
% 153.34/153.77 Deletedinuse: 22
% 153.34/153.77
% 153.34/153.77 Resimplifying inuse:
% 153.34/153.77 Done
% 153.34/153.77
% 153.34/153.77
% 153.34/153.77 Intermediate Status:
% 153.34/153.77 Generated: 699635
% 153.34/153.77 Kept: 180463
% 153.34/153.77 Inuse: 2223
% 153.34/153.77 Deleted: 5598
% 153.34/153.77 Deletedinuse: 22
% 153.34/153.77
% 153.34/153.77 Resimplifying inuse:
% 153.34/153.77 Done
% 153.34/153.77
% 153.34/153.77 Resimplifying inuse:
% 153.34/153.77 Done
% 153.34/153.77
% 153.34/153.77
% 153.34/153.77 Intermediate Status:
% 153.34/153.77 Generated: 714624
% 153.34/153.77 Kept: 184456
% 153.34/153.77 Inuse: 2238
% 153.34/153.77 Deleted: 5598
% 153.34/153.77 Deletedinuse: 22
% 153.34/153.77
% 153.34/153.77 Resimplifying inuse:
% 153.34/153.77 Done
% 153.34/153.77
% 153.34/153.77
% 153.34/153.77 Intermediate Status:
% 153.34/153.77 Generated: 725959
% 153.34/153.77 Kept: 187183
% 153.34/153.77 Inuse: 2243
% 153.34/153.77 Deleted: 5598
% 153.34/153.77 Deletedinuse: 22
% 153.34/153.77
% 153.34/153.77 Resimplifying inuse:
% 153.34/153.77 Done
% 153.34/153.77
% 153.34/153.77 Resimplifying clauses:
% 153.34/153.77 Done
% 153.34/153.77
% 153.34/153.77
% 153.34/153.77 Intermediate Status:
% 153.34/153.77 Generated: 737527
% 153.34/153.77 Kept: 189995
% 153.34/153.77 Inuse: 2248
% 153.34/153.77 Deleted: 5879
% 153.34/153.77 Deletedinuse: 22
% 153.34/153.77
% 153.34/153.77 Resimplifying inuse:
% 153.34/153.77 Done
% 153.34/153.77
% 153.34/153.77
% 153.34/153.77 Intermediate Status:
% 153.34/153.77 Generated: 749100
% 153.34/153.77 Kept: 192818
% 153.34/153.77 Inuse: 2253
% 153.34/153.77 Deleted: 5879
% 153.34/153.77 Deletedinuse: 22
% 256.98/257.40
% 256.98/257.40 Resimplifying inuse:
% 256.98/257.40 Done
% 256.98/257.40
% 256.98/257.40 Resimplifying inuse:
% 256.98/257.40 Done
% 256.98/257.40
% 256.98/257.40
% 256.98/257.40 Intermediate Status:
% 256.98/257.40 Generated: 769762
% 256.98/257.40 Kept: 197521
% 256.98/257.40 Inuse: 2273
% 256.98/257.40 Deleted: 5879
% 256.98/257.40 Deletedinuse: 22
% 256.98/257.40
% 256.98/257.40 Resimplifying inuse:
% 256.98/257.40 Done
% 256.98/257.40
% 256.98/257.40
% 256.98/257.40 Intermediate Status:
% 256.98/257.40 Generated: 782526
% 256.98/257.40 Kept: 200298
% 256.98/257.40 Inuse: 2278
% 256.98/257.40 Deleted: 5879
% 256.98/257.40 Deletedinuse: 22
% 256.98/257.40
% 256.98/257.40 Resimplifying inuse:
% 256.98/257.40 Done
% 256.98/257.40
% 256.98/257.40 Resimplifying inuse:
% 256.98/257.40 Done
% 256.98/257.40
% 256.98/257.40
% 256.98/257.40 Intermediate Status:
% 256.98/257.40 Generated: 788791
% 256.98/257.40 Kept: 203034
% 256.98/257.40 Inuse: 2288
% 256.98/257.40 Deleted: 5879
% 256.98/257.40 Deletedinuse: 22
% 256.98/257.40
% 256.98/257.40 Resimplifying inuse:
% 256.98/257.40 Done
% 256.98/257.40
% 256.98/257.40 Resimplifying inuse:
% 256.98/257.40 Done
% 256.98/257.40
% 256.98/257.40
% 256.98/257.40 Intermediate Status:
% 256.98/257.40 Generated: 795038
% 256.98/257.40 Kept: 205754
% 256.98/257.40 Inuse: 2298
% 256.98/257.40 Deleted: 5879
% 256.98/257.40 Deletedinuse: 22
% 256.98/257.40
% 256.98/257.40 Resimplifying inuse:
% 256.98/257.40 Done
% 256.98/257.40
% 256.98/257.40 Resimplifying inuse:
% 256.98/257.40 Done
% 256.98/257.40
% 256.98/257.40
% 256.98/257.40 Intermediate Status:
% 256.98/257.40 Generated: 801219
% 256.98/257.40 Kept: 208387
% 256.98/257.40 Inuse: 2308
% 256.98/257.40 Deleted: 5879
% 256.98/257.40 Deletedinuse: 22
% 256.98/257.40
% 256.98/257.40 Resimplifying inuse:
% 256.98/257.40 Done
% 256.98/257.40
% 256.98/257.40 Resimplifying clauses:
% 256.98/257.40 Done
% 256.98/257.40
% 256.98/257.40 Resimplifying inuse:
% 256.98/257.40 Done
% 256.98/257.40
% 256.98/257.40
% 256.98/257.40 Intermediate Status:
% 256.98/257.40 Generated: 807384
% 256.98/257.40 Kept: 210944
% 256.98/257.40 Inuse: 2318
% 256.98/257.40 Deleted: 5930
% 256.98/257.40 Deletedinuse: 22
% 256.98/257.40
% 256.98/257.40 Resimplifying inuse:
% 256.98/257.40 Done
% 256.98/257.40
% 256.98/257.40 Resimplifying inuse:
% 256.98/257.40 Done
% 256.98/257.40
% 256.98/257.40
% 256.98/257.40 Intermediate Status:
% 256.98/257.40 Generated: 816146
% 256.98/257.40 Kept: 212944
% 256.98/257.40 Inuse: 2329
% 256.98/257.40 Deleted: 5930
% 256.98/257.40 Deletedinuse: 22
% 256.98/257.40
% 256.98/257.40 Resimplifying inuse:
% 256.98/257.40 Done
% 256.98/257.40
% 256.98/257.40 Resimplifying inuse:
% 256.98/257.40 Done
% 256.98/257.40
% 256.98/257.40
% 256.98/257.40 Intermediate Status:
% 256.98/257.40 Generated: 823256
% 256.98/257.40 Kept: 215377
% 256.98/257.40 Inuse: 2343
% 256.98/257.40 Deleted: 5930
% 256.98/257.40 Deletedinuse: 22
% 256.98/257.40
% 256.98/257.40 Resimplifying inuse:
% 256.98/257.40 Done
% 256.98/257.40
% 256.98/257.40
% 256.98/257.40 Intermediate Status:
% 256.98/257.40 Generated: 831768
% 256.98/257.40 Kept: 217952
% 256.98/257.40 Inuse: 2358
% 256.98/257.40 Deleted: 5930
% 256.98/257.40 Deletedinuse: 22
% 256.98/257.40
% 256.98/257.40 Resimplifying inuse:
% 256.98/257.40 Done
% 256.98/257.40
% 256.98/257.40 Resimplifying inuse:
% 256.98/257.40 Done
% 256.98/257.40
% 256.98/257.40
% 256.98/257.40 Intermediate Status:
% 256.98/257.40 Generated: 843002
% 256.98/257.40 Kept: 220275
% 256.98/257.40 Inuse: 2373
% 256.98/257.40 Deleted: 5930
% 256.98/257.40 Deletedinuse: 22
% 256.98/257.40
% 256.98/257.40 Resimplifying inuse:
% 256.98/257.40 Done
% 256.98/257.40
% 256.98/257.40
% 256.98/257.40 Intermediate Status:
% 256.98/257.40 Generated: 855937
% 256.98/257.40 Kept: 222574
% 256.98/257.40 Inuse: 2388
% 256.98/257.40 Deleted: 5930
% 256.98/257.40 Deletedinuse: 22
% 256.98/257.40
% 256.98/257.40 Resimplifying inuse:
% 256.98/257.40 Done
% 256.98/257.40
% 256.98/257.40 Resimplifying inuse:
% 256.98/257.40 Done
% 256.98/257.40
% 256.98/257.40
% 256.98/257.40 Intermediate Status:
% 256.98/257.40 Generated: 863549
% 256.98/257.40 Kept: 225231
% 256.98/257.40 Inuse: 2403
% 256.98/257.40 Deleted: 5930
% 256.98/257.40 Deletedinuse: 22
% 256.98/257.40
% 256.98/257.40 Resimplifying inuse:
% 256.98/257.40 Done
% 256.98/257.40
% 256.98/257.40 Resimplifying inuse:
% 256.98/257.40 Done
% 256.98/257.40
% 256.98/257.40
% 256.98/257.40 Intermediate Status:
% 256.98/257.40 Generated: 873262
% 256.98/257.40 Kept: 227299
% 256.98/257.40 Inuse: 2418
% 256.98/257.40 Deleted: 5930
% 256.98/257.40 Deletedinuse: 22
% 256.98/257.40
% 256.98/257.40 Resimplifying inuse:
% 256.98/257.40 Done
% 256.98/257.40
% 256.98/257.40 Resimplifying clauses:
% 256.98/257.40 Done
% 256.98/257.40
% 256.98/257.40
% 256.98/257.40 Intermediate Status:
% 256.98/257.40 Generated: 880764
% 256.98/257.40 Kept: 229466
% 256.98/257.40 Inuse: 2433
% 256.98/257.40 Deleted: 6271
% 256.98/257.40 Deletedinuse: 22
% 256.98/257.40
% 256.98/257.40 Resimplifying inuse:
% 256.98/257.40 Done
% 256.98/257.40
% 256.98/257.40 Resimplifying inuse:
% 256.98/257.40 Done
% 256.98/257.40
% 256.98/257.40
% 256.98/257.40 Intermediate Status:
% 256.98/257.40 Generated: 887798
% 256.98/257.40 Kept: 231517
% 256.98/257.40 Inuse: 2448
% 256.98/257.40 Deleted: 6271
% 256.98/257.40 Deletedinuse: 22
% 256.98/257.40
% 256.98/257.40 Resimplifying inuse:
% 256.98/257.40 Done
% 256.98/257.40
% 256.98/257.40 Resimplifying inuse:
% 256.98/257.40 Done
% 256.98/257.40
% 256.98/257.40
% 256.98/257.40 Intermediate Status:
% 256.98/257.40 Generated: 897012
% 256.98/257.40 Kept: 233968
% 256.98/257.40 Inuse: 2468
% 256.98/257.40 Deleted: 6271
% 256.98/257.40 Deletedinuse: 22
% 256.98/257.40
% 256.98/257.40 Resimplifying inuse:
% 256.98/257.40 Done
% 256.98/257.40
% 256.98/257.40 Resimplifying inuse:
% 256.98/257.40 Done
% 256.98/257.40
% 256.98/257.40
% 256.98/257.40 Intermediate Status:
% 256.98/257.40 Generated: 904829
% 256.98/257.40 Kept: 235978
% 256.98/257.40 Inuse: 2492
% 256.98/257.40 Deleted: 6271
% 256.98/257.40 Deletedinuse: 22
% 256.98/257.40
% 256.98/257.40
% 256.98/257.40 Intermediate Status:
% 256.98/257.40 Generated: 927659
% 256.98/257.40 Kept: 238620
% 256.98/257.40 Inuse: 2493
% 256.98/257.40 Deleted: 6271
% 256.98/257.40 Deletedinuse: 22
% 256.98/257.40
% 256.98/257.40 Resimplifying inuse:
% 256.98/257.40 Done
% 256.98/257.40
% 256.98/257.40 Resimplifying inuse:
% 256.98/257.40 Done
% 256.98/257.40
% 256.98/257.40
% 256.98/257.40 Intermediate Status:
% 256.98/257.40 Generated: 935196
% 256.98/257.40 Kept: 240624
% 256.98/257.40 Inuse: 2519
% 256.98/257.40 Deleted: 6271
% 256.98/257.40 Deletedinuse: 22
% 256.98/257.40
% 256.98/257.40 Resimplifying inuse:
% 256.98/257.40 Done
% 256.98/257.40
% 256.98/257.40
% 256.98/257.40 Intermediate Status:
% 256.98/257.40 Generated: 966236
% 256.98/257.40 Kept: 244732
% 256.98/257.40 Inuse: 2546
% 256.98/257.40 Deleted: 6273
% 256.98/257.40 Deletedinuse: 22
% 256.98/257.40
% 256.98/257.40 Resimplifying inuse:
% 256.98/257.40 Done
% 256.98/257.40
% 256.98/257.40
% 256.98/257.40 Intermediate Status:
% 256.98/257.40 Generated: 995993
% 256.98/257.40 Kept: 249926
% 256.98/257.40 Inuse: 2551
% 256.98/257.40 Deleted: 6276
% 256.98/257.40 Deletedinuse: 25
% 256.98/257.40
% 256.98/257.40 Resimplifying inuse:
% 256.98/257.40 Done
% 256.98/257.40
% 256.98/257.40 Resimplifying clauses:
% 256.98/257.40 Done
% 256.98/257.40
% 256.98/257.40 Resimplifying inuse:
% 256.98/257.40 Done
% 256.98/257.40
% 256.98/257.40
% 256.98/257.40 Intermediate Status:
% 256.98/257.40 Generated: 1003962
% 256.98/257.40 Kept: 251945
% 256.98/257.40 Inuse: 2576
% 256.98/257.40 Deleted: 6487
% 256.98/257.40 Deletedinuse: 25
% 256.98/257.40
% 256.98/257.40 Resimplifying inuse:
% 256.98/257.40 Done
% 256.98/257.40
% 256.98/257.40 Resimplifying inuse:
% 256.98/257.40 Done
% 256.98/257.40
% 256.98/257.40
% 256.98/257.40 Intermediate Status:
% 256.98/257.40 Generated: 1012602
% 256.98/257.40 Kept: 254087
% 256.98/257.40 Inuse: 2601
% 256.98/257.40 Deleted: 6489
% 256.98/257.40 Deletedinuse: 27
% 256.98/257.40
% 256.98/257.40 Resimplifying inuse:
% 256.98/257.40 Done
% 256.98/257.40
% 256.98/257.40 Resimplifying inuse:
% 256.98/257.40 Done
% 256.98/257.40
% 256.98/257.40
% 256.98/257.40 Intermediate Status:
% 256.98/257.40 Generated: 1021713
% 256.98/257.40 Kept: 256158
% 256.98/257.40 Inuse: 2621
% 256.98/257.40 Deleted: 6489
% 256.98/257.40 Deletedinuse: 27
% 256.98/257.40
% 256.98/257.40 Resimplifying inuse:
% 256.98/257.40 Done
% 256.98/257.40
% 256.98/257.40
% 256.98/257.40 Intermediate StatCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------