TSTP Solution File: SWV691-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV691-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n009.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 16:27:49 EDT 2022
% Result : Timeout 300.01s 300.37s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV691-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Wed Jun 15 16:55:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.19/1.56 *** allocated 10000 integers for termspace/termends
% 1.19/1.56 *** allocated 10000 integers for clauses
% 1.19/1.56 *** allocated 10000 integers for justifications
% 1.19/1.56 *** allocated 15000 integers for termspace/termends
% 1.19/1.56 *** allocated 22500 integers for termspace/termends
% 1.19/1.56 *** allocated 33750 integers for termspace/termends
% 1.19/1.56 Bliksem 1.12
% 1.19/1.56
% 1.19/1.56
% 1.19/1.56 Automatic Strategy Selection
% 1.19/1.56
% 1.19/1.56 Clauses:
% 1.19/1.56 [
% 1.19/1.56 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.19/1.56 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( 'c_Suc',
% 1.19/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ) ],
% 1.19/1.56 [ ~( 'class_RealVector_Ometric__space'( X ) ), 'c_SEQ_OLIMSEQ'(
% 1.19/1.56 'c_COMBB'( Y, 'c_Suc', 'tc_nat', X, 'tc_nat' ), Z, X ), ~(
% 1.19/1.56 'c_SEQ_OLIMSEQ'( Y, Z, X ) ) ],
% 1.19/1.56 [ ~( 'class_RealVector_Ometric__space'( X ) ), 'c_SEQ_OLIMSEQ'( Y, Z, X
% 1.19/1.56 ), ~( 'c_SEQ_OLIMSEQ'( 'c_COMBB'( Y, 'c_Suc', 'tc_nat', X, 'tc_nat' ), Z
% 1.19/1.56 , X ) ) ],
% 1.19/1.56 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.19/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP(
% 1.19/1.56 'c_HOL_Oinverse__class_Oinverse'( X ), hAPP(
% 1.19/1.56 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ), Y ) ],
% 1.19/1.56 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.19/1.56 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ) ) ],
% 1.19/1.56 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.19/1.56 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.19/1.56 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ), ~( hBOOL( hAPP(
% 1.19/1.56 'c_HOL_Oord__class_Oless'( T, X ), Z ) ) ) ],
% 1.19/1.56 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP(
% 1.19/1.56 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.19/1.56 'c_HOL_Oord__class_Oless'( T, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.56 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.19/1.56 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.19/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.19/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.19/1.56 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.19/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.19/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.19/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.56 'tc_nat' ), 'tc_nat' ), X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.19/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.19/1.56 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X )
% 1.19/1.56 ) ) ) ],
% 1.19/1.56 [ ~( =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( X, Y
% 1.19/1.56 ), hAPP( hAPP( Z, T ), W ) ) ) ), =( U, W ), =( T, V0 ), ~(
% 1.19/1.56 'c_Groebner__Basis_Osemiringb'( X, Z, V1, V0, V2, V3 ) ) ],
% 1.19/1.56 [ ~( =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, U ), W
% 1.19/1.56 ) ), hAPP( hAPP( X, hAPP( hAPP( Y, Z ), W ) ), hAPP( hAPP( Y, U ), T ) )
% 1.19/1.56 ) ), ~( 'c_Groebner__Basis_Osemiringb'( X, Y, V0, V1, V2, V3 ) ), =( T,
% 1.19/1.56 W ), =( Z, U ) ],
% 1.19/1.56 [ ~( =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, U ), W
% 1.19/1.56 ) ), hAPP( hAPP( X, hAPP( hAPP( Y, Z ), W ) ), hAPP( hAPP( Y, U ), T ) )
% 1.19/1.56 ) ), =( T, W ), =( Z, U ), ~( 'c_Groebner__Basis_Osemiringb'( X, Y, V0,
% 1.19/1.56 V1, V2, V3 ) ) ],
% 1.19/1.56 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.19/1.56 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~(
% 1.19/1.56 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.56 'tc_nat' ), 'tc_nat' ), X ) ) ), =( Y, Z ) ],
% 1.19/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.56 'tc_nat' ), 'tc_nat' ), X ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.56 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat'
% 1.19/1.56 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ) )
% 1.19/1.56 ],
% 1.19/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.56 'tc_nat' ), 'tc_nat' ), X ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.56 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), 'tc_nat'
% 1.19/1.56 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ) ) ) )
% 1.19/1.56 ],
% 1.19/1.56 [ =( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X
% 1.19/1.56 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.19/1.56 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.19/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ) ) ],
% 1.19/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.56 'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ],
% 1.19/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.56 'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ],
% 1.19/1.56 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.19/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ), T ) ), hAPP( hAPP(
% 1.19/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ), T ) ) ],
% 1.19/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.56 'tc_nat' ), 'tc_nat' ), X ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), hAPP( hAPP(
% 1.19/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ) ],
% 1.19/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.56 'tc_nat' ), 'tc_nat' ), X ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), hAPP( hAPP(
% 1.19/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ) ) ) ) ],
% 1.19/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.19/1.56 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.56 'tc_nat' ), hAPP( 'c_Suc', Z ) ), X ), 'tc_nat' ), hAPP( hAPP(
% 1.19/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', Z ) ), Y ) ) ) )
% 1.19/1.56 ],
% 1.19/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', X ) ), Y ),
% 1.19/1.56 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP(
% 1.19/1.56 'c_Suc', X ) ), Z ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y,
% 1.19/1.56 'tc_nat' ), Z ) ) ) ],
% 1.19/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), 'tc_nat' )
% 1.19/1.56 , Y ) ), =( hAPP( 'c_Suc', X ), Y ), ~( hBOOL( hAPP(
% 1.19/1.56 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ) ],
% 1.19/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.19/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.19/1.56 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.19/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) )
% 1.19/1.56 ],
% 1.19/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.19/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.19/1.56 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.19/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) )
% 1.19/1.56 ],
% 1.19/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ),
% 1.19/1.57 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.57 ), X ), hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ) ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 'tc_nat' ) ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.19/1.57 ,
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ) ), T ),
% 1.19/1.57 'tc_nat' ), U ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), T ), 'tc_nat' ),
% 1.19/1.57 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), U ) ) ) ), ~( hBOOL(
% 1.19/1.57 hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Y ), X ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), 'tc_nat' ),
% 1.19/1.57 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ) ), ~( hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.57 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP(
% 1.19/1.57 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), T ) ), Y ) ), Z ),
% 1.19/1.57 'tc_nat' ), U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), T
% 1.19/1.57 ), X ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ), T ) ), U ) ) ), ~(
% 1.19/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), X ), 'tc_nat' ),
% 1.19/1.57 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ), U ) ) ) ), ~( hBOOL(
% 1.19/1.57 hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Z ), Y ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), 'tc_nat' ),
% 1.19/1.57 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ) ), ~( hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), X ) ), Y ) ), U ) ) ) ),
% 1.19/1.57 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), T ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( 'c_Suc',
% 1.19/1.57 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( 'c_Suc',
% 1.19/1.57 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( 'c_Suc',
% 1.19/1.57 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.19/1.57 hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( 'c_Suc', X ) ), Y ) ) ) ]
% 1.19/1.57 ,
% 1.19/1.57 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( 'c_Suc', X ) ), Y
% 1.19/1.57 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ) ]
% 1.19/1.57 ,
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.19/1.57 hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( 'c_Suc', X ) ), Y ) ) ) ]
% 1.19/1.57 ,
% 1.19/1.57 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( 'c_Suc', X ) ), Y
% 1.19/1.57 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ) ]
% 1.19/1.57 ,
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Z ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.57 'tc_nat' ), X ), Z ), 'tc_nat' ), Y ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Z ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ) ],
% 1.19/1.57 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.19/1.57 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 1.19/1.57 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.19/1.57 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.19/1.57 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, hAPP(
% 1.19/1.57 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.19/1.57 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.57 'c_Finite__Set_Osetsum'( 'tc_nat', X ), Y ),
% 1.19/1.57 'c_SetInterval_Oord__class_OatLeastAtMost'( Z, hAPP( 'c_Suc', T ),
% 1.19/1.57 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.57 'c_Finite__Set_Osetsum'( 'tc_nat', X ), Y ),
% 1.19/1.57 'c_SetInterval_Oord__class_OatLeastAtMost'( Z, T, 'tc_nat' ) ) ), hAPP( Y
% 1.19/1.57 , hAPP( 'c_Suc', T ) ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.19/1.57 'c_Suc', T ), 'tc_nat' ), Z ) ) ],
% 1.19/1.57 [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 1.19/1.57 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.19/1.57 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 'tc_nat' ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.57 'tc_nat' ), X ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), Y ) ) ), ~( hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.19/1.57 'tc_nat' ), X ) ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.19/1.57 , X ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ),
% 1.19/1.57 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.19/1.57 'c_Suc', Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.19/1.57 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.19/1.57 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ), =( Z, Y ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), X ) ), =( Y, X ) ],
% 1.19/1.57 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ), =( Z, Y ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' ), Y ) ) ],
% 1.19/1.57 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =( Y, Z ), ~(
% 1.19/1.57 'c_Deriv_Oderiv'( T, U, Z, X ) ), ~( 'c_Deriv_Oderiv'( T, U, Y, X ) ) ]
% 1.19/1.57 ,
% 1.19/1.57 [ ~( 'class_RealVector_Ometric__space'( X ) ), =( Y, Z ), ~(
% 1.19/1.57 'c_SEQ_OLIMSEQ'( T, Z, X ) ), ~( 'c_SEQ_OLIMSEQ'( T, Y, X ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), X ) ), =( Y, X ) ],
% 1.19/1.57 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), =( Z, Y ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ],
% 1.19/1.57 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ],
% 1.19/1.57 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ), =( Z, Y ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), 'tc_nat' )
% 1.19/1.57 , Y ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' ), Y ) )
% 1.19/1.57 ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Z ) ) ) ]
% 1.19/1.57 ,
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( 'c_Suc',
% 1.19/1.57 X ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( 'c_Suc',
% 1.19/1.57 X ) ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ), hAPP( hAPP( Z, Y ),
% 1.19/1.57 hAPP( 'c_Suc', T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Z, W
% 1.19/1.57 , V0, V1 ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ), hAPP( hAPP( Y, Z ),
% 1.19/1.57 hAPP( 'c_Suc', T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Y, W
% 1.19/1.57 , V0, V1 ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', Z ) ), hAPP( hAPP( T, Y ), hAPP(
% 1.19/1.57 hAPP( X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W,
% 1.19/1.57 V0, V1 ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', Z ) ), hAPP( hAPP( T, Y ), hAPP(
% 1.19/1.57 hAPP( X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W,
% 1.19/1.57 V0, V1 ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.57 'tc_nat' ), X ), Z ), 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.57 'tc_nat' ), Z ), X ), 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.19/1.57 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y
% 1.19/1.57 ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.57 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.19/1.57 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ) ) ), =( Z, T ), =( Y
% 1.19/1.57 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( 'c_Suc',
% 1.19/1.57 Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) )
% 1.19/1.57 ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), 'tc_nat' ), Y ) ) )
% 1.19/1.57 ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Oinverse'( X ), Z ) ) ), =( Y, Z ) ],
% 1.19/1.57 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP(
% 1.19/1.57 'c_Suc', X ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.19/1.57 , hAPP( 'c_Suc', X ) ), Z ) ) ), =( Y, Z ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.19/1.57 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 1.19/1.57 , X ) ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ) ],
% 1.19/1.57 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.19/1.57 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.19/1.57 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.19/1.57 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 1.19/1.57 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, hAPP( 'c_Suc'
% 1.19/1.57 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.19/1.57 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 'tc_nat' ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 1.19/1.57 ), X ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), Y ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 'tc_nat' ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 1.19/1.57 ), X ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ) ) ],
% 1.19/1.57 [ ~( =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Y ), T ) ) ), ~(
% 1.19/1.57 'c_Groebner__Basis_Osemiringb'( X, U, W, V0, V1, V2 ) ), =( Z, T ) ],
% 1.19/1.57 [ ~( =( X, hAPP( hAPP( Y, X ), Z ) ) ), ~(
% 1.19/1.57 'c_Groebner__Basis_Osemiringb'( Y, T, U, W, V0, V1 ) ), =( Z, W ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), X ) ), hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ]
% 1.19/1.57 ,
% 1.19/1.57 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ), ~(
% 1.19/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), hAPP( 'c_Suc', X )
% 1.19/1.57 ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( 'c_Suc',
% 1.19/1.57 Y ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), X ) ) ]
% 1.19/1.57 ,
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ), ~(
% 1.19/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X
% 1.19/1.57 ), hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ) ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, U ), T ) )
% 1.19/1.57 , hAPP( hAPP( Y, hAPP( hAPP( X, Z ), U ) ), T ) ), ~(
% 1.19/1.57 'c_Groebner__Basis_Ogb__semiring'( X, Y, W, V0, V1, V2 ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ), hAPP( hAPP( Y, hAPP(
% 1.19/1.57 hAPP( X, Z ), U ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Y, W
% 1.19/1.57 , V0, U, V1 ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ), hAPP( hAPP( Z, hAPP(
% 1.19/1.57 hAPP( X, T ), U ) ), Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, W
% 1.19/1.57 , V0, U, V1 ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, hAPP( hAPP( X, T ), T ) ),
% 1.19/1.57 Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, U, W, T, V0 ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.19/1.57 X, T, U, Y, W, V0 ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.19/1.57 X, T, U, Z, W, V0 ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.19/1.57 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.19/1.57 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.19/1.57 'c_Groebner__Basis_Ogb__semiring'( Y, X, W, V0, V1, V2 ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.19/1.57 T, X, U, Y, W, V0 ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.19/1.57 T, X, U, Z, W, V0 ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.19/1.57 T, X, U, W, Y, V0 ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.19/1.57 T, X, U, W, Z, V0 ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.19/1.57 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.19/1.57 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.19/1.57 , hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), hAPP( hAPP( X, T ), U ) ) ) ),
% 1.19/1.57 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.19/1.57 , hAPP( hAPP( X, T ), hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), U ) ) ),
% 1.19/1.57 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.19/1.57 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.19/1.57 , V0, V1, V2 ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.19/1.57 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.19/1.57 W, V0, V1, V2 ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.19/1.57 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.19/1.57 , V0, V1, V2 ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.19/1.57 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.19/1.57 W, V0, V1, V2 ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.19/1.57 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.19/1.57 ~( 'c_Groebner__Basis_Ogb__semiring'( X, W, V0, V1, V2, V3 ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.19/1.57 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.19/1.57 W, V0, V1, V2 ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.19/1.57 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.19/1.57 W, V0, V1, V2 ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.19/1.57 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.19/1.57 , V0, V1, V2 ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.19/1.57 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.19/1.57 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.19/1.57 , V0, V1, V2 ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.19/1.57 X, T, U, Y, W, V0 ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.19/1.57 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.19/1.57 , V0, V1, V2 ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.19/1.57 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.19/1.57 T, X, U, Y, W, V0 ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.19/1.57 T, X, U, W, Y, V0 ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.19/1.57 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.19/1.57 , V0, V1, V2 ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.19/1.57 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( Z, hAPP(
% 1.19/1.57 hAPP( X, Y ), T ) ), hAPP( hAPP( X, Y ), U ) ) ), ~(
% 1.19/1.57 'c_Groebner__Basis_Ogb__semiring'( Z, X, W, V0, V1, V2 ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.19/1.57 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.19/1.57 'c_Groebner__Basis_Ogb__semiring'( W, Y, X, V0, V1, V2 ) ) ],
% 1.19/1.57 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.19/1.57 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), =( X, Z
% 1.19/1.57 ) ],
% 1.19/1.57 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.19/1.57 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, hAPP( 'c_Suc',
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.19/1.57 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.19/1.57 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 1.19/1.57 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), Y ) ), ~( hBOOL(
% 1.19/1.57 hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', Z ) ), X ) ),
% 1.19/1.57 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', Z )
% 1.19/1.57 ), Y ) ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', X ) ), Y ) ),
% 1.19/1.57 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', X )
% 1.19/1.57 ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Y ), Z ) )
% 1.19/1.57 ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.19/1.57 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP(
% 1.19/1.57 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.19/1.57 'tc_nat' ), X ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.57 'tc_nat' ), Z ), X ), 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.19/1.57 'tc_nat' ), Z ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP(
% 1.19/1.57 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.19/1.57 'tc_nat' ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X,
% 1.19/1.57 'tc_nat' ), Z ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP(
% 1.19/1.57 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.19/1.57 'tc_nat' ), X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y,
% 1.19/1.57 'tc_nat' ), Z ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP(
% 1.19/1.57 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.19/1.57 'tc_nat' ), X ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP(
% 1.19/1.57 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.19/1.57 'tc_nat' ), Y ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), 'tc_nat' )
% 1.19/1.57 , hAPP( 'c_Suc', Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X,
% 1.19/1.57 'tc_nat' ), Y ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), 'tc_nat' ), hAPP(
% 1.19/1.57 'c_Suc', Y ) ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), 'tc_nat' )
% 1.19/1.57 , hAPP( 'c_Suc', Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X,
% 1.19/1.57 'tc_nat' ), Y ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.57 ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.57 ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Oinverse'( X ), hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ), Y ), =( Y,
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Oinverse'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.19/1.57 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Oinverse'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.19/1.57 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Oinverse'( X ), Z ) ) ), =( Y, Z ), =( Z,
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.19/1.57 ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ),
% 1.19/1.57 hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), Y ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Oinverse'( X ), Z ) ), hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ),
% 1.19/1.57 hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), Y ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Oinverse'( X ), Z ) ), hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( T, X ), Z ) ) ) ],
% 1.19/1.57 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), T ), Z ) ) ) ],
% 1.19/1.57 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), T ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.19/1.57 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( T, X ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), Y ), T ) ) ) ],
% 1.19/1.57 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ) ],
% 1.19/1.57 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.19/1.57 X ), Y ), Z ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Z ) )
% 1.19/1.57 ) ],
% 1.19/1.57 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), Z ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.19/1.57 ), Y ), Z ) ) ) ],
% 1.19/1.57 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), =( Z, Y ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), Y ), Z ) ) ) ],
% 1.19/1.57 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), Y ), Z ) ) ), =( Z, Y ) ],
% 1.19/1.57 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), Y ), Z ) ) ) ],
% 1.19/1.57 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), Y ), Z ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 Y, X ), Z ) ) ],
% 1.19/1.57 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), Y ), Z ) ) ), =( Y, Z ) ],
% 1.19/1.57 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), =( Y, Z ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), Y ), Z ) ) ) ],
% 1.19/1.57 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), Y ), Z ) ) ) ],
% 1.19/1.57 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), =( Y, Z ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), Y ), Z ) ) ) ],
% 1.19/1.57 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ) ],
% 1.19/1.57 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), Z ), Y ) ) ],
% 1.19/1.57 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), Y ), Y ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Y ) ) ) ],
% 1.19/1.57 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Y ) ), hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), Y ), Y ) ) ],
% 1.19/1.57 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), Z ), Y ) ) ) ],
% 1.19/1.57 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), Y ), Z ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 Z, X ), Y ) ) ],
% 1.19/1.57 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), Z ), Y ) ) ],
% 1.19/1.57 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ),
% 1.19/1.57 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.57 ), X ), Y ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ),
% 1.19/1.57 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.19/1.57 , X ), hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Oinverse'( X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Oinverse__class_Oinverse'(
% 1.19/1.57 X ), Y ) ), hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Z ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.57 , Z ), T ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.19/1.57 ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.57 , T ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y )
% 1.19/1.57 ) ) ) ],
% 1.19/1.57 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.19/1.57 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, Y, X ) ],
% 1.19/1.57 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.19/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.19/1.57 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.19/1.57 , hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.19/1.57 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.19/1.57 , hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.19/1.57 ), T ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) )
% 1.19/1.57 ],
% 1.19/1.57 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.19/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Z, X ), T ) ) ) ],
% 1.19/1.57 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.19/1.57 , hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Z, X ), T ) ) ) ],
% 1.19/1.57 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.19/1.57 , hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T
% 1.19/1.57 ), Y ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ) )
% 1.19/1.57 ],
% 1.19/1.57 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.19/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Z, X ), U ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.19/1.57 [ ~( 'class_RealVector_Oreal__normed__div__algebra'( X ) ),
% 1.19/1.57 'c_SEQ_OLIMSEQ'( 'c_COMBB'( 'c_HOL_Oinverse__class_Oinverse'( X ), Y, X,
% 1.19/1.57 X, 'tc_nat' ), hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Z ), X ), =(
% 1.19/1.57 Z, 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_SEQ_OLIMSEQ'( Y, Z, X ) ) ]
% 1.19/1.57 ,
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.19/1.57 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( 'c_Suc', Y ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.19/1.57 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ) ],
% 1.19/1.57 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.19/1.57 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( T, X ), U ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ) ],
% 1.19/1.57 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.19/1.57 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( T, X ), U ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Oinverse'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.19/1.57 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Oinverse'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.19/1.57 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.19/1.57 ) ), =( Y, 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.19/1.57 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ]
% 1.19/1.57 ,
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 'tc_nat' ), 'tc_nat' ), X ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.19/1.57 ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 'tc_nat' ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 'tc_nat' ) ) ],
% 1.19/1.57 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.19/1.57 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( Y
% 1.19/1.57 , Z ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.19/1.57 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.19/1.57 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( X
% 1.19/1.57 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 1.19/1.57 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.19/1.57 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), =( Y
% 1.19/1.57 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 1.19/1.57 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.19/1.57 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ),
% 1.19/1.57 ~( 'c_Groebner__Basis_Ogb__semiring'( T, U, X, W, Z, V0 ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 'tc_nat' ) ), Y ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 'tc_nat' ) ) ) ],
% 1.19/1.57 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.19/1.57 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.19/1.57 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.19/1.57 [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 1.19/1.57 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.19/1.57 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X
% 1.19/1.57 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.19/1.57 [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.19/1.57 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.19/1.57 ), Y ), Z ), X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.19/1.57 T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' ), T ) )
% 1.19/1.57 ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.19/1.57 X ), X ), Y ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.19/1.57 ), T ), Y ), X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ),
% 1.19/1.57 Z ) ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'c_HOL_Oone__class_Oone'( X ), X ), T ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.19/1.57 ), Y ), Z ), X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.19/1.57 T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'c_HOL_Oone__class_Oone'( X ), X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' ), T ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.19/1.57 ), T ), Y ), X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ),
% 1.19/1.57 Z ) ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'c_HOL_Oone__class_Oone'( X ), X ), T ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), hAPP( hAPP(
% 1.19/1.57 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ) ) ), ~(
% 1.19/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X
% 1.19/1.57 ), Y ) ) ) ],
% 1.19/1.57 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.19/1.57 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.19/1.57 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.19/1.57 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Oinverse'( X ), hAPP( hAPP(
% 1.19/1.57 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.57 'c_Power_Opower__class_Opower'( X ), hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ), Z ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.57 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.19/1.57 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.19/1.57 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( 'tc_nat' ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 'tc_nat' ) ) ), X ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( 'tc_nat' ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 'tc_nat' ) ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X )
% 1.19/1.57 , Y ) ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( 'tc_nat' ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 'tc_nat' ) ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y )
% 1.19/1.57 , X ) ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.19/1.57 'tc_nat' ), X ) ) ],
% 1.19/1.57 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.19/1.57 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.19/1.57 ) ],
% 1.19/1.57 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.19/1.57 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.19/1.57 ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc',
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 'tc_nat' ) ), 'tc_nat' ), X ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 'tc_nat' ) ), 'tc_nat' ), Y ) ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.19/1.57 X ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.19/1.57 'c_Suc', Y ) ) ) ],
% 1.19/1.57 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.19/1.57 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, hAPP(
% 1.19/1.57 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.19/1.57 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.19/1.57 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, hAPP( 'c_Suc',
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.19/1.57 [ =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 'tc_nat' ) ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) )
% 1.19/1.57 ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ),
% 1.19/1.57 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Oinverse'( X ), Z ), X ), hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y
% 1.19/1.57 ), X ), hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Z ) ) ), ~( hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z
% 1.19/1.57 ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Oinverse'( X ), Z ), X ), hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y
% 1.19/1.57 ), X ), hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Z ) ) ), ~( hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.19/1.57 ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP(
% 1.19/1.57 'c_Suc', X ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( 'c_Suc',
% 1.19/1.57 Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), Y ) ) ) ]
% 1.19/1.57 ,
% 1.19/1.57 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), Y ) ), ~( hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( 'c_Suc', Y ) ) ) )
% 1.19/1.57 ],
% 1.19/1.57 [ ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), X ) ) ), hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ]
% 1.19/1.57 ,
% 1.19/1.57 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.19/1.57 X ) ), Y ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.57 'tc_nat' ), X ), Y ) ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.19/1.57 'c_Suc', Y ) ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.57 'tc_nat' ), X ), Y ) ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.19/1.57 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.19/1.57 'c_Groebner__Basis_Ogb__semiring'( U, W, X, V0, V1, V2 ) ) ],
% 1.19/1.57 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.19/1.57 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.19/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' ), Y ) ) ), hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), T ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP(
% 1.19/1.57 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, Z ), U ) )
% 1.19/1.57 , hAPP( hAPP( Y, Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.19/1.57 , T ), U ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, Y, V0, V1, V2
% 1.19/1.57 ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 'tc_nat' ) ) ) ) ],
% 1.19/1.57 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.19/1.57 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.19/1.57 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.19/1.57 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, hAPP(
% 1.19/1.57 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, hAPP( 'c_Suc'
% 1.19/1.57 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.19/1.57 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.19/1.57 Y, X ) ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ) ],
% 1.19/1.57 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.19/1.57 , Z ) ],
% 1.19/1.57 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.19/1.57 , Z ) ],
% 1.19/1.57 [ =( X, Y ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ),
% 1.19/1.57 hAPP( 'c_Suc', Y ) ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X,
% 1.19/1.57 'tc_nat' ), Y ) ) ],
% 1.19/1.57 [ =( X, Y ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ),
% 1.19/1.57 hAPP( 'c_Suc', X ) ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y,
% 1.19/1.57 'tc_nat' ), X ) ) ],
% 1.19/1.57 [ =( X, Y ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y )
% 1.19/1.57 ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP(
% 1.19/1.57 'c_Suc', Y ) ) ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.19/1.57 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.19/1.57 [ =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 'tc_nat' ) ) ) ],
% 1.19/1.57 [ ~( 'class_Orderings_Oorder'( X ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Y ) ) ) ],
% 1.19/1.57 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), X ) ) ) ]
% 1.19/1.57 ,
% 1.19/1.57 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), X ) ) ) ]
% 1.19/1.57 ,
% 1.19/1.57 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Y ) ) ) ],
% 1.19/1.57 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Y ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.19/1.57 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), X ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y
% 1.19/1.57 ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.19/1.57 ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y
% 1.19/1.57 ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.19/1.57 ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), T ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Z ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.19/1.57 X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.19/1.57 X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ) ) ],
% 1.19/1.57 [ ~( 'c_Groebner__Basis_Osemiringb'( X, Y, Z, T, U, W ) ), =( V0, hAPP(
% 1.19/1.57 hAPP( X, V0 ), T ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, Z ), U ) )
% 1.19/1.57 , hAPP( hAPP( X, hAPP( hAPP( Y, Z ), U ) ), hAPP( hAPP( Y, Z ), T ) ) ),
% 1.19/1.57 ~( 'c_Groebner__Basis_Osemiringb'( X, Y, W, V0, V1, V2 ) ) ],
% 1.19/1.57 [ ~( 'c_Groebner__Basis_Osemiringb'( X, Y, Z, T, U, W ) ), =( hAPP( hAPP(
% 1.19/1.57 X, hAPP( hAPP( Y, V0 ), V1 ) ), hAPP( hAPP( Y, V0 ), V2 ) ), hAPP( hAPP(
% 1.19/1.57 X, hAPP( hAPP( Y, V0 ), V2 ) ), hAPP( hAPP( Y, V0 ), V1 ) ) ) ],
% 1.19/1.57 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =( Y,
% 1.19/1.57 'c_Series_Osuminf'( Z, X ) ), ~( 'c_Series_Osums'( Z, Y, X ) ) ],
% 1.19/1.57 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 1.19/1.57 'c_Series_Osuminf'( Y, X ), Z ), ~( 'c_Series_Osums'( Y, Z, X ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.19/1.57 'tc_nat' ), Y ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.19/1.57 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.19/1.57 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.19/1.57 'tc_nat' ), Y ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 'tc_nat' ) ), 'tc_nat' ), Y ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 'tc_nat' ) ), 'tc_nat' ), X ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 'tc_nat' ) ), 'tc_nat' ), Y ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 'tc_nat' ) ), 'tc_nat' ), X ) ) ) ],
% 1.19/1.57 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), Y ) ) ) ]
% 1.19/1.57 ,
% 1.19/1.57 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), X ) ) ) ]
% 1.19/1.57 ,
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.57 'tc_nat' ), X ), Z ), 'tc_nat' ), Y ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), Z ) ), ~(
% 1.19/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Z ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.57 'tc_nat' ), Z ), X ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.57 'tc_nat' ), Z ), Y ) ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y
% 1.19/1.57 ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), Y ) ) ) ]
% 1.19/1.57 ,
% 1.19/1.57 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( 'c_Suc',
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.19/1.57 [ =( X, Y ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ),
% 1.19/1.57 hAPP( 'c_Suc', Y ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat'
% 1.19/1.57 ), Y ), X ) ) ) ],
% 1.19/1.57 [ =( 'c_SetInterval_Oord__class_OatLeastLessThan'( X, hAPP( 'c_Suc', Y )
% 1.19/1.57 , 'tc_nat' ), 'c_SetInterval_Oord__class_OatLeastAtMost'( X, Y, 'tc_nat'
% 1.19/1.57 ) ) ],
% 1.19/1.57 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.57 'c_Finite__Set_Osetsum'( 'tc_nat', X ), Y ),
% 1.19/1.57 'c_SetInterval_Oord__class_OatLeastAtMost'( Z, hAPP( 'c_Suc', T ),
% 1.19/1.57 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', T ), 'tc_nat' ), Z ) ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ) ), Y ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), X ) ) ],
% 1.19/1.57 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ) ],
% 1.19/1.57 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ) ],
% 1.19/1.57 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ) ],
% 1.19/1.57 [ ~( 'class_Orderings_Oorder'( X ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), hAPP( hAPP(
% 1.19/1.57 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.19/1.57 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'c_HOL_Oone__class_Oone'( X ), X ), Y ) ) ) ],
% 1.19/1.57 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~( =( hAPP( Y,
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.19/1.57 ) ), 'c_Series_Osums'( Y, Z, X ), ~( 'c_Series_Osums'( 'c_COMBB'( Y,
% 1.19/1.57 'c_Suc', 'tc_nat', X, 'tc_nat' ), Z, X ) ) ],
% 1.19/1.57 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.57 'c_Finite__Set_Osetsum'( 'tc_nat', X ), Y ),
% 1.19/1.57 'c_SetInterval_Oord__class_OatLeastAtMost'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), U ), T ), 'tc_nat' ) ), hAPP(
% 1.19/1.57 hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat', X ), 'c_COMBB'( Y, hAPP(
% 1.19/1.57 'c_COMBC'( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'tc_nat', 'tc_nat',
% 1.19/1.57 'tc_nat' ), T ), 'tc_nat', X, 'tc_nat' ) ),
% 1.19/1.57 'c_SetInterval_Oord__class_OatLeastAtMost'( Z, U, 'tc_nat' ) ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' )
% 1.19/1.57 , 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.57 'tc_nat' ), X ), Y ) ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.57 'tc_nat' ), X ), Z ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.19/1.57 'tc_Complex_Ocomplex' ), 'c_FFT__Mirabelle_Oroot'( Y ) ), Z ) ), ~( hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.19/1.57 'tc_nat' ), X ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.19/1.57 hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.19/1.57 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.19/1.57 hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.19/1.57 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL(
% 1.19/1.57 hAPP( hAPP( 'c_lessequals'( X ), hAPP( 'c_HOL_Oinverse__class_Oinverse'(
% 1.19/1.57 X ), Y ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.19/1.57 X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ), ~( hBOOL(
% 1.19/1.57 hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.57 , T ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y )
% 1.19/1.57 ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.57 , Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.19/1.57 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ), Z ) ) ), ~(
% 1.19/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.57 , T ), Y ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.19/1.57 ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.57 , Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.19/1.57 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), T ) ) ), ~(
% 1.19/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.57 X ), Y ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.57 , Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.19/1.57 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( T, X ), Z ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.57 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.19/1.57 ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Z, X ), T ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.57 , Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.19/1.57 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), T ) ) ), ~(
% 1.19/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.57 X ), Y ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.57 , Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.19/1.57 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ), Z ) ) ), ~(
% 1.19/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.57 , Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.19/1.57 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( T, X ), Y ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.57 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z
% 1.19/1.57 ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.57 , Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.19/1.57 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ), ~(
% 1.19/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.57 X ), Z ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.57 , Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.19/1.57 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ), Y ) ) ), ~(
% 1.19/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 1.19/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), T ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.19/1.57 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.19/1.57 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z
% 1.19/1.57 ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.19/1.57 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.19/1.57 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.19/1.57 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.19/1.57 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.57 X ), Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.57 X ), Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 X ), X ), Y ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.57 X ), Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 X ), X ), Z ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.19/1.57 'tc_nat' ), Y ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 hAPP( 'c_lessequals'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.19/1.57 'tc_nat' ), X ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), Y ) ), ~( hBOOL(
% 1.19/1.57 hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.19/1.57 'tc_nat' ), Z ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), Y ) ), ~( hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.19/1.57 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ),
% 1.19/1.57 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ) ), hAPP(
% 1.19/1.57 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), Y ) ), ~( hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.19/1.57 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ),
% 1.19/1.57 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP(
% 1.19/1.57 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Oinverse'( X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP( 'c_Suc', Y ) ),
% 1.19/1.57 'tc_nat' ), X ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ) ) ],
% 1.19/1.57 [ =( hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' )
% 1.19/1.57 , X ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ),
% 1.19/1.57 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 'tc_nat' ), 'tc_nat' ), X ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), Y ) ), ~( hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), Y ) ), ~( hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 hAPP( 'c_lessequals'( 'tc_nat' ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), X ) ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 hAPP( 'c_lessequals'( 'tc_nat' ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), =( X, Y
% 1.19/1.57 ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.19/1.57 [ =( X, Y ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y )
% 1.19/1.57 ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), =( X, Y
% 1.19/1.57 ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 hAPP( 'c_lessequals'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 hAPP( 'c_lessequals'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 hAPP( 'c_lessequals'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 hAPP( 'c_lessequals'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 hAPP( 'c_lessequals'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), Y ) ), ~( hBOOL(
% 1.19/1.57 hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), X ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 hAPP( 'c_lessequals'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 hAPP( 'c_lessequals'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 hAPP( 'c_lessequals'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), Y ) ), ~( hBOOL(
% 1.19/1.57 hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), Y ) ), ~( hBOOL(
% 1.19/1.57 hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), X ) ), Y ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 hAPP( 'c_lessequals'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 hAPP( 'c_lessequals'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), X ) ) ) ],
% 1.19/1.57 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.57 'c_Finite__Set_Osetsum'( 'tc_nat', X ), Y ),
% 1.19/1.57 'c_SetInterval_Oord__class_OatLeastAtMost'( Z, hAPP( 'c_Suc', T ),
% 1.19/1.57 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( Y, Z ) )
% 1.19/1.57 , hAPP( hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat', X ), 'c_COMBB'( Y,
% 1.19/1.57 'c_Suc', 'tc_nat', X, 'tc_nat' ) ),
% 1.19/1.57 'c_SetInterval_Oord__class_OatLeastAtMost'( Z, T, 'tc_nat' ) ) ) ), hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', T ), 'tc_nat' ), Z ) ) ]
% 1.19/1.57 ,
% 1.19/1.57 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ) ), ~( hBOOL(
% 1.19/1.57 hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Z ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), X ) ), Y ) ), U ) ) ) ),
% 1.19/1.57 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), T ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ), T ) ), U ) ) ), ~(
% 1.19/1.57 hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), X ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ), U ) ) ) ), ~( hBOOL(
% 1.19/1.57 hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Z ), Y ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ) ), ~( hBOOL(
% 1.19/1.57 hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), T ) ), Y ) ), Z ) ), U ) )
% 1.19/1.57 ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), T ), X ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ) ), T ) ), U ) )
% 1.19/1.57 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), T ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), U ) ) ) ), ~( hBOOL(
% 1.19/1.57 hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Y ), X ) ) ) ],
% 1.19/1.57 [ ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), Y ) ) ), =(
% 1.19/1.57 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ) ), Z ) ), T ) ), hAPP(
% 1.19/1.57 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), T ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), X ) ), Y ) ), U ) ) ), ~(
% 1.19/1.57 hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), T ) ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), T ) ), Y ) ), Z ) ), U ) )
% 1.19/1.57 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), T ), X ) ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP(
% 1.19/1.57 'c_Suc', hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) )
% 1.19/1.57 ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), hAPP( 'c_Suc', Y ) )
% 1.19/1.57 ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Z ), Y ) ) ) ],
% 1.19/1.57 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ) ), ~( hBOOL(
% 1.19/1.57 hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), T ) ) ), =( Z, hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), X ) ), Y ) ), U ) ) ],
% 1.19/1.57 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ) ), ~( hBOOL(
% 1.19/1.57 hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), T ), X ) ) ), =( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), T ) ), Y ) ), Z ), U ) ]
% 1.19/1.57 ,
% 1.19/1.57 [ ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), Y ) ) ), =(
% 1.19/1.57 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ) ), Z ) ), T ) ) ) ]
% 1.19/1.57 ,
% 1.19/1.57 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.19/1.57 , hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ) ), Z )
% 1.19/1.57 , hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc', X
% 1.19/1.57 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ),
% 1.19/1.57 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Y ), X ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), Z ) ),
% 1.19/1.57 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Z ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP(
% 1.19/1.57 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' ), X ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' ), Y ) ) ) ],
% 1.19/1.57 [ ~( hBOOL( hAPP( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.19/1.57 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), Y ) )
% 1.19/1.57 ) ), hBOOL( hAPP( X, Z ) ) ],
% 1.19/1.57 [ ~( hBOOL( hAPP( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.19/1.57 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), Y ) )
% 1.19/1.57 ) ), hBOOL( hAPP( X, Z ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.19/1.57 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), X ), Y ) ],
% 1.19/1.57 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Y ), X ) ],
% 1.19/1.57 [ ~( 'class_RealVector_Ometric__space'( X ) ), 'c_SEQ_OLIMSEQ'(
% 1.19/1.57 'c_COMBB'( Y, hAPP( 'c_COMBC'( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.19/1.57 'tc_nat', 'tc_nat', 'tc_nat' ), Z ), 'tc_nat', X, 'tc_nat' ), T, X ), ~(
% 1.19/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 'tc_nat' ), 'tc_nat' ), Z ) ) ), ~( 'c_SEQ_OLIMSEQ'( Y, T, X ) ) ],
% 1.19/1.57 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.57 'c_Finite__Set_Osetsum'( 'tc_nat', X ), Y ),
% 1.19/1.57 'c_SetInterval_Oord__class_OatLeastAtMost'( hAPP( 'c_Suc', Z ), hAPP(
% 1.19/1.57 'c_Suc', T ), 'tc_nat' ) ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat'
% 1.19/1.57 , X ), 'c_COMBB'( Y, 'c_Suc', 'tc_nat', X, 'tc_nat' ) ),
% 1.19/1.57 'c_SetInterval_Oord__class_OatLeastAtMost'( Z, T, 'tc_nat' ) ) ) ],
% 1.19/1.57 [ =( 'c_HOL_Oord__class_Oless'( 'v_n', 'tc_nat' ), hAPP( 'c_lessequals'(
% 1.19/1.57 'tc_nat' ), hAPP( 'c_Suc', 'v_n' ) ) ) ],
% 1.19/1.57 [ ~( 'class_RealVector_Ometric__space'( X ) ), 'c_SEQ_OLIMSEQ'(
% 1.19/1.57 'c_COMBB'( Y, hAPP( 'c_COMBC'( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.19/1.57 'tc_nat', 'tc_nat', 'tc_nat' ), Z ), 'tc_nat', X, 'tc_nat' ), T, X ), ~(
% 1.19/1.57 'c_SEQ_OLIMSEQ'( Y, T, X ) ) ],
% 1.19/1.57 [ ~( 'class_RealVector_Ometric__space'( X ) ), 'c_SEQ_OLIMSEQ'( Y, Z, X
% 1.19/1.57 ), ~( 'c_SEQ_OLIMSEQ'( 'c_COMBB'( Y, hAPP( 'c_COMBC'(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'tc_nat', 'tc_nat', 'tc_nat' ), T
% 1.19/1.57 ), 'tc_nat', X, 'tc_nat' ), Z, X ) ) ],
% 1.19/1.57 [ ~( =( 'c_FFT__Mirabelle_Oroot'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 'tc_Complex_Ocomplex' ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), 'c_HOL_Oone__class_Oone'( X ) ), hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ) ) ), ~( hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.19/1.57 ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y
% 1.19/1.57 ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ),
% 1.19/1.57 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Oone__class_Oone'( X )
% 1.19/1.57 ), hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), Y ) ),
% 1.19/1.57 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), X ), 'c_HOL_Oone__class_Oone'(
% 1.19/1.57 X ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.19/1.57 ), Y ), Z ), X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.19/1.57 T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.19/1.57 'c_HOL_Oone__class_Oone'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, 'tc_nat' ), Z ) ) ) ]
% 1.19/1.57 ,
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.19/1.57 ), Y ), hAPP( 'c_Suc', Z ) ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.19/1.57 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.19/1.57 'c_HOL_Oone__class_Oone'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) )
% 1.19/1.57 ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.57 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U
% 1.19/1.57 ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ), ~( hBOOL(
% 1.19/1.57 hAPP( hAPP( 'c_lessequals'( X ), Z ), U ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.57 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U
% 1.19/1.57 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), U ) ) ), ~( hBOOL(
% 1.19/1.57 hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.57 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U
% 1.19/1.57 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ), ~( hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), U ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) ) ), ~( hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.57 X ), Y ), T ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T
% 1.19/1.57 ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) ) ), ~( hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.57 X ), T ), Y ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z
% 1.19/1.57 ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) ) ), ~( hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.57 X ), Y ), T ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T
% 1.19/1.57 ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) ) ), ~( hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.57 X ), T ), Y ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z
% 1.19/1.57 ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.57 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U
% 1.19/1.57 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), U ) ) ), ~( hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.19/1.57 hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.19/1.57 hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.19/1.57 hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.57 , Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) )
% 1.19/1.57 ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.19/1.57 hAPP( 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.19/1.57 Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ), ~(
% 1.19/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.57 X ), T ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.19/1.57 hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.57 , Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), T ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.19/1.57 ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.19/1.57 hAPP( 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.19/1.57 Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ) ) ), ~(
% 1.19/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.19/1.57 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.57 X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) )
% 1.19/1.57 ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 X ), X ), Z ) ) ) ],
% 1.19/1.57 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.19/1.57 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ),
% 1.19/1.57 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.57 ), X ), Y ) ) ) ],
% 1.19/1.57 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.19/1.57 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 X ) ), Y ) ) ) ],
% 1.19/1.57 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.57 X ), Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.57 X ), Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 hAPP( 'c_lessequals'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ),
% 1.19/1.57 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.19/1.57 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.57 X ), Z ), T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), T )
% 1.19/1.57 ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Oinverse__class_Oinverse'(
% 1.19/1.57 X ), Y ) ), hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Z ) ), hAPP(
% 1.19/1.57 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Oinverse__class_Oinverse'(
% 1.19/1.57 X ), Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ),
% 1.19/1.57 hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Z ) ) ), =( Z,
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.19/1.57 ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Oinverse__class_Oinverse'(
% 1.19/1.57 X ), Y ) ), hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Z ) ), hAPP(
% 1.19/1.57 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.57 X ), Y ), Z ) ), hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ) ),
% 1.19/1.57 hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Z ) ) ), =( Z,
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.19/1.57 ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.19/1.57 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.57 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP(
% 1.19/1.57 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), X ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.19/1.57 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ) ), =( Z,
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.19/1.57 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ) ), =( Y,
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ),
% 1.19/1.57 'c_HOL_Oone__class_Oone'( X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.19/1.57 X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ) ), hBOOL( hAPP(
% 1.19/1.57 hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~(
% 1.19/1.57 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ), 'c_HOL_Oone__class_Oone'( X
% 1.19/1.57 ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( X ), hAPP( 'c_HOL_Oinverse__class_Oinverse'(
% 1.19/1.57 X ), Y ) ), hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Z ) ), hAPP(
% 1.19/1.57 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Oinverse__class_Oinverse'(
% 1.19/1.57 X ), Y ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Z ), Y ) ) ),
% 1.19/1.57 hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Z ) ) ), =( Z,
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.19/1.57 ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ), 'c_HOL_Oone__class_Oone'( X
% 1.19/1.57 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.19/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.57 X ), Y ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.19/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.57 X ), Y ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.57 X ), Y ), Y ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Oinverse'( X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Oinverse__class_Oinverse'(
% 1.19/1.57 X ), Z ) ), hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ) ), =( Z,
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.19/1.57 ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ),
% 1.19/1.57 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.19/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), T ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.57 , Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.19/1.57 ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ),
% 1.19/1.57 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.19/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), T ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.57 , Z ), Y ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y )
% 1.19/1.57 ) ) ) ],
% 1.19/1.57 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.57 X ), Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.19/1.57 ), Y ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.19/1.57 ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.19/1.57 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.19/1.57 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.19/1.57 ), Y ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.19/1.57 ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.57 X ), Z ), T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), T )
% 1.19/1.57 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ) ],
% 1.19/1.57 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ),
% 1.19/1.57 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.57 ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ) ) ]
% 1.19/1.57 ,
% 1.19/1.57 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.19/1.57 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) )
% 1.19/1.57 ],
% 1.19/1.57 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.19/1.57 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 X ), X ), Y ) ) ) ],
% 1.19/1.57 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.19/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Z, X ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), Y ), T ) ) ) ],
% 1.19/1.57 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.19/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), Z ), U ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.19/1.57 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.19/1.57 'c_COMBB'( Y, Z, X, X, X ), T, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.57 X ), U ), W ), X ), ~( 'c_Deriv_Oderiv'( Z, T, W, X ) ), ~(
% 1.19/1.57 'c_Deriv_Oderiv'( Y, hAPP( Z, T ), U, X ) ) ],
% 1.19/1.57 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.19/1.57 'c_COMBB'( Y, Z, X, X, X ), T, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.57 X ), U ), W ), X ), ~( 'c_Deriv_Oderiv'( Y, hAPP( Z, T ), U, X ) ), ~(
% 1.19/1.57 'c_Deriv_Oderiv'( Z, T, W, X ) ) ],
% 1.19/1.57 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.19/1.57 'c_COMBB'( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, X, X, X ), T
% 1.19/1.57 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ), X ), ~(
% 1.19/1.57 'c_Deriv_Oderiv'( Z, T, U, X ) ) ],
% 1.19/1.57 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X )
% 1.19/1.57 , Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ) ],
% 1.19/1.57 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X )
% 1.19/1.57 , Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.19/1.57 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ),
% 1.19/1.57 'c_HOL_Oone__class_Oone'( X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.19/1.57 X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ) ), ~( hBOOL(
% 1.19/1.57 hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Oone__class_Oone'( X ) ), hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.19/1.57 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.19/1.57 ), Y ), Z ), X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ),
% 1.19/1.57 Z ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), Z ) ) ), ~( hBOOL(
% 1.19/1.57 hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.19/1.57 ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), Z ) ) ),
% 1.19/1.57 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.19/1.57 , X ), Y ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Oone__class_Oone'( X
% 1.19/1.57 ) ) ), =( hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), Z ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.57 X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.19/1.57 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.57 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.19/1.57 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) )
% 1.19/1.57 ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Oinverse'( X ), hAPP( hAPP(
% 1.19/1.57 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.57 'c_Power_Opower__class_Opower'( X ), hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ), Z ) ), =( Y,
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.57 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_SEQ_OLIMSEQ'(
% 1.19/1.57 'c_COMBB'( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, X, X,
% 1.19/1.57 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.19/1.57 , ~( 'c_SEQ_OLIMSEQ'( Z, T, X ) ) ],
% 1.19/1.57 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_Series_Osums'(
% 1.19/1.57 'c_COMBB'( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, X, X,
% 1.19/1.57 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.19/1.57 , ~( 'c_Series_Osums'( Z, T, X ) ) ],
% 1.19/1.57 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_Series_Osums'(
% 1.19/1.57 'c_COMBB'( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, X, X,
% 1.19/1.57 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.19/1.57 , ~( 'c_Series_Osums'( Z, T, X ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.19/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.57 X ), Y ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ),
% 1.19/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.57 X ), Z ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ), X ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.19/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.57 ), Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ),
% 1.19/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.57 ), Z ), Y ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.19/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.57 X ), Y ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.19/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.57 X ), Z ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.19/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.57 X ), Z ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.19/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.57 X ), Y ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ),
% 1.19/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ),
% 1.19/1.57 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ), Y ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.57 ), Y ), Z ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.19/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.57 X ), Z ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.19/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ),
% 1.19/1.57 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.19/1.57 , hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ]
% 1.19/1.57 ,
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.19/1.57 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.19/1.57 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 X ), X ), Y ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.19/1.57 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 X ), X ), Y ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.19/1.57 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.57 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T )
% 1.19/1.57 , Z ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.57 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T )
% 1.19/1.57 , Z ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( T, X ), Y ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.57 ), Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.57 ), Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 X ), X ), Y ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.57 ), Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 X ), X ), Y ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.57 ), Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.19/1.57 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.57 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.57 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.57 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.57 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.57 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Oinverse'( X ), Z ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.57 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Oinverse'( X ), Z ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.19/1.57 hAPP( 'c_lessequals'( 'tc_nat' ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ),
% 1.19/1.57 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.19/1.57 hAPP( 'c_lessequals'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) )
% 1.19/1.57 , 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.19/1.57 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.57 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), Y ) ) ),
% 1.19/1.57 =( Z, T ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.57 'class_Int_Onumber__ring'( X ) ), =( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.19/1.57 ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.19/1.57 ) ) ],
% 1.19/1.57 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.19/1.57 hAPP( 'c_COMBC'( 'c_COMBB'( 'c_Power_Opower__class_Opower'( X ), Y, X,
% 1.19/1.57 'tc_fun'( 'tc_nat', X ), X ), X, 'tc_nat', X ), hAPP( 'c_Suc', Z ) ), T,
% 1.19/1.57 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.19/1.57 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), U ), hAPP( hAPP(
% 1.19/1.57 'c_Power_Opower__class_Opower'( X ), hAPP( Y, T ) ), Z ) ) ), X ), ~(
% 1.19/1.57 'c_Deriv_Oderiv'( Y, T, U, X ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP(
% 1.19/1.57 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 'tc_nat' ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.19/1.57 'tc_nat' ), X ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y,
% 1.19/1.57 'tc_nat' ), X ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.19/1.57 'tc_nat' ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X
% 1.19/1.57 ) ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ) ) ]
% 1.19/1.57 ,
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), X ) ),
% 1.19/1.57 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 'tc_nat' ), 'tc_nat' ), X ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.19/1.57 'tc_nat' ), Y ) ) ) ],
% 1.19/1.57 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.19/1.57 hAPP( 'c_COMBC'( 'c_COMBB'( 'c_Power_Opower__class_Opower'( X ), Y, X,
% 1.19/1.57 'tc_fun'( 'tc_nat', X ), X ), X, 'tc_nat', X ), Z ), T, hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.19/1.57 Z, X ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), hAPP( hAPP(
% 1.19/1.57 'c_Power_Opower__class_Opower'( X ), hAPP( Y, T ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), hAPP( 'c_Suc',
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ) ), X ), ~(
% 1.19/1.57 'c_Deriv_Oderiv'( Y, T, U, X ) ) ],
% 1.19/1.57 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( 't_a' ) ), ~( =( hAPP( X,
% 1.19/1.57 'v_sko__FFT__Mirabelle__Xsetsum__add__split__nat__ivl__2'( Y, X, Z, T ) )
% 1.19/1.57 , hAPP( Y, 'v_sko__FFT__Mirabelle__Xsetsum__add__split__nat__ivl__2'( Y,
% 1.19/1.57 X, Z, T ) ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'v_sko__FFT__Mirabelle__Xsetsum__add__split__nat__ivl__2'( Y, U, W, Z ),
% 1.19/1.57 'tc_nat' ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Z )
% 1.19/1.57 , T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), W ), Z ) ) )
% 1.19/1.57 , =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 't_a' ), hAPP( hAPP(
% 1.19/1.57 'c_Finite__Set_Osetsum'( 'tc_nat', 't_a' ), U ),
% 1.19/1.57 'c_SetInterval_Oord__class_OatLeastLessThan'( W, Z, 'tc_nat' ) ) ), hAPP(
% 1.19/1.57 hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat', 't_a' ), X ),
% 1.19/1.57 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ) ) ), hAPP(
% 1.19/1.57 hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat', 't_a' ), Y ),
% 1.19/1.57 'c_SetInterval_Oord__class_OatLeastLessThan'( W, T, 'tc_nat' ) ) ) ],
% 1.19/1.57 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( 't_a' ) ), ~( =( hAPP( X,
% 1.19/1.57 'v_sko__FFT__Mirabelle__Xsetsum__add__split__nat__ivl__2'( Y, X, Z, T ) )
% 1.19/1.57 , hAPP( Y, 'v_sko__FFT__Mirabelle__Xsetsum__add__split__nat__ivl__2'( Y,
% 1.19/1.57 X, Z, T ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), T ), U
% 1.19/1.57 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Z ), T ) ) ),
% 1.19/1.57 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 't_a' ), hAPP( hAPP(
% 1.19/1.57 'c_Finite__Set_Osetsum'( 'tc_nat', 't_a' ), X ),
% 1.19/1.57 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ) ) ), hAPP(
% 1.19/1.57 hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat', 't_a' ), W ),
% 1.19/1.57 'c_SetInterval_Oord__class_OatLeastLessThan'( T, U, 'tc_nat' ) ) ), hAPP(
% 1.19/1.57 hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat', 't_a' ), Y ),
% 1.19/1.57 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, U, 'tc_nat' ) ) ), hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'v_sko__FFT__Mirabelle__Xsetsum__add__split__nat__ivl__2'( Y, W, T, U ),
% 1.19/1.57 'tc_nat' ), U ) ) ],
% 1.19/1.57 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( 't_a' ) ), =( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 't_a' ), hAPP( hAPP( 'c_Finite__Set_Osetsum'(
% 1.19/1.57 'tc_nat', 't_a' ), X ), 'c_SetInterval_Oord__class_OatLeastLessThan'( Y,
% 1.19/1.57 Z, 'tc_nat' ) ) ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat', 't_a' )
% 1.19/1.57 , T ), 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, U, 'tc_nat' ) ) )
% 1.19/1.57 , hAPP( hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat', 't_a' ), W ),
% 1.19/1.57 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, U, 'tc_nat' ) ) ), hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'v_sko__FFT__Mirabelle__Xsetsum__add__split__nat__ivl__2'( W, T, Z, U ),
% 1.19/1.57 'tc_nat' ), U ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'v_sko__FFT__Mirabelle__Xsetsum__add__split__nat__ivl__2'( W, X, Y, Z ),
% 1.19/1.57 'tc_nat' ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Z )
% 1.19/1.57 , U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Y ), Z ) ) )
% 1.19/1.57 ],
% 1.19/1.57 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( 't_a' ) ), =( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 't_a' ), hAPP( hAPP( 'c_Finite__Set_Osetsum'(
% 1.19/1.57 'tc_nat', 't_a' ), X ), 'c_SetInterval_Oord__class_OatLeastLessThan'( Y,
% 1.19/1.57 Z, 'tc_nat' ) ) ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat', 't_a' )
% 1.19/1.57 , T ), 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, U, 'tc_nat' ) ) )
% 1.19/1.57 , hAPP( hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat', 't_a' ), W ),
% 1.19/1.57 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, U, 'tc_nat' ) ) ), hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'v_sko__FFT__Mirabelle__Xsetsum__add__split__nat__ivl__2'( W, T, Z, U ),
% 1.19/1.57 'tc_nat' ), U ) ), hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Y ),
% 1.19/1.57 'v_sko__FFT__Mirabelle__Xsetsum__add__split__nat__ivl__2'( W, X, Y, Z ) )
% 1.19/1.57 ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Z ), U ) ) ), ~(
% 1.19/1.57 hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.19/1.57 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( 't_a' ) ), =( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 't_a' ), hAPP( hAPP( 'c_Finite__Set_Osetsum'(
% 1.19/1.57 'tc_nat', 't_a' ), X ), 'c_SetInterval_Oord__class_OatLeastLessThan'( Y,
% 1.19/1.57 Z, 'tc_nat' ) ) ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat', 't_a' )
% 1.19/1.57 , T ), 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, U, 'tc_nat' ) ) )
% 1.19/1.57 , hAPP( hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat', 't_a' ), W ),
% 1.19/1.57 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, U, 'tc_nat' ) ) ), hBOOL(
% 1.19/1.57 hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Z ),
% 1.19/1.57 'v_sko__FFT__Mirabelle__Xsetsum__add__split__nat__ivl__2'( W, T, Z, U ) )
% 1.19/1.57 ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'v_sko__FFT__Mirabelle__Xsetsum__add__split__nat__ivl__2'( W, X, Y, Z ),
% 1.19/1.57 'tc_nat' ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Z )
% 1.19/1.57 , U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Y ), Z ) ) )
% 1.19/1.57 ],
% 1.19/1.57 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), Z ) ) ), ~( hBOOL(
% 1.19/1.57 hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Z ), Y ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP(
% 1.19/1.57 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL(
% 1.19/1.57 hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Y ), X ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Z ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.57 'tc_nat' ), X ), Z ) ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.19/1.57 'tc_nat' ), Z ), Y ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ) ), ~( hBOOL( hAPP(
% 1.19/1.57 hAPP( 'c_lessequals'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 hAPP( 'c_lessequals'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ), Y ) ), ~( hBOOL(
% 1.19/1.57 hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Z ), X ) ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 hAPP( 'c_lessequals'( 'tc_nat' ), Z ), Y ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ) ), ~( hBOOL(
% 1.19/1.57 hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ), Y ) ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP(
% 1.19/1.57 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ), ~( hBOOL( hAPP(
% 1.19/1.57 hAPP( 'c_lessequals'( 'tc_nat' ), Z ), Y ) ) ) ],
% 1.19/1.57 [ ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ) ), =( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), X ), Y ) ],
% 1.19/1.57 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Y ), X ), ~( hBOOL(
% 1.19/1.57 hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Y ), X ) ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ) ), Y ), ~( hBOOL( hAPP(
% 1.19/1.57 hAPP( 'c_lessequals'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.19/1.57 [ ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), Y ) ) ), =( Y,
% 1.19/1.57 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ) ), X ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ), ~( hBOOL( hAPP(
% 1.19/1.57 hAPP( 'c_lessequals'( 'tc_nat' ), Y ), X ) ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ) ), ~( hBOOL( hAPP(
% 1.19/1.57 hAPP( 'c_lessequals'( 'tc_nat' ), Z ), Y ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP(
% 1.19/1.57 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 hAPP( 'c_lessequals'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( 'tc_nat' ), Y ), X ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.19/1.57 'tc_nat' ), X ), Z ), 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 hAPP( 'c_lessequals'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( 'tc_nat' ), Z ), X ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'v_i', 'tc_nat' ), 'v_n' ) ) ]
% 1.19/1.57 ,
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Oinverse__class_Oinverse'(
% 1.19/1.57 X ), Y ) ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y,
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Oinverse__class_Oinverse'(
% 1.19/1.57 X ), Y ) ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y,
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.19/1.57 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.19/1.57 'c_HOL_Oone__class_Oone'( X ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.57 'c_Power_Opower__class_Opower'( X ), Y ), T ), X ), hAPP( hAPP(
% 1.19/1.57 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y
% 1.19/1.57 ), Z ) ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), U ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), U ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ]
% 1.19/1.57 ,
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 X ) ), Y ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.57 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T )
% 1.19/1.57 , U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), U ), Z ) ) ), ~(
% 1.19/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.57 X ), U ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 X ) ), Y ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y
% 1.19/1.57 ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y
% 1.19/1.57 ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 X ) ), Y ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.57 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T )
% 1.19/1.57 , U ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( U, X ), Z ) ) ),
% 1.19/1.57 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.57 ), X ), U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 X ), X ), Y ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.57 ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( T, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.19/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.57 X ), T ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.19/1.57 ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 X ), X ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), hAPP(
% 1.19/1.57 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y
% 1.19/1.57 ), Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ), T ) ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.19/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.57 X ), Z ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ), hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.19/1.57 ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 X ), X ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ), Y ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.19/1.57 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), X ), hAPP(
% 1.19/1.57 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.57 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( X ), U ), Y ) ), Z ) ), W ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.57 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), U ) ), W ) ) ), ~( hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.57 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), Y ), X )
% 1.19/1.57 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ), W ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.19/1.57 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), X ), hAPP(
% 1.19/1.57 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.19/1.57 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T ), X ), W ) ) ) ]
% 1.19/1.57 ,
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.19/1.57 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ) ), U ), X ), W ) ),
% 1.19/1.57 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.57 X ), Y ), T ) ), U ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.19/1.57 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), W ) ) ) ) ]
% 1.19/1.57 ,
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.57 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y )
% 1.19/1.57 , T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), T ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.57 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y )
% 1.19/1.57 , T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ), Z ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.19/1.57 , hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.57 , Y ), T ), X ), Z ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ]
% 1.19/1.57 ,
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( T, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ]
% 1.19/1.57 ,
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( T, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.19/1.57 , hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.19/1.57 , X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), hAPP(
% 1.19/1.57 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.57 ), Y ), Z ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.19/1.57 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.57 ), Y ), Z ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.57 , T ), Z ), X ), Y ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.57 ), Y ), Z ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X
% 1.19/1.57 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.57 , T ), Z ), X ), Y ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.57 , Y ), Z ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X )
% 1.19/1.57 , 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ),
% 1.19/1.57 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ), Y ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.57 , Y ), T ), X ), Z ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( T, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.57 , Y ), T ), X ), Z ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.57 ), Y ), Z ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.57 , T ), Z ), X ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X
% 1.19/1.57 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.57 ), Y ), Z ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X
% 1.19/1.57 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.57 , T ), Z ), X ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X
% 1.19/1.57 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.57 , Y ), T ), X ), Z ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.57 ), Y ), Z ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X
% 1.19/1.57 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ), ~(
% 1.19/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.19/1.57 X ), Z ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), Z ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.57 , Y ), Z ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.57 ), Y ), Z ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), X ), Z ) ) ) ],
% 1.19/1.57 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.19/1.57 'c_COMBS'( 'c_COMBB'( 'c_HOL_Oplus__class_Oplus'( X ), Y, X, 'tc_fun'( X
% 1.19/1.57 , X ), X ), Z, X, X, X ), T, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.19/1.57 , U ), W ), X ), ~( 'c_Deriv_Oderiv'( Z, T, W, X ) ), ~( 'c_Deriv_Oderiv'(
% 1.19/1.57 Y, T, U, X ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.19/1.57 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.19/1.57 hAPP( 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.57 ) ), Y ) ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.19/1.57 ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.19/1.57 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X )
% 1.19/1.57 ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ),
% 1.19/1.57 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.57 ), X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ),
% 1.19/1.57 'c_HOL_Oone__class_Oone'( X ) ), Y ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.57 ), 'c_HOL_Oone__class_Oone'( X ) ), Y ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.19/1.57 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.19/1.57 ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.19/1.57 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.57 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.19/1.57 'c_COMBS'( 'c_COMBB'( 'c_HOL_Ominus__class_Ominus'( X ), Y, X, 'tc_fun'(
% 1.19/1.57 X, X ), X ), Z, X, X, X ), T, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.19/1.57 ), U ), W ), X ), ~( 'c_Deriv_Oderiv'( Z, T, W, X ) ), ~(
% 1.19/1.57 'c_Deriv_Oderiv'( Y, T, U, X ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.19/1.57 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.19/1.57 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ), ~( hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.19/1.57 ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.19/1.57 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), Y ) ) ) ]
% 1.19/1.57 ,
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.19/1.57 'c_HOL_Oone__class_Oone'( X ) ) ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.57 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.19/1.57 'c_HOL_Oone__class_Oone'( X ) ) ), X ), Z ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.19/1.57 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ), hAPP( hAPP(
% 1.19/1.57 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), U ), Z ) ) ), hAPP( hAPP(
% 1.19/1.57 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.19/1.57 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.57 'c_Power_Opower__class_Opower'( X ), Y ), U ) ) ), Z ) ), =( Y,
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.57 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.19/1.57 hAPP( 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( X ), Y, X,
% 1.19/1.57 'tc_fun'( X, X ), X ), X, X, X ), Z ), T, hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Odivide'( X ), U ), Z ), X ), ~( 'c_Deriv_Oderiv'(
% 1.19/1.57 Y, T, U, X ) ) ],
% 1.19/1.57 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_SEQ_OLIMSEQ'(
% 1.19/1.57 'c_COMBS'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'(
% 1.19/1.57 X, X ), 'tc_nat' ), Z, 'tc_nat', X, X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_SEQ_OLIMSEQ'( Z,
% 1.19/1.57 U, X ) ), ~( 'c_SEQ_OLIMSEQ'( Y, T, X ) ) ],
% 1.19/1.57 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_Series_Osums'(
% 1.19/1.57 'c_COMBS'( 'c_COMBB'( 'c_HOL_Oplus__class_Oplus'( X ), Y, X, 'tc_fun'( X
% 1.19/1.57 , X ), 'tc_nat' ), Z, 'tc_nat', X, X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~( 'c_Series_Osums'( Z, U
% 1.19/1.57 , X ) ), ~( 'c_Series_Osums'( Y, T, X ) ) ],
% 1.19/1.57 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_SEQ_OLIMSEQ'(
% 1.19/1.57 'c_COMBS'( 'c_COMBB'( 'c_HOL_Oplus__class_Oplus'( X ), Y, X, 'tc_fun'( X
% 1.19/1.57 , X ), 'tc_nat' ), Z, 'tc_nat', X, X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~( 'c_SEQ_OLIMSEQ'( Z, U
% 1.19/1.57 , X ) ), ~( 'c_SEQ_OLIMSEQ'( Y, T, X ) ) ],
% 1.19/1.57 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_Series_Osums'(
% 1.19/1.57 hAPP( 'c_COMBC'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), Y, X,
% 1.19/1.57 'tc_fun'( X, X ), 'tc_nat' ), 'tc_nat', X, X ), Z ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_Series_Osums'( Y
% 1.19/1.57 , T, X ) ) ],
% 1.19/1.57 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_Series_Osums'(
% 1.19/1.57 hAPP( 'c_COMBC'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), Y, X,
% 1.19/1.57 'tc_fun'( X, X ), 'tc_nat' ), 'tc_nat', X, X ), Z ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_Series_Osums'( Y
% 1.19/1.57 , T, X ) ) ],
% 1.19/1.57 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_SEQ_OLIMSEQ'(
% 1.19/1.57 hAPP( 'c_COMBC'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), Y, X,
% 1.19/1.57 'tc_fun'( X, X ), 'tc_nat' ), 'tc_nat', X, X ), Z ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_SEQ_OLIMSEQ'( Y,
% 1.19/1.57 T, X ) ) ],
% 1.19/1.57 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_SEQ_OLIMSEQ'(
% 1.19/1.57 hAPP( 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oplus__class_Oplus'( X ), Y, X,
% 1.19/1.57 'tc_fun'( X, X ), 'tc_nat' ), 'tc_nat', X, X ), Z ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~( 'c_SEQ_OLIMSEQ'( Y, T
% 1.19/1.57 , X ) ) ],
% 1.19/1.57 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_SEQ_OLIMSEQ'(
% 1.19/1.57 'c_COMBS'( 'c_COMBB'( 'c_HOL_Ominus__class_Ominus'( X ), Y, X, 'tc_fun'(
% 1.19/1.57 X, X ), 'tc_nat' ), Z, 'tc_nat', X, X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( X ), T ), U ), X ), ~( 'c_SEQ_OLIMSEQ'( Z,
% 1.19/1.57 U, X ) ), ~( 'c_SEQ_OLIMSEQ'( Y, T, X ) ) ],
% 1.19/1.57 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_Series_Osums'(
% 1.19/1.57 'c_COMBS'( 'c_COMBB'( 'c_HOL_Ominus__class_Ominus'( X ), Y, X, 'tc_fun'(
% 1.19/1.57 X, X ), 'tc_nat' ), Z, 'tc_nat', X, X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( X ), T ), U ), X ), ~( 'c_Series_Osums'( Z
% 1.19/1.57 , U, X ) ), ~( 'c_Series_Osums'( Y, T, X ) ) ],
% 1.19/1.57 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_SEQ_OLIMSEQ'(
% 1.19/1.57 hAPP( 'c_COMBC'( 'c_COMBB'( 'c_HOL_Ominus__class_Ominus'( X ), Y, X,
% 1.19/1.57 'tc_fun'( X, X ), 'tc_nat' ), 'tc_nat', X, X ), Z ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( X ), T ), Z ), X ), ~( 'c_SEQ_OLIMSEQ'( Y,
% 1.19/1.57 T, X ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =(
% 1.19/1.57 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ), X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.19/1.57 Y, X ) ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), ~( hBOOL(
% 1.19/1.57 hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Z ), Y ) ) ) ],
% 1.19/1.57 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_SEQ_OLIMSEQ'(
% 1.19/1.57 hAPP( 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( X ), Y, X,
% 1.19/1.57 'tc_fun'( X, X ), 'tc_nat' ), 'tc_nat', X, X ), Z ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ), ~( 'c_SEQ_OLIMSEQ'(
% 1.19/1.57 Y, T, X ) ) ],
% 1.19/1.57 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Series_Osums'(
% 1.19/1.57 hAPP( 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( X ), Y, X,
% 1.19/1.57 'tc_fun'( X, X ), 'tc_nat' ), 'tc_nat', X, X ), Z ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ), ~( 'c_Series_Osums'(
% 1.19/1.57 Y, T, X ) ) ],
% 1.19/1.57 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Series_Osums'(
% 1.19/1.57 hAPP( 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( X ), Y, X,
% 1.19/1.57 'tc_fun'( X, X ), 'tc_nat' ), 'tc_nat', X, X ), Z ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ), ~( 'c_Series_Osums'(
% 1.19/1.57 Y, T, X ) ) ],
% 1.19/1.57 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_Series_Osums'(
% 1.19/1.57 'c_COMBB'( Y, hAPP( 'c_COMBC'( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.19/1.57 'tc_nat', 'tc_nat', 'tc_nat' ), Z ), 'tc_nat', X, 'tc_nat' ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( X ), T ), hAPP( hAPP(
% 1.19/1.57 'c_Finite__Set_Osetsum'( 'tc_nat', X ), Y ),
% 1.19/1.57 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 'tc_nat' ), Z, 'tc_nat' ) ) ), X ), ~( 'c_Series_Osums'( Y, T, X ) ) ]
% 1.19/1.57 ,
% 1.19/1.57 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), ~(
% 1.19/1.57 'class_Power_Opower'( X ) ), 'c_SEQ_OLIMSEQ'( hAPP( 'c_COMBC'( 'c_COMBB'(
% 1.19/1.57 'c_Power_Opower__class_Opower'( X ), Y, X, 'tc_fun'( 'tc_nat', X ),
% 1.19/1.57 'tc_nat' ), 'tc_nat', 'tc_nat', X ), Z ), hAPP( hAPP(
% 1.19/1.57 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~( 'c_SEQ_OLIMSEQ'( Y
% 1.19/1.57 , T, X ) ) ],
% 1.19/1.57 [ =( hAPP( hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat',
% 1.19/1.57 'tc_Complex_Ocomplex' ), hAPP( 'c_Power_Opower__class_Opower'(
% 1.19/1.57 'tc_Complex_Ocomplex' ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.19/1.57 'tc_Complex_Ocomplex' ), 'c_FFT__Mirabelle_Oroot'( X ) ), Y ) ) ),
% 1.19/1.57 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 'tc_nat' ), X, 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 'tc_Complex_Ocomplex' ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y,
% 1.19/1.57 'tc_nat' ), X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), Y ) ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), 'v_i' ), X ), 'tc_nat' ), 'v_n'
% 1.19/1.57 ) ) ],
% 1.19/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), 'v_i' ), 'tc_nat' ), 'v_n'
% 1.19/1.57 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), 'v_n' ) )
% 1.19/1.57 ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.57 ), Z ), T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.19/1.57 Y ), T ) ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.19/1.57 Z ), T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ),
% 1.19/1.57 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y
% 1.19/1.57 ), Z ) ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.19/1.57 Z ) ), Y ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.19/1.57 Z ) ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ),
% 1.19/1.57 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ), Y ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.57 ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( T, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.19/1.57 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.57 ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.19/1.57 Y ), T ) ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y
% 1.19/1.57 ), Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ), T ) ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.19/1.57 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y
% 1.19/1.57 ), Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.19/1.57 Z ) ), Y ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.57 ), Z ), T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.19/1.57 Y ), T ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y
% 1.19/1.57 ), Z ) ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.19/1.57 Z ) ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), hAPP(
% 1.19/1.57 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.57 ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) )
% 1.19/1.57 ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y
% 1.19/1.57 ), Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), hAPP(
% 1.19/1.57 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ), ~( hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.19/1.57 ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.57 ), Z ), T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.19/1.57 T ) ), Z ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.19/1.57 Z ) ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.57 ), T ), Z ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y
% 1.19/1.57 ), Z ) ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.19/1.57 T ), Z ) ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.19/1.57 Z ), T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y
% 1.19/1.57 ), T ) ), Z ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y
% 1.19/1.57 ), Z ) ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 X ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ),
% 1.19/1.57 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), Z ), T ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y
% 1.19/1.57 ), Z ) ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 X ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ),
% 1.19/1.57 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.57 ) ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), T ), Z ) ) ) ]
% 1.19/1.57 ,
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.19/1.57 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.57 'c_Power_Opower__class_Opower'( X ), T ), Z ) ) ), =( Y, T ), ~( hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.19/1.57 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ) ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.19/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.57 , Y ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ),
% 1.19/1.57 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ), ~( hBOOL(
% 1.19/1.57 hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.19/1.57 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.19/1.57 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.19/1.57 'c_COMBS'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'(
% 1.19/1.57 X, X ), X ), Z, X, X, X ), T, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.19/1.57 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), hAPP( Z, T ) ) ),
% 1.19/1.57 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), W ), hAPP( Y, T ) ) ), X )
% 1.19/1.57 , ~( 'c_Deriv_Oderiv'( Z, T, W, X ) ), ~( 'c_Deriv_Oderiv'( Y, T, U, X )
% 1.19/1.57 ) ],
% 1.19/1.57 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.19/1.57 'c_COMBS'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'(
% 1.19/1.57 X, X ), X ), Z, X, X, X ), T, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.19/1.57 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( Y, T ) ), U ) ),
% 1.19/1.57 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), W ), hAPP( Z, T ) ) ), X )
% 1.19/1.57 , ~( 'c_Deriv_Oderiv'( Z, T, U, X ) ), ~( 'c_Deriv_Oderiv'( Y, T, W, X )
% 1.19/1.57 ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.19/1.57 hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.19/1.57 ), Y ), Z ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T )
% 1.19/1.57 ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.19/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X
% 1.19/1.57 ), Y ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.19/1.57 hAPP( 'c_lessequals'( 'tc_nat' ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T )
% 1.19/1.57 , Y ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Z ) ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X
% 1.19/1.57 ), X ), T ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.19/1.57 hAPP( 'c_lessequals'( 'tc_nat' ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.57 'c_lessequals'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T )
% 1.19/1.57 , Y ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Z ) ) ) )
% 1.19/1.57 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X
% 1.19/1.57 ), X ), T ) ) ) ],
% 1.19/1.57 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_SEQ_OLIMSEQ'( Y
% 1.19/1.57 , Z, X ), ~( 'c_SEQ_OLIMSEQ'( 'c_COMBS'( 'c_COMBB'(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( X ), T, X, 'tc_fun'( X, X ), 'tc_nat' ), Y
% 1.19/1.57 , 'tc_nat', X, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.19/1.57 'c_SEQ_OLIMSEQ'( T, Z, X ) ) ],
% 1.19/1.57 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_SEQ_OLIMSEQ'( Y
% 1.19/1.57 , Z, X ), ~( 'c_SEQ_OLIMSEQ'( 'c_COMBS'( 'c_COMBB'(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( X ), Y, X, 'tc_fun'( X, X ), 'tc_nat' ), T
% 1.19/1.57 , 'tc_nat', X, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.19/1.57 'c_SEQ_OLIMSEQ'( T, Z, X ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), ~(
% 1.19/1.57 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.19/1.57 'c_Finite__Set_Osetsum'( 'tc_nat', X ), 'c_COMBS'( 'c_COMBB'(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_Power_Opower__class_Opower'(
% 1.19/1.57 X ), Y ), X, 'tc_fun'( X, X ), 'tc_nat' ), 'c_COMBB'( hAPP(
% 1.19/1.57 'c_Power_Opower__class_Opower'( X ), Z ), hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc', T ) ), 'tc_nat'
% 1.19/1.57 , X, 'tc_nat' ), 'tc_nat', X, X ) ),
% 1.19/1.57 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 'tc_nat' ), hAPP( 'c_Suc', T ), 'tc_nat' ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.19/1.57 'c_Finite__Set_Osetsum'( 'tc_nat', X ), 'c_COMBS'( 'c_COMBB'(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_Power_Opower__class_Opower'(
% 1.19/1.57 X ), Y ), X, 'tc_fun'( X, X ), 'tc_nat' ), 'c_COMBB'( hAPP(
% 1.19/1.57 'c_Power_Opower__class_Opower'( X ), Z ), hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), 'tc_nat', X, 'tc_nat' ),
% 1.19/1.57 'tc_nat', X, X ) ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', T ), 'tc_nat' ) )
% 1.19/1.57 ) ) ],
% 1.19/1.57 [ ~( 'class_Power_Opower'( X ) ), ~(
% 1.19/1.57 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.57 'c_Finite__Set_Osetsum'( 'tc_nat', X ), 'c_COMBS'( 'c_COMBB'(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_Power_Opower__class_Opower'(
% 1.19/1.57 X ), Y ), X, 'tc_fun'( X, X ), 'tc_nat' ), 'c_COMBB'( hAPP(
% 1.19/1.57 'c_Power_Opower__class_Opower'( X ), Z ), hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), 'tc_nat', X, 'tc_nat' ),
% 1.19/1.57 'tc_nat', X, X ) ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', T ), 'tc_nat' ) )
% 1.19/1.57 , hAPP( hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat', X ), 'c_COMBS'(
% 1.19/1.57 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), 'c_COMBB'( hAPP(
% 1.19/1.57 'c_Power_Opower__class_Opower'( X ), Y ), hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), 'tc_nat', X, 'tc_nat' ), X
% 1.19/1.57 , 'tc_fun'( X, X ), 'tc_nat' ), hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.19/1.57 , Z ), 'tc_nat', X, X ) ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', T ), 'tc_nat' ) )
% 1.19/1.57 ) ],
% 1.19/1.57 [ =( 'c_FFT__Mirabelle_OIDFT'( X, Y, 'v_i' ), hAPP( hAPP(
% 1.19/1.57 'c_Finite__Set_Osetsum'( 'tc_nat', 'tc_Complex_Ocomplex' ), 'c_COMBS'(
% 1.19/1.57 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( 'tc_Complex_Ocomplex' ), Y,
% 1.19/1.57 'tc_Complex_Ocomplex', 'tc_fun'( 'tc_Complex_Ocomplex',
% 1.19/1.57 'tc_Complex_Ocomplex' ), 'tc_nat' ), 'c_COMBB'( hAPP(
% 1.19/1.57 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.19/1.57 'c_FFT__Mirabelle_Oroot'( X ) ), hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.57 'tc_nat' ), 'v_i' ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ),
% 1.19/1.57 'tc_nat', 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ) ),
% 1.19/1.57 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 'tc_nat' ), X, 'tc_nat' ) ) ) ],
% 1.19/1.57 [ =( 'c_FFT__Mirabelle_ODFT'( X, Y, 'v_i' ), hAPP( hAPP(
% 1.19/1.57 'c_Finite__Set_Osetsum'( 'tc_nat', 'tc_Complex_Ocomplex' ), 'c_COMBS'(
% 1.19/1.57 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( 'tc_Complex_Ocomplex' ),
% 1.19/1.57 'c_COMBB'( hAPP( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' )
% 1.19/1.57 , 'c_FFT__Mirabelle_Oroot'( X ) ), hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.57 'tc_nat' ), 'v_i' ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ),
% 1.19/1.57 'tc_Complex_Ocomplex', 'tc_fun'( 'tc_Complex_Ocomplex',
% 1.19/1.57 'tc_Complex_Ocomplex' ), 'tc_nat' ), Y, 'tc_nat', 'tc_Complex_Ocomplex',
% 1.19/1.57 'tc_Complex_Ocomplex' ) ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ) ],
% 1.19/1.57 [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.57 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 'c_Finite__Set_Osetsum'(
% 1.19/1.57 'tc_nat', X ), Y ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.19/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ) ), hAPP( hAPP(
% 1.19/1.57 'c_HOL_Otimes__class_Otimes'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.19/1.57 Z, X ) ), T ) ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat', X ), hAPP(
% 1.19/1.57 'c_COMBC'( 'c_COMBB'( 'c_HOL_Ominus__class_Ominus'( X ), Y, X, 'tc_fun'(
% 1.19/1.57 X, X ), 'tc_nat' ), 'tc_nat', X, X ), T ) ),
% 1.19/1.57 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.57 'tc_nat' ), Z, 'tc_nat' ) ) ) ],
% 1.19/1.57 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_Finite__Set_Osetsum'( 'tc_nat', X ), 'c_COMBB'( Y, hAPP( 'c_COMBC'(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'tc_nat', 'tc_nat', 'tc_nat' ), Z
% 1.19/1.58 ), 'tc_nat', X, 'tc_nat' ) ),
% 1.19/1.58 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.58 'tc_nat' ), T, 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.19/1.58 ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat', X ), Y ),
% 1.19/1.58 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.58 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), Z )
% 1.19/1.58 , 'tc_nat' ) ) ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat', X ), Y )
% 1.19/1.58 , 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ) ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_Finite__Set_Osetsum'( 'tc_nat', X ), Y ),
% 1.19/1.58 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.58 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T )
% 1.19/1.58 , 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.58 'c_Finite__Set_Osetsum'( 'tc_nat', X ), 'c_COMBB'( Y, hAPP( 'c_COMBC'(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'tc_nat', 'tc_nat', 'tc_nat' ), T
% 1.19/1.58 ), 'tc_nat', X, 'tc_nat' ) ),
% 1.19/1.58 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.58 'tc_nat' ), Z, 'tc_nat' ) ) ), hAPP( hAPP( 'c_Finite__Set_Osetsum'(
% 1.19/1.58 'tc_nat', X ), Y ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), T, 'tc_nat' ) ) ) ) ],
% 1.19/1.58 [ ~( 'class_RealVector_Oreal__normed__algebra__1'( X ) ), =(
% 1.19/1.58 'c_Series_Osuminf'( 'c_COMBS'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X
% 1.19/1.58 ), Y, X, 'tc_fun'( X, X ), 'tc_nat' ), hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.19/1.58 'tc_nat', X, X ), X ), hAPP( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.19/1.58 ) ],
% 1.19/1.58 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.19/1.58 'c_COMBS'( 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( X ), Y, X,
% 1.19/1.58 'tc_fun'( X, X ), X ), Z, X, X, X ), T, hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), U ), hAPP( Z, T ) ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( Y, T ) ), W ) ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( Z, T ) ), hAPP( Z, T ) ) ), X )
% 1.19/1.58 , =( hAPP( Z, T ), 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Deriv_Oderiv'(
% 1.19/1.58 Z, T, W, X ) ), ~( 'c_Deriv_Oderiv'( Y, T, U, X ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( 'tc_nat' ), T ), Z ) ) ), =( Y,
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.19/1.58 'c_Groebner__Basis_Ogb__semiring'( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_Power_Opower__class_Opower'( X ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.19/1.58 ,
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.19/1.58 X ) ), 'c_Groebner__Basis_Osemiringb'( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_Power_Opower__class_Opower'( X ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.19/1.58 ,
% 1.19/1.58 [ ~( 'class_Archimedean__Field_Oarchimedean__field'( X ) ),
% 1.19/1.58 'c_Archimedean__Field_Oarchimedean__field__axioms'(
% 1.19/1.58 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ominus__class_Ominus'( X ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ),
% 1.19/1.58 'c_lessequals'( X ), X ) ],
% 1.19/1.58 [ =( hAPP( hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat',
% 1.19/1.58 'tc_Complex_Ocomplex' ), hAPP( 'c_Power_Opower__class_Opower'(
% 1.19/1.58 'tc_Complex_Ocomplex' ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.19/1.58 'tc_Complex_Ocomplex' ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.19/1.58 'tc_Complex_Ocomplex' ), 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex'
% 1.19/1.58 ) ), 'c_FFT__Mirabelle_Oroot'( X ) ) ), Y ) ) ),
% 1.19/1.58 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.58 'tc_nat' ), X, 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.58 'tc_Complex_Ocomplex' ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y,
% 1.19/1.58 'tc_nat' ), X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), Y ) ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_Finite__Set_Osetsum'( 'tc_nat', X ), Y ),
% 1.19/1.58 'c_SetInterval_Oord__class_OatLeastLessThan'( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), U ), T ), 'tc_nat' ) ), hAPP(
% 1.19/1.58 hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat', X ), 'c_COMBB'( Y, hAPP(
% 1.19/1.58 'c_COMBC'( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'tc_nat', 'tc_nat',
% 1.19/1.58 'tc_nat' ), T ), 'tc_nat', X, 'tc_nat' ) ),
% 1.19/1.58 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, U, 'tc_nat' ) ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( 't_a' ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( 't_a' ), hAPP( hAPP( 'c_Finite__Set_Osetsum'(
% 1.19/1.58 'tc_nat', 't_a' ), X ), 'c_SetInterval_Oord__class_OatLeastLessThan'( Y,
% 1.19/1.58 Z, 'tc_nat' ) ) ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat', 't_a' )
% 1.19/1.58 , T ), 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, U, 'tc_nat' ) ) )
% 1.19/1.58 , hAPP( hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat', 't_a' ), W ),
% 1.19/1.58 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, U, 'tc_nat' ) ) ), hBOOL(
% 1.19/1.58 hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Z ),
% 1.19/1.58 'v_sko__FFT__Mirabelle__Xsetsum__add__split__nat__ivl__2'( W, T, Z, U ) )
% 1.19/1.58 ), hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Y ),
% 1.19/1.58 'v_sko__FFT__Mirabelle__Xsetsum__add__split__nat__ivl__2'( W, X, Y, Z ) )
% 1.19/1.58 ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Z ), U ) ) ), ~(
% 1.19/1.58 hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( 't_a' ) ), ~( =( hAPP( X,
% 1.19/1.58 'v_sko__FFT__Mirabelle__Xsetsum__add__split__nat__ivl__2'( Y, X, Z, T ) )
% 1.19/1.58 , hAPP( Y, 'v_sko__FFT__Mirabelle__Xsetsum__add__split__nat__ivl__2'( Y,
% 1.19/1.58 X, Z, T ) ) ) ), ~( =( hAPP( U,
% 1.19/1.58 'v_sko__FFT__Mirabelle__Xsetsum__add__split__nat__ivl__2'( Y, U, W, Z ) )
% 1.19/1.58 , hAPP( Y, 'v_sko__FFT__Mirabelle__Xsetsum__add__split__nat__ivl__2'( Y,
% 1.19/1.58 U, W, Z ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Z ), T
% 1.19/1.58 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), W ), Z ) ) ),
% 1.19/1.58 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 't_a' ), hAPP( hAPP(
% 1.19/1.58 'c_Finite__Set_Osetsum'( 'tc_nat', 't_a' ), U ),
% 1.19/1.58 'c_SetInterval_Oord__class_OatLeastLessThan'( W, Z, 'tc_nat' ) ) ), hAPP(
% 1.19/1.58 hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat', 't_a' ), X ),
% 1.19/1.58 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ) ) ), hAPP(
% 1.19/1.58 hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat', 't_a' ), Y ),
% 1.19/1.58 'c_SetInterval_Oord__class_OatLeastLessThan'( W, T, 'tc_nat' ) ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( 't_a' ) ), ~( =( hAPP( X,
% 1.19/1.58 'v_sko__FFT__Mirabelle__Xsetsum__add__split__nat__ivl__2'( Y, X, Z, T ) )
% 1.19/1.58 , hAPP( Y, 'v_sko__FFT__Mirabelle__Xsetsum__add__split__nat__ivl__2'( Y,
% 1.19/1.58 X, Z, T ) ) ) ), hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), U ),
% 1.19/1.58 'v_sko__FFT__Mirabelle__Xsetsum__add__split__nat__ivl__2'( Y, W, U, Z ) )
% 1.19/1.58 ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.19/1.58 hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), U ), Z ) ) ), =( hAPP(
% 1.19/1.58 hAPP( 'c_HOL_Oplus__class_Oplus'( 't_a' ), hAPP( hAPP(
% 1.19/1.58 'c_Finite__Set_Osetsum'( 'tc_nat', 't_a' ), W ),
% 1.19/1.58 'c_SetInterval_Oord__class_OatLeastLessThan'( U, Z, 'tc_nat' ) ) ), hAPP(
% 1.19/1.58 hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat', 't_a' ), X ),
% 1.19/1.58 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ) ) ), hAPP(
% 1.19/1.58 hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat', 't_a' ), Y ),
% 1.19/1.58 'c_SetInterval_Oord__class_OatLeastLessThan'( U, T, 'tc_nat' ) ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( 't_a' ) ), ~( =( hAPP( X,
% 1.19/1.58 'v_sko__FFT__Mirabelle__Xsetsum__add__split__nat__ivl__2'( Y, X, Z, T ) )
% 1.19/1.58 , hAPP( Y, 'v_sko__FFT__Mirabelle__Xsetsum__add__split__nat__ivl__2'( Y,
% 1.19/1.58 X, Z, T ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), T ), U
% 1.19/1.58 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Z ), T ) ) ),
% 1.19/1.58 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 't_a' ), hAPP( hAPP(
% 1.19/1.58 'c_Finite__Set_Osetsum'( 'tc_nat', 't_a' ), X ),
% 1.19/1.58 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ) ) ), hAPP(
% 1.19/1.58 hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat', 't_a' ), W ),
% 1.19/1.58 'c_SetInterval_Oord__class_OatLeastLessThan'( T, U, 'tc_nat' ) ) ), hAPP(
% 1.19/1.58 hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat', 't_a' ), Y ),
% 1.19/1.58 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, U, 'tc_nat' ) ) ), hBOOL(
% 1.19/1.58 hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), T ),
% 1.19/1.58 'v_sko__FFT__Mirabelle__Xsetsum__add__split__nat__ivl__2'( Y, W, T, U ) )
% 1.19/1.58 ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), ~( =( hAPP( Y,
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.19/1.58 ) ), =( hAPP( hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat', X ), Y ),
% 1.19/1.58 'c_SetInterval_Oord__class_OatLeastLessThan'( hAPP( 'c_Suc',
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z, 'tc_nat' ) ), hAPP( hAPP(
% 1.19/1.58 'c_Finite__Set_Osetsum'( 'tc_nat', X ), Y ),
% 1.19/1.58 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.58 'tc_nat' ), Z, 'tc_nat' ) ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc', Z ) ), T ) ),
% 1.19/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), T ) ) ), Y ) ), ~( hBOOL(
% 1.19/1.58 hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), T ), Z ) ) ) ],
% 1.19/1.58 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_SEQ_OLIMSEQ'(
% 1.19/1.58 'c_COMBS'( 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( X ), Y, X,
% 1.19/1.58 'tc_fun'( X, X ), 'tc_nat' ), Z, 'tc_nat', X, X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ), X ), =( U,
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_SEQ_OLIMSEQ'( Z, U, X ) ), ~(
% 1.19/1.58 'c_SEQ_OLIMSEQ'( Y, T, X ) ) ],
% 1.19/1.58 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.19/1.58 'c_COMBS'( 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( X ), Y, X,
% 1.19/1.58 'tc_fun'( X, X ), X ), Z, X, X, X ), T, hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), U ), hAPP( Z, T ) ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), W ), hAPP( Y, T ) ) ) ), hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), hAPP( Z, T ) ), hAPP( 'c_Suc', hAPP(
% 1.19/1.58 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ), X ), =( hAPP( Z
% 1.19/1.58 , T ), 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Deriv_Oderiv'( Z, T, W, X
% 1.19/1.58 ) ), ~( 'c_Deriv_Oderiv'( Y, T, U, X ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_Finite__Set_Osetsum'( 'tc_nat', X ), Y ),
% 1.19/1.58 'c_SetInterval_Oord__class_OatLeastLessThan'( hAPP( 'c_Suc', Z ), hAPP(
% 1.19/1.58 'c_Suc', T ), 'tc_nat' ) ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat'
% 1.19/1.58 , X ), 'c_COMBB'( Y, 'c_Suc', 'tc_nat', X, 'tc_nat' ) ),
% 1.19/1.58 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.19/1.58 hAPP( 'c_Power_Opower__class_Opower'( X ), T ), hAPP( 'c_Suc', Z ) ) ) )
% 1.19/1.58 , =( Y, T ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL(
% 1.19/1.58 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', T ) ) ), hAPP(
% 1.19/1.58 hAPP( 'c_Power_Opower__class_Opower'( X ), Z ), hAPP( 'c_Suc', T ) ) ) )
% 1.19/1.58 ) ],
% 1.19/1.58 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc', X ) ), Y ) ),
% 1.19/1.58 hAPP( 'c_Suc', Z ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.19/1.58 ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z )
% 1.19/1.58 ) ],
% 1.19/1.58 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.19/1.58 , X ) ), hAPP( 'c_Suc', Y ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.19/1.58 'tc_nat' ), X ), Y ) ) ],
% 1.19/1.58 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( 'c_Suc', X ) ),
% 1.19/1.58 hAPP( 'c_Suc', X ) ) ) ],
% 1.19/1.58 [ ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), Y ) ) ), ~(
% 1.19/1.58 hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( 'c_Suc', Y ) ), X )
% 1.19/1.58 ) ) ],
% 1.19/1.58 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( 'c_Suc', X ) ), Y
% 1.19/1.58 ) ), hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Y ), X ) ) ],
% 1.19/1.58 [ =( X, hAPP( 'c_Suc', Y ) ), hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.19/1.58 'tc_nat' ), X ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' )
% 1.19/1.58 , X ), hAPP( 'c_Suc', Y ) ) ) ) ],
% 1.19/1.58 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), hAPP( 'c_Suc', Y )
% 1.19/1.58 ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), Y ) ) ) ]
% 1.19/1.58 ,
% 1.19/1.58 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), Y ) ), ~( hBOOL(
% 1.19/1.58 hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( 'c_Suc', X ) ), Y ) ) ) ]
% 1.19/1.58 ,
% 1.19/1.58 [ ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( 'c_Suc', X ) )
% 1.19/1.58 , X ) ) ) ],
% 1.19/1.58 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( 'c_Suc', X ) ),
% 1.19/1.58 hAPP( 'c_Suc', Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' )
% 1.19/1.58 , X ), Y ) ) ) ],
% 1.19/1.58 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), Y ) ), ~( hBOOL(
% 1.19/1.58 hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( 'c_Suc', X ) ), hAPP(
% 1.19/1.58 'c_Suc', Y ) ) ) ) ],
% 1.19/1.58 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ]
% 1.19/1.58 ,
% 1.19/1.58 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ]
% 1.19/1.58 ,
% 1.19/1.58 [ ~( =( hAPP( 'c_Suc', X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.19/1.58 ,
% 1.19/1.58 [ ~( =( hAPP( 'c_Suc', X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.19/1.58 ,
% 1.19/1.58 [ ~( =( X, hAPP( 'c_Suc', X ) ) ) ],
% 1.19/1.58 [ ~( =( hAPP( 'c_Suc', X ), X ) ) ],
% 1.19/1.58 [ ~( =( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ) ) ), =( X, Y ) ],
% 1.19/1.58 [ ~( =( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ) ) ), =( X, Y ) ],
% 1.19/1.58 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_Series_Osums'(
% 1.19/1.58 Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( Y,
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X ), ~( 'c_Series_Osums'(
% 1.19/1.58 'c_COMBB'( Y, 'c_Suc', 'tc_nat', X, 'tc_nat' ), Z, X ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_Finite__Set_Osetsum'( 'tc_nat', X ), Y ),
% 1.19/1.58 'c_SetInterval_Oord__class_OatLeastAtMost'( Z, T, 'tc_nat' ) ), hAPP(
% 1.19/1.58 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( Y, Z ) ), hAPP( hAPP(
% 1.19/1.58 'c_Finite__Set_Osetsum'( 'tc_nat', X ), Y ),
% 1.19/1.58 'c_SetInterval_Oord__class_OatLeastAtMost'( hAPP( 'c_Suc', Z ), T,
% 1.19/1.58 'tc_nat' ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Z ),
% 1.19/1.58 T ) ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_Finite__Set_Osetsum'( 'tc_nat', X ), Y ),
% 1.19/1.58 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, hAPP( 'c_Suc', T ),
% 1.19/1.58 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ), ~( hBOOL( hAPP(
% 1.19/1.58 'c_HOL_Oord__class_Oless'( T, 'tc_nat' ), Z ) ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_Finite__Set_Osetsum'( 'tc_nat', X ), Y ),
% 1.19/1.58 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, hAPP( 'c_Suc', T ),
% 1.19/1.58 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.58 'c_Finite__Set_Osetsum'( 'tc_nat', X ), Y ),
% 1.19/1.58 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ) ) ), hAPP(
% 1.19/1.58 Y, T ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, 'tc_nat' ), Z ) )
% 1.19/1.58 ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_Finite__Set_Osetsum'( 'tc_nat', X ), Y ),
% 1.19/1.58 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ) ), hAPP(
% 1.19/1.58 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( Y, Z ) ), hAPP( hAPP(
% 1.19/1.58 'c_Finite__Set_Osetsum'( 'tc_nat', X ), Y ),
% 1.19/1.58 'c_SetInterval_Oord__class_OatLeastLessThan'( hAPP( 'c_Suc', Z ), T,
% 1.19/1.58 'tc_nat' ) ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, 'tc_nat'
% 1.19/1.58 ), T ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.19/1.58 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.19/1.58 hAPP( 'c_Suc', Y ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.19/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.19/1.58 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.19/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.19/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.19/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ) ) ],
% 1.19/1.58 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.19/1.58 , X ) ), Y ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.19/1.58 'tc_nat' ), X ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat'
% 1.19/1.58 ), Y ), X ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ), ~(
% 1.19/1.58 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ) ), hAPP(
% 1.19/1.58 hAPP( 'c_Power_Opower__class_Opower'( X ), T ), hAPP( 'c_Suc', Z ) ) ),
% 1.19/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.58 'c_Finite__Set_Osetsum'( 'tc_nat', X ), 'c_COMBS'( 'c_COMBB'(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_Power_Opower__class_Opower'(
% 1.19/1.58 X ), Y ), X, 'tc_fun'( X, X ), 'tc_nat' ), 'c_COMBB'( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), T ), hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), 'tc_nat', X, 'tc_nat' ),
% 1.19/1.58 'tc_nat', X, X ) ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', Z ), 'tc_nat' ) )
% 1.19/1.58 ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), Z ) ), =( Z,
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.19/1.58 ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), Z ) ) )
% 1.19/1.58 , hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), T ), Z ) ), =( Y,
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.58 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP(
% 1.19/1.58 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Y ), ~( hBOOL(
% 1.19/1.58 hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Y ), X ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.58 , Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) )
% 1.19/1.58 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.58 X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.19/1.58 X ), Y ), T ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.58 , Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) )
% 1.19/1.58 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.58 X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.19/1.58 X ), Y ), T ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ), =( U,
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.19/1.58 ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.58 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.19/1.58 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.19/1.58 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.19/1.58 , Y ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.19/1.58 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.19/1.58 , Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.19/1.58 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.19/1.58 , Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.19/1.58 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.19/1.58 , Y ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.58 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.19/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.58 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.19/1.58 ) ) ],
% 1.19/1.58 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.58 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.19/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.19/1.58 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.58 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.19/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.19/1.58 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.58 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.19/1.58 ) ) ],
% 1.19/1.58 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.58 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.19/1.58 ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.58 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.19/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), 'c_HOL_Oone__class_Oone'(
% 1.19/1.58 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, Z ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.19/1.58 hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.19/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ),
% 1.19/1.58 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.58 ) ), Y ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.19/1.58 hAPP( hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.19/1.58 ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL(
% 1.19/1.58 hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.19/1.58 ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.19/1.58 hAPP( hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.19/1.58 ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.19/1.58 hAPP( hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.19/1.58 ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL(
% 1.19/1.58 hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.19/1.58 ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y
% 1.19/1.58 ), Z ) ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ) )
% 1.19/1.58 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), T ), Y ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y
% 1.19/1.58 ), Z ) ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ) )
% 1.19/1.58 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.58 X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ]
% 1.19/1.58 ,
% 1.19/1.58 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.19/1.58 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), U ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.19/1.58 ), Z ), Y ) ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.19/1.58 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), Z ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.19/1.58 ), U ), T ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y
% 1.19/1.58 , X ), Z ), T ) ), U ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y, X ), hAPP(
% 1.19/1.58 'c_COMBC'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), Z, X, 'tc_fun'(
% 1.19/1.58 X, X ), Y ), Y, X, X ), U ) ), T ) ) ],
% 1.19/1.58 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y
% 1.19/1.58 , X ), Z ), T ) ), U ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y, X ), hAPP(
% 1.19/1.58 'c_COMBC'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), Z, X, 'tc_fun'(
% 1.19/1.58 X, X ), Y ), Y, X, X ), U ) ), T ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.19/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), Y ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Finite__Set_Osetsum'(
% 1.19/1.58 'tc_nat', X ), Y ), 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T,
% 1.19/1.58 'tc_nat' ) ) ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat', X ), Y ),
% 1.19/1.58 'c_SetInterval_Oord__class_OatLeastLessThan'( T, U, 'tc_nat' ) ) ), hAPP(
% 1.19/1.58 hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat', X ), Y ),
% 1.19/1.58 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, U, 'tc_nat' ) ) ), ~(
% 1.19/1.58 hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), T ), U ) ) ), ~( hBOOL(
% 1.19/1.58 hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.19/1.58 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.58 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.19/1.58 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.58 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.19/1.58 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ), =( T, U ), =( Z,
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.19/1.58 Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), ~(
% 1.19/1.58 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.58 X ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), T ), Y ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.19/1.58 Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~(
% 1.19/1.58 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.58 X ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), T ), Z ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.19/1.58 Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), ~(
% 1.19/1.58 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.19/1.58 , Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.19/1.58 Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~(
% 1.19/1.58 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.19/1.58 , Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), T ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.19/1.58 Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~(
% 1.19/1.58 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.19/1.58 , Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), T ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ),
% 1.19/1.58 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.58 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.58 X ) ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.19/1.58 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.58 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.58 X ) ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ),
% 1.19/1.58 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.19/1.58 , Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.58 X ) ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.19/1.58 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.19/1.58 , Y ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.58 X ) ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.19/1.58 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.19/1.58 ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.58 'tc_nat' ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.19/1.58 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.19/1.58 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.19/1.58 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.19/1.58 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.58 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.19/1.58 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.58 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 1.19/1.58 =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.58 ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.19/1.58 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.19/1.58 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.19/1.58 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.58 ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.19/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.19/1.58 , hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), Y ), T ) ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.19/1.58 , hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.19/1.58 ), T ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ) ]
% 1.19/1.58 ,
% 1.19/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.19/1.58 , hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), Z ), T ) ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.19/1.58 , hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T
% 1.19/1.58 ), Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ) ) ]
% 1.19/1.58 ,
% 1.19/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ), hBOOL(
% 1.19/1.58 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.58 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) )
% 1.19/1.58 ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ), hBOOL(
% 1.19/1.58 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.58 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) )
% 1.19/1.58 ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), T ) ) ) ],
% 1.19/1.58 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.19/1.58 X ), Z ), Y ) ) ) ],
% 1.19/1.58 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Y ), X )
% 1.19/1.58 ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), Y ) ) ) ]
% 1.19/1.58 ,
% 1.19/1.58 [ ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ],
% 1.19/1.58 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), Z ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.19/1.58 X ), Y ), Z ) ) ) ],
% 1.19/1.58 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), Z ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.19/1.58 X ), Y ), Z ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.19/1.58 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.19/1.58 ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), Y ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), Y ), Z ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y, hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), Z ) ), =( Z,
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), Z ), Y ), =( Z,
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ),
% 1.19/1.58 'c_HOL_Oone__class_Oone'( X ) ), Y ) ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.19/1.58 ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL(
% 1.19/1.58 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.19/1.58 ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.58 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' )
% 1.19/1.58 , 'c_FFT__Mirabelle_Oroot'( X ) ), X ), 'c_HOL_Oone__class_Oone'(
% 1.19/1.58 'tc_Complex_Ocomplex' ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), U ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.19/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.58 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.19/1.58 ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.19/1.58 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 1.19/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.58 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.19/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.58 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.19/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.58 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ) ],
% 1.19/1.58 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.19/1.58 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.19/1.58 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ), =( Z,
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.19/1.58 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.19/1.58 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ), =( Y,
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.19/1.58 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.58 ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 'c_Finite__Set_Osetsum'(
% 1.19/1.58 'tc_nat', X ), Y ), 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T,
% 1.19/1.58 'tc_nat' ) ) ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat', X ), Y ),
% 1.19/1.58 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, U, 'tc_nat' ) ) ), hAPP(
% 1.19/1.58 hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat', X ), Y ),
% 1.19/1.58 'c_SetInterval_Oord__class_OatLeastLessThan'( U, T, 'tc_nat' ) ) ), ~(
% 1.19/1.58 hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), U ), T ) ) ), ~( hBOOL(
% 1.19/1.58 hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Z ), U ) ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.58 X ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.58 X ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.19/1.58 , Y ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), T ) ), =( T,
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.58 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.19/1.58 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.19/1.58 Z ) ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ),
% 1.19/1.58 'c_HOL_Oone__class_Oone'( X ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.19/1.58 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.19/1.58 Z ) ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ),
% 1.19/1.58 'c_HOL_Oone__class_Oone'( X ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.19/1.58 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.19/1.58 ), Y ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.19/1.58 ,
% 1.19/1.58 [ =( 'c_FFT__Mirabelle_Oroot'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.19/1.58 , 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.19/1.58 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 1.19/1.58 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =( hAPP(
% 1.19/1.58 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.19/1.58 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.19/1.58 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.58 , Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.19/1.58 hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.19/1.58 ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.19/1.58 , Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL(
% 1.19/1.58 hAPP( hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.19/1.58 ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.19/1.58 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.58 X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ),
% 1.19/1.58 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.58 ) ), Y ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.19/1.58 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.58 X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ),
% 1.19/1.58 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.19/1.58 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.58 X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ),
% 1.19/1.58 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.58 ) ), Y ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.19/1.58 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.58 X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ),
% 1.19/1.58 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.19/1.58 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.58 X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ),
% 1.19/1.58 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.58 ) ), Z ) ) ) ],
% 1.19/1.58 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.19/1.58 'c_Finite__Set_Osetsum'( Z, X ), T ), U ) ), hAPP( hAPP(
% 1.19/1.58 'c_Finite__Set_Osetsum'( Z, X ), 'c_COMBB'( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T, X, X, Z ) ), U ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.19/1.58 'c_Finite__Set_Osetsum'( Z, X ), T ), U ) ), hAPP( hAPP(
% 1.19/1.58 'c_Finite__Set_Osetsum'( Z, X ), 'c_COMBB'( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T, X, X, Z ) ), U ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.19/1.58 ), Y ), Z ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T )
% 1.19/1.58 ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Oone__class_Oone'(
% 1.19/1.58 X ) ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Z ), T
% 1.19/1.58 ) ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y )
% 1.19/1.58 , 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.19/1.58 hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.19/1.58 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL(
% 1.19/1.58 hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.19/1.58 ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ), ~(
% 1.19/1.58 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_Finite__Set_Osetsum'( 'tc_nat', X ), hAPP( 'c_COMBC'( 'c_COMBB'(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), 'c_COMBS'( 'c_COMBB'(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_COMBB'( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), 'tc_nat', X, 'tc_nat' ), X
% 1.19/1.58 , 'tc_fun'( X, X ), 'tc_nat' ), hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.19/1.58 , Y ), 'tc_nat', X, X ), X, 'tc_fun'( X, X ), 'tc_nat' ), 'tc_nat', X, X
% 1.19/1.58 ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ),
% 1.19/1.58 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.58 'tc_nat' ), T, 'tc_nat' ) ), hAPP( hAPP( 'c_Finite__Set_Osetsum'(
% 1.19/1.58 'tc_nat', X ), 'c_COMBS'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.19/1.58 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), X, 'tc_fun'( X, X ),
% 1.19/1.58 'tc_nat' ), 'c_COMBS'( 'c_COMBB'( 'c_HOL_Ominus__class_Ominus'( X ),
% 1.19/1.58 'c_COMBB'( hAPP( 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), 'tc_nat', X, 'tc_nat' ), X
% 1.19/1.58 , 'tc_fun'( X, X ), 'tc_nat' ), 'c_COMBB'( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), Y ), hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), 'tc_nat', X, 'tc_nat' ),
% 1.19/1.58 'tc_nat', X, X ), 'tc_nat', X, X ) ),
% 1.19/1.58 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.58 'tc_nat' ), T, 'tc_nat' ) ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ), hBOOL(
% 1.19/1.58 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.58 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.19/1.58 ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), U ) ) ), ~( hBOOL(
% 1.19/1.58 hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ), ~(
% 1.19/1.58 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.19/1.58 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.19/1.58 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.19/1.58 ],
% 1.19/1.58 [ ~( 'class_RealVector_Oreal__field'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), W ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.58 X ), Y ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), Z ), U ) ), W ) ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ) ), W ) ), U ) ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_Finite__Set_Osetsum'( Y, X ), 'c_COMBS'( 'c_COMBB'(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), Z, X, 'tc_fun'( X, X ), Y ), T, Y, X,
% 1.19/1.58 X ) ), U ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.19/1.58 'c_Finite__Set_Osetsum'( Y, X ), Z ), U ) ), hAPP( hAPP(
% 1.19/1.58 'c_Finite__Set_Osetsum'( Y, X ), T ), U ) ) ) ],
% 1.19/1.58 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.19/1.58 [ ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( 'tc_nat' ), X ), Y ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.58 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.19/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.58 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T
% 1.19/1.58 ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( X ), 'c_HOL_Oone__class_Oone'( X ) ), hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.58 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.19/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( hAPP(
% 1.19/1.58 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T ), W ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.58 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.19/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( T, hAPP(
% 1.19/1.58 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), U ), Y ) ), Z ) ), W ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.19/1.58 ), Y ), Z ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T )
% 1.19/1.58 ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ),
% 1.19/1.58 'c_HOL_Oone__class_Oone'( X ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.19/1.58 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( 'tc_nat' ), T ), Z ) ) ) ],
% 1.19/1.58 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP( 'c_Finite__Set_Osetsum'(
% 1.19/1.58 Y, X ), Z ), T ) ), U ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y, X ),
% 1.19/1.58 hAPP( 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( X ), Z, X,
% 1.19/1.58 'tc_fun'( X, X ), Y ), Y, X, X ), U ) ), T ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP( 'c_Finite__Set_Osetsum'(
% 1.19/1.58 Y, X ), Z ), T ) ), U ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y, X ),
% 1.19/1.58 hAPP( 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( X ), Z, X,
% 1.19/1.58 'tc_fun'( X, X ), Y ), Y, X, X ), U ) ), T ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL(
% 1.19/1.58 hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.19/1.58 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ), hBOOL(
% 1.19/1.58 hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.19/1.58 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ) ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL(
% 1.19/1.58 hAPP( hAPP( 'c_lessequals'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.19/1.58 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ), hBOOL(
% 1.19/1.58 hAPP( hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.19/1.58 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ) ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.58 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.19/1.58 Y ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.19/1.58 ), Y ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.19/1.58 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.58 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.19/1.58 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.19/1.58 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.58 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.19/1.58 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.58 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.19/1.58 ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ), =( U,
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.19/1.58 ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y, hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), Z ) ), =( Z,
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), Z ), Y ), =( Z,
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.19/1.58 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.19/1.58 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.19/1.58 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.58 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.19/1.58 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.58 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.19/1.58 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.58 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.19/1.58 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.58 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.19/1.58 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.19/1.58 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.19/1.58 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.19/1.58 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.19/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.19/1.58 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.19/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.58 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.58 X ), Y ), Z ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.19/1.58 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.19/1.58 ) ), Z ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.58 X ), Z ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( 'tc_nat' ), T ), Z ) ) ), =( Y,
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X )
% 1.19/1.58 , Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), Y ), Z ) ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ),
% 1.19/1.58 Z ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL(
% 1.19/1.58 hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.19/1.58 ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.19/1.58 hAPP( hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.19/1.58 ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.19/1.58 ), Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~(
% 1.19/1.58 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.58 X ) ) ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.19/1.58 ), Y ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ), =( Z,
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.58 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.58 'tc_nat' ) ) ) ],
% 1.19/1.58 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), Y ), Y ) ) ],
% 1.19/1.58 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.19/1.58 X ), Y ), Y ) ) ],
% 1.19/1.58 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), X ) ) ],
% 1.19/1.58 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), Y ) ), ~( hBOOL(
% 1.19/1.58 hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.19/1.58 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), X ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.19/1.58 ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), U ), T ) ) )
% 1.19/1.58 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ) ],
% 1.19/1.58 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.19/1.58 ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) )
% 1.19/1.58 ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.19/1.58 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.58 X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ),
% 1.19/1.58 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.58 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.19/1.58 X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) )
% 1.19/1.58 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), T ), Z ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( hAPP(
% 1.19/1.58 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.19/1.58 ,
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.58 ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ) ), =( U,
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.19/1.58 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ), hAPP(
% 1.19/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), =( Z,
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ), =( U, 'c_HOL_Ozero__class_Ozero'( X )
% 1.19/1.58 ), =( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), U ), hAPP(
% 1.19/1.58 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.19/1.58 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_Finite__Set_Osetsum'( Y, X ), hAPP( 'c_COMBC'( 'c_COMBB'(
% 1.19/1.58 'c_Finite__Set_Osetsum'( Z, X ), T, 'tc_fun'( Z, X ), 'tc_fun'( 'tc_fun'(
% 1.19/1.58 Z, 'tc_bool' ), X ), Y ), Y, 'tc_fun'( Z, 'tc_bool' ), X ), U ) ), W ),
% 1.19/1.58 hAPP( hAPP( 'c_Finite__Set_Osetsum'( Z, X ), hAPP( 'c_COMBC'( 'c_COMBB'(
% 1.19/1.58 'c_Finite__Set_Osetsum'( Y, X ), 'c_COMBC'( T, Y, Z, X ), 'tc_fun'( Y, X
% 1.19/1.58 ), 'tc_fun'( 'tc_fun'( Y, 'tc_bool' ), X ), Z ), Z, 'tc_fun'( Y,
% 1.19/1.58 'tc_bool' ), X ), W ) ), U ) ) ],
% 1.19/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.19/1.58 Z ), Y ) ) ],
% 1.19/1.58 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), Y ) ), hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( 'tc_nat' ), Y ), X ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.58 X ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.19/1.58 X ) ), =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.58 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), X ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.19/1.58 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.19/1.58 X ) ), ~( =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) )
% 1.19/1.58 , =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.58 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.19/1.58 ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.19/1.58 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ), ~( hBOOL(
% 1.19/1.58 hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.19/1.58 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X )
% 1.19/1.58 ), Y ) ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.19/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.58 X ), U ), Z ) ), W ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), T )
% 1.19/1.58 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), U ), Y ) ), Z ) ), W ) ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.19/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), U ) ), W ) ) ), ~( hBOOL(
% 1.19/1.58 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.58 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), Y ) ),
% 1.19/1.58 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ), W ) ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.19/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.58 X ), U ), Z ) ), W ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP(
% 1.19/1.58 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T ) ), W ) ) ) ]
% 1.19/1.58 ,
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.19/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ) ), U ) ), W ) ), ~(
% 1.19/1.58 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.58 X ), Y ), T ) ), U ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.19/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), W ) ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y
% 1.19/1.58 ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL(
% 1.19/1.58 hAPP( hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.19/1.58 ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y
% 1.19/1.58 ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.19/1.58 hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.19/1.58 ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.19/1.58 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z
% 1.19/1.58 ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ) ), ~(
% 1.19/1.58 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.19/1.58 , T ) ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.19/1.58 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z
% 1.19/1.58 ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ), ~(
% 1.19/1.58 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.19/1.58 , Z ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.58 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), T ), Y ) ), Z ) ), U ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.58 X ), T ), Z ) ), U ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.19/1.58 Y ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.19/1.58 Y ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.19/1.58 Y ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.19/1.58 Y ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.19/1.58 Y ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.19/1.58 Y ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.19/1.58 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.19/1.58 ) ), Z ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.19/1.58 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.58 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.19/1.58 ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.19/1.58 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.58 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.19/1.58 ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.19/1.58 X ), Y ), Z ) ), Z ), Y ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( hBOOL(
% 1.19/1.58 hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.19/1.58 ,
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.19/1.58 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.19/1.58 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.19/1.58 ,
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.58 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.19/1.58 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.58 X ), Y ), Z ) ), T ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.58 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.19/1.58 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.58 X ), Y ), Z ) ), T ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.58 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.19/1.58 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.58 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.19/1.58 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.19/1.58 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.19/1.58 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.19/1.58 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.19/1.58 ) ) ],
% 1.19/1.58 [ =( hAPP( 'c_COMBB'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y, W ) ) ) ]
% 1.19/1.58 ,
% 1.19/1.58 [ =( hAPP( hAPP( 'c_COMBC'( X, Y, Z, T ), U ), W ), hAPP( hAPP( X, W ),
% 1.19/1.58 U ) ) ],
% 1.19/1.58 [ =( hAPP( 'c_COMBS'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), hAPP( Y
% 1.19/1.58 , W ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.19/1.58 X ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.19/1.58 X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.19/1.58 X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL(
% 1.19/1.58 hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.19/1.58 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.58 X ) ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ) ) ) ) ]
% 1.19/1.58 ,
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL(
% 1.19/1.58 hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.19/1.58 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.58 X ) ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ) ) ]
% 1.19/1.58 ,
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL(
% 1.19/1.58 hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.19/1.58 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.58 X ) ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ) ) ) ) ]
% 1.19/1.58 ,
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL(
% 1.19/1.58 hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.19/1.58 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.58 X ) ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ) ) ]
% 1.19/1.58 ,
% 1.19/1.58 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), Y ) ), ~( hBOOL(
% 1.19/1.58 hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ) ), ~( hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( 'tc_nat' ), Z ), X ) ) ) ],
% 1.19/1.58 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( 'tc_nat' ), Y ), X ) ) ) ],
% 1.19/1.58 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.19/1.58 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( 'tc_nat' ), Z ), Y ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.19/1.58 ), Y ), Z ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Z )
% 1.19/1.58 ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), Y ), T ) ) ) ],
% 1.19/1.58 [ ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ),
% 1.19/1.58 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ) ), ~(
% 1.19/1.58 hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL(
% 1.19/1.58 hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Y ), X ) ) ), =( X, Z ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ) ), =( Z, T ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), T ), T ) ) ), =( Y, Z ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ), hBOOL( hAPP( hAPP( 'c_lessequals'( X )
% 1.19/1.58 , Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y )
% 1.19/1.58 , Z ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.58 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.58 'tc_nat' ) ) ],
% 1.19/1.58 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.58 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), Z ), U ) ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ) ), U ) ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), Z ), U ) ) ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_Finite__Set_Osetsum'( Y, X ), 'c_COMBS'( 'c_COMBB'(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z, X, 'tc_fun'( X, X ), Y ), T, Y, X, X
% 1.19/1.58 ) ), U ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.58 'c_Finite__Set_Osetsum'( Y, X ), Z ), U ) ), hAPP( hAPP(
% 1.19/1.58 'c_Finite__Set_Osetsum'( Y, X ), T ), U ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.58 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), U ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.19/1.58 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ), U )
% 1.19/1.58 ) ],
% 1.19/1.58 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), X ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.58 X ) ) ), =( Y, Z ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.58 X ) ) ), =( Y, Z ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.19/1.58 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.19/1.58 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.19/1.58 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.19/1.58 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.19/1.58 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.19/1.58 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.19/1.58 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( 'tc_nat' ), T ), Z ) ) ), =( Y,
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.58 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.19/1.58 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), Z ), U ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.19/1.58 Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.58 ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.19/1.58 ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.58 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.19/1.58 Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.58 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ), Y ) ) ],
% 1.19/1.58 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ), ~( hBOOL( hAPP(
% 1.19/1.58 hAPP( 'c_lessequals'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( 'tc_nat' ), Y ), X ) ) ) ],
% 1.19/1.58 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), =( Z,
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ), =( Y,
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.19/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_Finite__Set_Osetsum'( 'tc_nat', X ), hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), Y ) ),
% 1.19/1.58 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.58 'tc_nat' ), Z, 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.19/1.58 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), 'c_HOL_Oone__class_Oone'(
% 1.19/1.58 X ) ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ),
% 1.19/1.58 'c_HOL_Oone__class_Oone'( X ) ) ) ), =( Y, 'c_HOL_Oone__class_Oone'( X )
% 1.19/1.58 ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.19/1.58 Y ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.19/1.58 Y ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.19/1.58 Y ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.19/1.58 X ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.19/1.58 Y ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.19/1.58 Y ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.19/1.58 Y ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.19/1.58 Y ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.19/1.58 ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.19/1.58 Y ), T ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.19/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y
% 1.19/1.58 ), Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero'( X ) ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.19/1.58 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.19/1.58 Z ) ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), hAPP(
% 1.19/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.19/1.58 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.58 X ), Y ), Z ) ), Z ), Y ) ],
% 1.19/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ) ],
% 1.19/1.58 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =( hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ) ],
% 1.19/1.58 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'v_i', 'tc_nat' ), 'v_n' ) ) ]
% 1.19/1.58 ,
% 1.19/1.58 [ ~( =( hAPP( hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat',
% 1.19/1.58 'tc_Complex_Ocomplex' ), 'c_COMBS'( 'c_COMBB'(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( 'tc_Complex_Ocomplex' ), hAPP( 'c_COMBC'(
% 1.19/1.58 'c_COMBB'( 'c_Finite__Set_Osetsum'( 'tc_nat', 'tc_Complex_Ocomplex' ),
% 1.19/1.58 'c_COMBB'( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.19/1.58 'c_COMBS'( 'c_COMBS'( 'c_COMBB'( 'c_HOL_OIf'( 'tc_Complex_Ocomplex' ),
% 1.19/1.58 hAPP( 'c_lessequals'( 'tc_nat' ), 'v_i' ), 'tc_bool', 'tc_fun'(
% 1.19/1.58 'tc_Complex_Ocomplex', 'tc_fun'( 'tc_Complex_Ocomplex',
% 1.19/1.58 'tc_Complex_Ocomplex' ) ), 'tc_nat' ), 'c_COMBB'( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.19/1.58 'c_FFT__Mirabelle_Oroot'( 'v_n' ) ), hAPP( 'c_COMBC'(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), 'tc_nat', 'tc_nat', 'tc_nat' )
% 1.19/1.58 , 'v_i' ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ), 'tc_nat',
% 1.19/1.58 'tc_Complex_Ocomplex', 'tc_fun'( 'tc_Complex_Ocomplex',
% 1.19/1.58 'tc_Complex_Ocomplex' ) ), 'c_COMBB'( hAPP(
% 1.19/1.58 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ), hAPP( hAPP(
% 1.19/1.58 'c_HOL_Oinverse__class_Odivide'( 'tc_Complex_Ocomplex' ),
% 1.19/1.58 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ) ),
% 1.19/1.58 'c_FFT__Mirabelle_Oroot'( 'v_n' ) ) ), hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.19/1.58 'tc_nat' ), 'v_i' ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ),
% 1.19/1.58 'tc_nat', 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ),
% 1.19/1.58 'tc_Complex_Ocomplex', 'tc_fun'( 'tc_nat', 'tc_Complex_Ocomplex' ),
% 1.19/1.58 'tc_nat' ), 'tc_fun'( 'tc_nat', 'tc_Complex_Ocomplex' ), 'tc_fun'(
% 1.19/1.58 'tc_fun'( 'tc_nat', 'tc_bool' ), 'tc_Complex_Ocomplex' ), 'tc_nat' ),
% 1.19/1.58 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_bool' ), 'tc_Complex_Ocomplex' ),
% 1.19/1.58 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.58 'tc_nat' ), 'v_n', 'tc_nat' ) ), 'tc_Complex_Ocomplex', 'tc_fun'(
% 1.19/1.58 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ), 'tc_nat' ), 'v_a',
% 1.19/1.58 'tc_nat', 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ) ),
% 1.19/1.58 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.58 'tc_nat' ), 'v_n', 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.19/1.58 'tc_Complex_Ocomplex' ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat',
% 1.19/1.58 'tc_Complex_Ocomplex' ), 'c_COMBS'( 'c_COMBB'(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( 'tc_Complex_Ocomplex' ), hAPP( 'c_COMBC'(
% 1.19/1.58 'c_COMBB'( 'c_Finite__Set_Osetsum'( 'tc_nat', 'tc_Complex_Ocomplex' ),
% 1.19/1.58 'c_COMBB'( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.19/1.58 'c_COMBB'( hAPP( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' )
% 1.19/1.58 , hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( 'tc_Complex_Ocomplex' ),
% 1.19/1.58 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ) ),
% 1.19/1.58 'c_FFT__Mirabelle_Oroot'( 'v_n' ) ) ), hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.19/1.58 'tc_nat' ), 'v_i' ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ),
% 1.19/1.58 'tc_Complex_Ocomplex', 'tc_fun'( 'tc_nat', 'tc_Complex_Ocomplex' ),
% 1.19/1.58 'tc_nat' ), 'tc_fun'( 'tc_nat', 'tc_Complex_Ocomplex' ), 'tc_fun'(
% 1.19/1.58 'tc_fun'( 'tc_nat', 'tc_bool' ), 'tc_Complex_Ocomplex' ), 'tc_nat' ),
% 1.19/1.58 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_bool' ), 'tc_Complex_Ocomplex' ),
% 1.19/1.58 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.58 'tc_nat' ), 'v_n', 'tc_nat' ) ), 'tc_Complex_Ocomplex', 'tc_fun'(
% 1.19/1.58 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ), 'tc_nat' ), 'v_a',
% 1.19/1.58 'tc_nat', 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ) ),
% 1.19/1.58 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.58 'tc_nat' ), 'v_i', 'tc_nat' ) ) ), hAPP( hAPP( 'c_Finite__Set_Osetsum'(
% 1.19/1.58 'tc_nat', 'tc_Complex_Ocomplex' ), 'c_COMBS'( 'c_COMBB'(
% 1.19/1.58 'c_HOL_Otimes__class_Otimes'( 'tc_Complex_Ocomplex' ), hAPP( 'c_COMBC'(
% 1.19/1.58 'c_COMBB'( 'c_Finite__Set_Osetsum'( 'tc_nat', 'tc_Complex_Ocomplex' ),
% 1.19/1.58 'c_COMBB'( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.19/1.58 'c_COMBB'( hAPP( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' )
% 1.19/1.58 , 'c_FFT__Mirabelle_Oroot'( 'v_n' ) ), hAPP( 'c_COMBC'(
% 1.19/1.58 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), 'tc_nat', 'tc_nat', 'tc_nat' )
% 1.19/1.58 , 'v_i' ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ),
% 1.19/1.58 'tc_Complex_Ocomplex', 'tc_fun'( 'tc_nat', 'tc_Complex_Ocomplex' ),
% 1.19/1.58 'tc_nat' ), 'tc_fun'( 'tc_nat', 'tc_Complex_Ocomplex' ), 'tc_fun'(
% 1.19/1.58 'tc_fun'( 'tc_nat', 'tc_bool' ), 'tc_Complex_Ocomplex' ), 'tc_nat' ),
% 1.19/1.58 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_bool' ), 'tc_Complex_Ocomplex' ),
% 1.19/1.58 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.19/1.58 'tc_nat' ), 'v_n', 'tc_nat' ) ), 'tc_Complex_Ocomplex', 'tc_fun'(
% 1.19/1.58 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ), 'tc_nat' ), 'v_a',
% 1.19/1.58 'tc_nat', 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ) ),
% 1.19/1.58 'c_SetInterval_Oord__class_OatLeastLessThan'( 'v_i', 'v_n', 'tc_nat' ) )
% 1.19/1.58 ) ) ) ],
% 1.19/1.58 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 1.19/1.58 'class_Orderings_Opreorder'( Y ) ) ],
% 1.19/1.58 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 1.19/1.58 'class_Orderings_Oorder'( Y ) ) ],
% 1.19/1.58 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 1.19/1.58 ],
% 1.19/1.58 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 1.19/1.58 ) ],
% 1.19/1.58 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 1.19/1.58 ],
% 1.19/1.58 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 1.19/1.58 ,
% 1.19/1.58 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 1.19/1.58 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 1.19/1.58 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 1.19/1.58 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 1.19/1.58 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 1.19/1.58 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 1.19/1.58 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 1.19/1.58 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 1.19/1.58 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 1.19/1.58 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 1.19/1.58 [ 'class_Ring__and__Field_Ocomm__semiring__0'( 'tc_nat' ) ],
% 1.19/1.58 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 1.19/1.58 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 1.19/1.58 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 1.19/1.58 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 1.19/1.58 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 1.19/1.58 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 1.19/1.58 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 1.19/1.58 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 1.19/1.58 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 1.19/1.58 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 1.19/1.58 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 1.19/1.58 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 1.19/1.58 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 1.19/1.58 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 1.19/1.58 [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ],
% 1.19/1.58 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 1.19/1.58 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 1.19/1.58 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 1.19/1.58 [ 'class_Power_Opower'( 'tc_nat' ) ],
% 1.19/1.58 [ 'class_Orderings_Opreorder'( 'tc_bool' ) ],
% 1.19/1.58 [ 'class_Orderings_Oorder'( 'tc_bool' ) ],
% 1.19/1.58 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 1.19/1.58 'tc_Complex_Ocomplex' ) ],
% 1.19/1.58 [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 1.19/1.58 'tc_Complex_Ocomplex' ) ],
% 1.19/1.58 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 1.19/1.58 'tc_Complex_Ocomplex' ) ],
% 1.19/1.58 [ 'class_RealVector_Oreal__normed__div__algebra'( 'tc_Complex_Ocomplex'
% 1.19/1.58 ) ],
% 1.19/1.58 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Complex_Ocomplex' )
% 1.19/1.58 ],
% 1.19/1.58 [ 'class_RealVector_Oreal__normed__algebra__1'( 'tc_Complex_Ocomplex' )
% 1.19/1.58 ],
% 1.19/1.58 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Complex_Ocomplex' )
% 1.19/1.58 ],
% 1.19/1.58 [ 'class_Ring__and__Field_Odivision__by__zero'( 'tc_Complex_Ocomplex' )
% 1.19/1.58 ],
% 1.19/1.58 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Complex_Ocomplex' ) ]
% 1.19/1.58 ,
% 1.19/1.58 [ 'class_Ring__and__Field_Ocomm__semiring__0'( 'tc_Complex_Ocomplex' ) ]
% 1.19/1.58 ,
% 1.19/1.58 [ 'class_RealVector_Oreal__normed__algebra'( 'tc_Complex_Ocomplex' ) ]
% 1.19/1.58 ,
% 1.19/1.58 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Complex_Ocomplex' ) ]
% 1.19/1.58 ,
% 1.19/1.58 [ 'class_RealVector_Oreal__normed__vector'( 'tc_Complex_Ocomplex' ) ]
% 1.19/1.58 ,
% 1.19/1.58 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Complex_Ocomplex' ) ]
% 1.19/1.58 ,
% 1.19/1.58 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Complex_Ocomplex' ) ]
% 1.19/1.58 ,
% 1.19/1.58 [ 'class_Ring__and__Field_Odivision__ring'( 'tc_Complex_Ocomplex' ) ]
% 1.19/1.58 ,
% 1.19/1.58 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Complex_Ocomplex' ) ]
% 1.19/1.58 ,
% 1.19/1.58 [ 'class_RealVector_Oreal__normed__field'( 'tc_Complex_Ocomplex' ) ]
% 1.19/1.58 ,
% 1.19/1.58 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Complex_Ocomplex' ) ]
% 1.19/1.58 ,
% 1.19/1.58 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Complex_Ocomplex' ) ]
% 1.19/1.58 ,
% 1.19/1.58 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Complex_Ocomplex' ) ],
% 1.19/1.58 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Complex_Ocomplex' ) ],
% 1.19/1.58 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Complex_Ocomplex' ) ],
% 1.19/1.58 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Complex_Ocomplex' ) ],
% 1.19/1.58 [ 'class_Ring__and__Field_Ocomm__ring'( 'tc_Complex_Ocomplex' ) ],
% 1.19/1.58 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Complex_Ocomplex' ) ],
% 1.19/1.58 [ 'class_Ring__and__Field_Osemiring'( 'tc_Complex_Ocomplex' ) ],
% 1.19/1.58 [ 'class_RealVector_Ometric__space'( 'tc_Complex_Ocomplex' ) ],
% 1.19/1.58 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Complex_Ocomplex' ) ],
% 1.19/1.58 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Complex_Ocomplex' ) ],
% 1.19/1.58 [ 'class_Ring__and__Field_Oring__1'( 'tc_Complex_Ocomplex' ) ],
% 1.19/1.58 [ 'class_RealVector_Oreal__field'( 'tc_Complex_Ocomplex' ) ],
% 1.19/1.58 [ 'class_Ring__and__Field_Ofield'( 'tc_Complex_Ocomplex' ) ],
% 1.19/1.58 [ 'class_Ring__and__Field_Oring'( 'tc_Complex_Ocomplex' ) ],
% 1.19/1.58 [ 'class_Ring__and__Field_Oidom'( 'tc_Complex_Ocomplex' ) ],
% 1.19/1.58 [ 'class_Nat_Osemiring__char__0'( 'tc_Complex_Ocomplex' ) ],
% 1.19/1.58 [ 'class_Int_Onumber__ring'( 'tc_Complex_Ocomplex' ) ],
% 1.19/1.58 [ 'class_Power_Opower'( 'tc_Complex_Ocomplex' ) ],
% 1.19/1.58 [ =( hAPP( 'c_COMBS'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), hAPP( Y
% 1.19/1.58 , W ) ) ) ],
% 1.19/1.58 [ =( hAPP( hAPP( 'c_COMBC'( X, Y, Z, T ), U ), W ), hAPP( hAPP( X, W ),
% 1.19/1.58 U ) ) ],
% 1.19/1.58 [ =( hAPP( 'c_COMBB'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y, W ) ) ) ]
% 1.19/1.58 ,
% 1.19/1.58 [ 'c_fequal'( X, X, Y ) ],
% 1.19/1.58 [ =( X, Y ), ~( 'c_fequal'( X, Y, Z ) ) ]
% 1.19/1.58 ] .
% 1.19/1.58
% 1.19/1.58
% 1.19/1.58 percentage equality = 0.201325, percentage horn = 0.835821
% 1.19/1.58 This is a problem with some equality
% 1.19/1.58
% 1.19/1.58
% 1.19/1.58
% 1.19/1.58 Options Used:
% 1.19/1.58
% 1.19/1.58 useres = 1
% 1.19/1.58 useparamod = 1
% 1.19/1.58 useeqrefl = 1
% 1.19/1.58 useeqfact = 1
% 1.19/1.58 usefactor = 1
% 1.19/1.58 usesimpsplitting = 0
% 1.19/1.58 usesimpdemod = 5
% 1.19/1.58 usesimpres = 3
% 1.19/1.58
% 1.19/1.58 resimpinuse = 1000
% 1.19/1.58 resimpclauses = 20000
% 1.19/1.58 substype = eqrewr
% 1.19/1.58 backwardsubs = 1
% 1.19/1.58 selectoldest = 5
% 1.19/1.58
% 1.19/1.58 litorderings [0] = split
% 1.19/1.58 litorderings [1] = extend the termordering, first sorting on arguments
% 1.19/1.58
% 1.19/1.58 termordering = kbo
% 1.19/1.58
% 1.19/1.58 litapriori = 0
% 1.19/1.58 termapriori = 1
% 1.19/1.58 litaposteriori = 0
% 1.19/1.58 termaposteriori = 0
% 1.19/1.58 demodaposteriori = 0
% 1.19/1.58 ordereqreflfact = 0
% 1.19/1.58
% 1.19/1.58 litselect = negord
% 1.19/1.58
% 1.19/1.58 maxweight = 15
% 1.19/1.58 maxdepth = 30000
% 1.19/1.58 maxlength = 115
% 1.19/1.58 maxnrvars = 195
% 1.19/1.58 excuselevel = 1
% 1.19/1.58 increasemaxweight = 1
% 1.19/1.58
% 1.19/1.58 maxselected = 10000000
% 1.19/1.58 maxnrclauses = 10000000
% 1.19/1.58
% 1.19/1.58 showgenerated = 0
% 1.19/1.58 showkept = 0
% 1.19/1.58 showselected = 0
% 1.19/1.58 showdeleted = 0
% 1.19/1.58 showresimp = 1
% 1.19/1.58 showstatus = 2000
% 1.19/1.58
% 1.19/1.58 prologoutput = 1
% 1.19/1.58 nrgoals = 5000000
% 1.19/1.58 totalproof = 1
% 1.19/1.58
% 1.19/1.58 Symbols occurring in the translation:
% 1.19/1.58
% 1.19/1.58 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.19/1.58 . [1, 2] (w:1, o:153, a:1, s:1, b:0),
% 1.19/1.58 ! [4, 1] (w:0, o:75, a:1, s:1, b:0),
% 1.19/1.58 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.19/1.58 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.19/1.58 'tc_nat' [40, 0] (w:1, o:14, a:1, s:1, b:0),
% 1.19/1.58 'c_HOL_Ozero__class_Ozero' [41, 1] (w:1, o:80, a:1, s:1, b:0),
% 1.19/1.58 'c_HOL_Oord__class_Oless' [42, 2] (w:1, o:178, a:1, s:1, b:0),
% 1.19/1.58 'c_Suc' [43, 0] (w:1, o:15, a:1, s:1, b:0),
% 1.19/1.58 hAPP [44, 2] (w:1, o:179, a:1, s:1, b:0),
% 1.19/1.58 hBOOL [45, 1] (w:1, o:81, a:1, s:1, b:0),
% 1.19/1.58 'class_RealVector_Ometric__space' [47, 1] (w:1, o:82, a:1, s:1, b:0)
% 1.19/1.58 ,
% 1.19/1.58 'c_COMBB' [49, 5] (w:1, o:194, a:1, s:1, b:0),
% 1.19/1.58 'c_SEQ_OLIMSEQ' [51, 3] (w:1, o:184, a:1, s:1, b:0),
% 1.19/1.58 'class_Ring__and__Field_Odivision__ring' [52, 1] (w:1, o:87, a:1, s:1
% 1.19/1.58 , b:0),
% 1.19/1.58 'class_Ring__and__Field_Odivision__by__zero' [53, 1] (w:1, o:88, a:1
% 1.19/1.58 , s:1, b:0),
% 1.19/1.58 'c_HOL_Oinverse__class_Oinverse' [54, 1] (w:1, o:89, a:1, s:1, b:0),
% 1.95/2.36
% 1.95/2.36 'c_HOL_Otimes__class_Otimes' [56, 1] (w:1, o:90, a:1, s:1, b:0),
% 1.95/2.36 'class_Orderings_Oorder' [58, 1] (w:1, o:92, a:1, s:1, b:0),
% 1.95/2.36 'class_Orderings_Opreorder' [62, 1] (w:1, o:93, a:1, s:1, b:0),
% 1.95/2.36 'c_HOL_Oplus__class_Oplus' [63, 1] (w:1, o:95, a:1, s:1, b:0),
% 1.95/2.36 'c_Groebner__Basis_Osemiringb' [73, 6] (w:1, o:196, a:1, s:1, b:0),
% 1.95/2.36 'class_Ring__and__Field_Oordered__field' [79, 1] (w:1, o:98, a:1, s:1
% 1.95/2.36 , b:0),
% 1.95/2.36 'c_HOL_Ominus__class_Ominus' [80, 1] (w:1, o:99, a:1, s:1, b:0),
% 1.95/2.36 'c_lessequals' [81, 1] (w:1, o:100, a:1, s:1, b:0),
% 1.95/2.36 'class_OrderedGroup_Ocomm__monoid__add' [82, 1] (w:1, o:101, a:1, s:1
% 1.95/2.36 , b:0),
% 1.95/2.36 'c_Finite__Set_Osetsum' [83, 2] (w:1, o:180, a:1, s:1, b:0),
% 1.95/2.36 'c_SetInterval_Oord__class_OatLeastAtMost' [84, 3] (w:1, o:185, a:1
% 1.95/2.36 , s:1, b:0),
% 1.95/2.36 'class_Nat_Osemiring__char__0' [85, 1] (w:1, o:91, a:1, s:1, b:0),
% 1.95/2.36 'c_Nat_Osemiring__1__class_Oof__nat' [86, 2] (w:1, o:181, a:1, s:1
% 1.95/2.36 , b:0),
% 1.95/2.36 'class_Orderings_Olinorder' [87, 1] (w:1, o:102, a:1, s:1, b:0),
% 2.04/2.36 'class_RealVector_Oreal__normed__field' [89, 1] (w:1, o:103, a:1, s:1
% 2.04/2.36 , b:0),
% 2.04/2.36 'c_Deriv_Oderiv' [92, 4] (w:1, o:192, a:1, s:1, b:0),
% 2.04/2.36 'class_Ring__and__Field_Oordered__idom' [94, 1] (w:1, o:104, a:1, s:1
% 2.04/2.36 , b:0),
% 2.04/2.36 'c_Groebner__Basis_Ogb__semiring' [96, 6] (w:1, o:197, a:1, s:1, b:0)
% 2.04/2.36 ,
% 2.04/2.36 'class_Ring__and__Field_Osemiring__1' [97, 1] (w:1, o:110, a:1, s:1
% 2.04/2.36 , b:0),
% 2.04/2.36 'c_HOL_Oone__class_Oone' [98, 1] (w:1, o:94, a:1, s:1, b:0),
% 2.04/2.36 'class_Ring__and__Field_Oordered__semidom' [103, 1] (w:1, o:112, a:1
% 2.04/2.36 , s:1, b:0),
% 2.04/2.36 'class_Ring__and__Field_Ofield' [104, 1] (w:1, o:113, a:1, s:1, b:0)
% 2.04/2.36 ,
% 2.04/2.36 'class_Ring__and__Field_Oordered__ring__strict' [105, 1] (w:1, o:111
% 2.04/2.36 , a:1, s:1, b:0),
% 2.04/2.36 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [106, 1]
% 2.04/2.36 (w:1, o:114, a:1, s:1, b:0),
% 2.04/2.36 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [107, 1]
% 2.04/2.36 (w:1, o:115, a:1, s:1, b:0),
% 2.04/2.36 'class_RealVector_Oreal__normed__div__algebra' [108, 1] (w:1, o:116
% 2.04/2.36 , a:1, s:1, b:0),
% 2.04/2.36 'class_OrderedGroup_Opordered__ab__group__add' [109, 1] (w:1, o:117
% 2.04/2.36 , a:1, s:1, b:0),
% 2.04/2.36 'c_Power_Opower__class_Opower' [112, 1] (w:1, o:118, a:1, s:1, b:0),
% 2.04/2.36
% 2.04/2.36 'class_OrderedGroup_Omonoid__mult' [114, 1] (w:1, o:120, a:1, s:1, b:
% 2.04/2.36 0),
% 2.04/2.36 'class_Ring__and__Field_Ocomm__semiring__1' [115, 1] (w:1, o:85, a:1
% 2.04/2.36 , s:1, b:0),
% 2.04/2.36 'class_RealVector_Oreal__normed__vector' [118, 1] (w:1, o:121, a:1
% 2.04/2.36 , s:1, b:0),
% 2.04/2.36 'c_Series_Osuminf' [120, 2] (w:1, o:182, a:1, s:1, b:0),
% 2.04/2.36 'c_Series_Osums' [121, 3] (w:1, o:186, a:1, s:1, b:0),
% 2.04/2.36 'c_SetInterval_Oord__class_OatLeastLessThan' [122, 3] (w:1, o:187, a:
% 2.04/2.36 1, s:1, b:0),
% 2.04/2.36 'c_COMBC' [123, 4] (w:1, o:191, a:1, s:1, b:0),
% 2.04/2.36 'tc_Complex_Ocomplex' [124, 0] (w:1, o:56, a:1, s:1, b:0),
% 2.04/2.36 'c_FFT__Mirabelle_Oroot' [125, 1] (w:1, o:122, a:1, s:1, b:0),
% 2.04/2.36 'class_Ring__and__Field_Oordered__semiring__strict' [126, 1] (w:1, o:
% 2.04/2.36 123, a:1, s:1, b:0),
% 2.04/2.36 'class_Ring__and__Field_Oordered__comm__semiring__strict' [127, 1]
% 2.04/2.36 (w:1, o:124, a:1, s:1, b:0),
% 2.04/2.36 'c_HOL_Oinverse__class_Odivide' [128, 1] (w:1, o:125, a:1, s:1, b:0)
% 2.04/2.36 ,
% 2.04/2.36 'v_n' [129, 0] (w:1, o:57, a:1, s:1, b:0),
% 2.04/2.36 'class_Ring__and__Field_Oordered__semiring' [130, 1] (w:1, o:126, a:1
% 2.04/2.36 , s:1, b:0),
% 2.04/2.36 'class_OrderedGroup_Opordered__comm__monoid__add' [131, 1] (w:1, o:
% 2.04/2.36 127, a:1, s:1, b:0),
% 2.04/2.36 'class_OrderedGroup_Olordered__ab__group__add' [132, 1] (w:1, o:119
% 2.04/2.36 , a:1, s:1, b:0),
% 2.04/2.36 'class_RealVector_Oreal__normed__algebra' [136, 1] (w:1, o:128, a:1
% 2.04/2.36 , s:1, b:0),
% 2.04/2.36 'class_Int_Onumber__ring' [137, 1] (w:1, o:129, a:1, s:1, b:0),
% 2.04/2.36 'tc_fun' [138, 2] (w:1, o:183, a:1, s:1, b:0),
% 2.04/2.36 't_a' [139, 0] (w:1, o:59, a:1, s:1, b:0),
% 2.04/2.36 'v_sko__FFT__Mirabelle__Xsetsum__add__split__nat__ivl__2' [141, 4]
% 2.04/2.36 (w:1, o:193, a:1, s:1, b:0),
% 2.04/2.36 'v_i' [142, 0] (w:1, o:60, a:1, s:1, b:0),
% 2.04/2.36 'class_Ring__and__Field_Opordered__ring' [143, 1] (w:1, o:130, a:1
% 2.04/2.36 , s:1, b:0),
% 2.04/2.36 'c_COMBS' [145, 5] (w:1, o:195, a:1, s:1, b:0),
% 18.00/18.35 'class_Ring__and__Field_Oring__1' [147, 1] (w:1, o:105, a:1, s:1, b:0
% 18.00/18.35 ),
% 18.00/18.35 'class_Power_Opower' [148, 1] (w:1, o:141, a:1, s:1, b:0),
% 18.00/18.35 'class_Ring__and__Field_Ocomm__semiring__0' [150, 1] (w:1, o:84, a:1
% 18.00/18.35 , s:1, b:0),
% 18.00/18.35 'c_FFT__Mirabelle_OIDFT' [151, 3] (w:1, o:188, a:1, s:1, b:0),
% 18.00/18.35 'c_FFT__Mirabelle_ODFT' [152, 3] (w:1, o:189, a:1, s:1, b:0),
% 18.00/18.35 'class_OrderedGroup_Oab__group__add' [153, 1] (w:1, o:131, a:1, s:1
% 18.00/18.35 , b:0),
% 18.00/18.35 'class_RealVector_Oreal__normed__algebra__1' [154, 1] (w:1, o:142, a:
% 18.00/18.35 1, s:1, b:0),
% 18.00/18.35 'class_Ring__and__Field_Oidom' [155, 1] (w:1, o:143, a:1, s:1, b:0),
% 18.00/18.35
% 18.00/18.35 'class_Archimedean__Field_Oarchimedean__field' [156, 1] (w:1, o:144
% 18.00/18.35 , a:1, s:1, b:0),
% 18.00/18.35 'c_Archimedean__Field_Oarchimedean__field__axioms' [157, 6] (w:1, o:
% 18.00/18.35 198, a:1, s:1, b:0),
% 18.00/18.35 'class_Ring__and__Field_Osemiring__0' [160, 1] (w:1, o:109, a:1, s:1
% 18.00/18.35 , b:0),
% 18.00/18.35 'class_Ring__and__Field_Ocomm__ring' [161, 1] (w:1, o:83, a:1, s:1
% 18.00/18.35 , b:0),
% 18.00/18.35 'class_Ring__and__Field_Opordered__semiring' [162, 1] (w:1, o:145, a:
% 18.00/18.35 1, s:1, b:0),
% 18.00/18.35 'class_Ring__and__Field_Ocomm__semiring' [163, 1] (w:1, o:86, a:1, s:
% 18.00/18.35 1, b:0),
% 18.00/18.35 'class_OrderedGroup_Oab__semigroup__mult' [167, 1] (w:1, o:132, a:1
% 18.00/18.35 , s:1, b:0),
% 18.00/18.35 'class_Ring__and__Field_Opordered__cancel__semiring' [168, 1] (w:1
% 18.00/18.35 , o:146, a:1, s:1, b:0),
% 18.00/18.35 'class_OrderedGroup_Ocomm__monoid__mult' [169, 1] (w:1, o:133, a:1
% 18.00/18.35 , s:1, b:0),
% 18.00/18.35 'class_OrderedGroup_Oab__semigroup__idem__mult' [172, 1] (w:1, o:134
% 18.00/18.35 , a:1, s:1, b:0),
% 18.00/18.35 'class_Ring__and__Field_Omult__mono' [173, 1] (w:1, o:147, a:1, s:1
% 18.00/18.35 , b:0),
% 18.00/18.35 'class_Ring__and__Field_Omult__mono1' [174, 1] (w:1, o:148, a:1, s:1
% 18.00/18.35 , b:0),
% 18.00/18.35 'class_Ring__and__Field_Ozero__neq__one' [175, 1] (w:1, o:149, a:1
% 18.00/18.35 , s:1, b:0),
% 18.00/18.35 'class_Ring__and__Field_Ono__zero__divisors' [176, 1] (w:1, o:97, a:1
% 18.00/18.35 , s:1, b:0),
% 18.00/18.35 'class_Ring__and__Field_Omult__zero' [177, 1] (w:1, o:96, a:1, s:1
% 18.00/18.35 , b:0),
% 18.00/18.35 'class_Ring__and__Field_Oring__1__no__zero__divisors' [178, 1] (w:1
% 18.00/18.35 , o:106, a:1, s:1, b:0),
% 18.00/18.35 'class_OrderedGroup_Opordered__ab__semigroup__add' [179, 1] (w:1, o:
% 18.00/18.35 135, a:1, s:1, b:0),
% 18.00/18.35 'class_Ring__and__Field_Oring__no__zero__divisors' [180, 1] (w:1, o:
% 18.00/18.35 107, a:1, s:1, b:0),
% 18.00/18.35 'class_OrderedGroup_Ogroup__add' [181, 1] (w:1, o:136, a:1, s:1, b:0)
% 18.00/18.35 ,
% 18.00/18.35 'class_OrderedGroup_Ocancel__ab__semigroup__add' [182, 1] (w:1, o:137
% 18.00/18.35 , a:1, s:1, b:0),
% 18.00/18.35 'class_OrderedGroup_Ocancel__semigroup__add' [183, 1] (w:1, o:138, a:
% 18.00/18.35 1, s:1, b:0),
% 18.00/18.35 'class_RealVector_Oreal__field' [184, 1] (w:1, o:150, a:1, s:1, b:0)
% 18.00/18.35 ,
% 18.00/18.35 'class_Ring__and__Field_Oring' [185, 1] (w:1, o:108, a:1, s:1, b:0),
% 18.00/18.35
% 18.00/18.35 'tc_bool' [187, 0] (w:1, o:68, a:1, s:1, b:0),
% 18.00/18.35 'class_OrderedGroup_Oab__semigroup__add' [189, 1] (w:1, o:139, a:1
% 18.00/18.35 , s:1, b:0),
% 18.00/18.35 'class_Ring__and__Field_Osemiring' [192, 1] (w:1, o:151, a:1, s:1, b:
% 18.00/18.35 0),
% 18.00/18.35 'class_OrderedGroup_Omonoid__add' [193, 1] (w:1, o:140, a:1, s:1, b:0
% 18.00/18.35 ),
% 18.00/18.35 'c_HOL_OIf' [194, 1] (w:1, o:152, a:1, s:1, b:0),
% 18.00/18.35 'v_a' [195, 0] (w:1, o:72, a:1, s:1, b:0),
% 18.00/18.35 'c_fequal' [198, 3] (w:1, o:190, a:1, s:1, b:0).
% 18.00/18.35
% 18.00/18.35
% 18.00/18.35 Starting Search:
% 18.00/18.35
% 18.00/18.35 Resimplifying inuse:
% 18.00/18.35 Done
% 18.00/18.35
% 18.00/18.35
% 18.00/18.35 Intermediate Status:
% 18.00/18.35 Generated: 8730
% 18.00/18.35 Kept: 2101
% 18.00/18.35 Inuse: 66
% 18.00/18.35 Deleted: 0
% 18.00/18.35 Deletedinuse: 0
% 18.00/18.35
% 18.00/18.35 Resimplifying inuse:
% 18.00/18.35 Done
% 18.00/18.35
% 18.00/18.35 Resimplifying inuse:
% 18.00/18.35 Done
% 18.00/18.35
% 18.00/18.35
% 18.00/18.35 Intermediate Status:
% 18.00/18.35 Generated: 17535
% 18.00/18.35 Kept: 4112
% 18.00/18.35 Inuse: 137
% 18.00/18.35 Deleted: 4
% 18.00/18.35 Deletedinuse: 0
% 18.00/18.35
% 18.00/18.35 Resimplifying inuse:
% 18.00/18.35 Done
% 18.00/18.35
% 18.00/18.35 Resimplifying inuse:
% 18.00/18.35 Done
% 18.00/18.35
% 18.00/18.35
% 18.00/18.35 Intermediate Status:
% 18.00/18.35 Generated: 25753
% 18.00/18.35 Kept: 6545
% 18.00/18.35 Inuse: 195
% 18.00/18.35 Deleted: 6
% 18.00/18.35 Deletedinuse: 0
% 18.00/18.35
% 18.00/18.35 Resimplifying inuse:
% 18.00/18.35 Done
% 18.00/18.35
% 18.00/18.35 Resimplifying inuse:
% 18.00/18.35 Done
% 18.00/18.35
% 18.00/18.35
% 18.00/18.35 Intermediate Status:
% 18.00/18.35 Generated: 32465
% 18.00/18.35 Kept: 8545
% 18.00/18.35 Inuse: 217
% 18.00/18.35 Deleted: 12
% 18.00/18.35 Deletedinuse: 6
% 18.00/18.35
% 18.00/18.35 Resimplifying inuse:
% 18.00/18.35 Done
% 18.00/18.35
% 18.00/18.35 Resimplifying inuse:
% 18.00/18.35 Done
% 18.00/18.35
% 18.00/18.35
% 18.00/18.35 Intermediate Status:
% 18.00/18.35 Generated: 44734
% 18.00/18.35 Kept: 10822
% 18.00/18.35 Inuse: 245
% 18.00/18.35 Deleted: 13
% 18.00/18.35 Deletedinuse: 7
% 18.00/18.35
% 18.00/18.35 Resimplifying inuse:
% 18.00/18.35 Done
% 18.00/18.35
% 60.27/60.67 Resimplifying inuse:
% 60.27/60.67 Done
% 60.27/60.67
% 60.27/60.67
% 60.27/60.67 Intermediate Status:
% 60.27/60.67 Generated: 60257
% 60.27/60.67 Kept: 13595
% 60.27/60.67 Inuse: 285
% 60.27/60.67 Deleted: 13
% 60.27/60.67 Deletedinuse: 7
% 60.27/60.67
% 60.27/60.67 Resimplifying inuse:
% 60.27/60.67 Done
% 60.27/60.67
% 60.27/60.67 Resimplifying inuse:
% 60.27/60.67 Done
% 60.27/60.67
% 60.27/60.67
% 60.27/60.67 Intermediate Status:
% 60.27/60.67 Generated: 75549
% 60.27/60.67 Kept: 16220
% 60.27/60.67 Inuse: 315
% 60.27/60.67 Deleted: 13
% 60.27/60.67 Deletedinuse: 7
% 60.27/60.67
% 60.27/60.67 Resimplifying inuse:
% 60.27/60.67 Done
% 60.27/60.67
% 60.27/60.67 Resimplifying inuse:
% 60.27/60.67 Done
% 60.27/60.67
% 60.27/60.67
% 60.27/60.67 Intermediate Status:
% 60.27/60.67 Generated: 91284
% 60.27/60.67 Kept: 18679
% 60.27/60.67 Inuse: 340
% 60.27/60.67 Deleted: 13
% 60.27/60.67 Deletedinuse: 7
% 60.27/60.67
% 60.27/60.67 Resimplifying inuse:
% 60.27/60.67 Done
% 60.27/60.67
% 60.27/60.67 Resimplifying inuse:
% 60.27/60.67 Done
% 60.27/60.67
% 60.27/60.67 Resimplifying clauses:
% 60.27/60.67 Done
% 60.27/60.67
% 60.27/60.67
% 60.27/60.67 Intermediate Status:
% 60.27/60.67 Generated: 98753
% 60.27/60.67 Kept: 20914
% 60.27/60.67 Inuse: 365
% 60.27/60.67 Deleted: 186
% 60.27/60.67 Deletedinuse: 7
% 60.27/60.67
% 60.27/60.67 Resimplifying inuse:
% 60.27/60.67 Done
% 60.27/60.67
% 60.27/60.67 Resimplifying inuse:
% 60.27/60.67 Done
% 60.27/60.67
% 60.27/60.67
% 60.27/60.67 Intermediate Status:
% 60.27/60.67 Generated: 106298
% 60.27/60.67 Kept: 22939
% 60.27/60.67 Inuse: 390
% 60.27/60.67 Deleted: 186
% 60.27/60.67 Deletedinuse: 7
% 60.27/60.67
% 60.27/60.67 Resimplifying inuse:
% 60.27/60.67 Done
% 60.27/60.67
% 60.27/60.67 Resimplifying inuse:
% 60.27/60.67 Done
% 60.27/60.67
% 60.27/60.67
% 60.27/60.67 Intermediate Status:
% 60.27/60.67 Generated: 117505
% 60.27/60.67 Kept: 25150
% 60.27/60.67 Inuse: 425
% 60.27/60.67 Deleted: 186
% 60.27/60.67 Deletedinuse: 7
% 60.27/60.67
% 60.27/60.67 Resimplifying inuse:
% 60.27/60.67 Done
% 60.27/60.67
% 60.27/60.67 Resimplifying inuse:
% 60.27/60.67 Done
% 60.27/60.67
% 60.27/60.67
% 60.27/60.67 Intermediate Status:
% 60.27/60.67 Generated: 129549
% 60.27/60.67 Kept: 27152
% 60.27/60.67 Inuse: 458
% 60.27/60.67 Deleted: 186
% 60.27/60.67 Deletedinuse: 7
% 60.27/60.67
% 60.27/60.67 Resimplifying inuse:
% 60.27/60.67 Done
% 60.27/60.67
% 60.27/60.67
% 60.27/60.67 Intermediate Status:
% 60.27/60.67 Generated: 140296
% 60.27/60.67 Kept: 29192
% 60.27/60.67 Inuse: 475
% 60.27/60.67 Deleted: 186
% 60.27/60.67 Deletedinuse: 7
% 60.27/60.67
% 60.27/60.67 Resimplifying inuse:
% 60.27/60.67 Done
% 60.27/60.67
% 60.27/60.67 Resimplifying inuse:
% 60.27/60.67 Done
% 60.27/60.67
% 60.27/60.67
% 60.27/60.67 Intermediate Status:
% 60.27/60.67 Generated: 157707
% 60.27/60.67 Kept: 32164
% 60.27/60.67 Inuse: 485
% 60.27/60.67 Deleted: 186
% 60.27/60.67 Deletedinuse: 7
% 60.27/60.67
% 60.27/60.67 Resimplifying inuse:
% 60.27/60.67 Done
% 60.27/60.67
% 60.27/60.67 Resimplifying inuse:
% 60.27/60.67 Done
% 60.27/60.67
% 60.27/60.67
% 60.27/60.67 Intermediate Status:
% 60.27/60.67 Generated: 166484
% 60.27/60.67 Kept: 34328
% 60.27/60.67 Inuse: 510
% 60.27/60.67 Deleted: 187
% 60.27/60.67 Deletedinuse: 8
% 60.27/60.67
% 60.27/60.67 Resimplifying inuse:
% 60.27/60.67 Done
% 60.27/60.67
% 60.27/60.67 Resimplifying inuse:
% 60.27/60.67 Done
% 60.27/60.67
% 60.27/60.67
% 60.27/60.67 Intermediate Status:
% 60.27/60.67 Generated: 175081
% 60.27/60.67 Kept: 36501
% 60.27/60.67 Inuse: 525
% 60.27/60.67 Deleted: 188
% 60.27/60.67 Deletedinuse: 9
% 60.27/60.67
% 60.27/60.67 Resimplifying inuse:
% 60.27/60.67 Done
% 60.27/60.67
% 60.27/60.67 Resimplifying inuse:
% 60.27/60.67 Done
% 60.27/60.67
% 60.27/60.67
% 60.27/60.67 Intermediate Status:
% 60.27/60.67 Generated: 209141
% 60.27/60.67 Kept: 38724
% 60.27/60.67 Inuse: 540
% 60.27/60.67 Deleted: 188
% 60.27/60.67 Deletedinuse: 9
% 60.27/60.67
% 60.27/60.67 Resimplifying inuse:
% 60.27/60.67 Done
% 60.27/60.67
% 60.27/60.67 Resimplifying inuse:
% 60.27/60.67 Done
% 60.27/60.67
% 60.27/60.67 Resimplifying clauses:
% 60.27/60.67 Done
% 60.27/60.67
% 60.27/60.67
% 60.27/60.67 Intermediate Status:
% 60.27/60.67 Generated: 216950
% 60.27/60.67 Kept: 40789
% 60.27/60.67 Inuse: 560
% 60.27/60.67 Deleted: 443
% 60.27/60.67 Deletedinuse: 9
% 60.27/60.67
% 60.27/60.67 Resimplifying inuse:
% 60.27/60.67 Done
% 60.27/60.67
% 60.27/60.67 Resimplifying inuse:
% 60.27/60.67 Done
% 60.27/60.67
% 60.27/60.67
% 60.27/60.67 Intermediate Status:
% 60.27/60.67 Generated: 226322
% 60.27/60.67 Kept: 42828
% 60.27/60.67 Inuse: 585
% 60.27/60.67 Deleted: 443
% 60.27/60.67 Deletedinuse: 9
% 60.27/60.67
% 60.27/60.67
% 60.27/60.67 Intermediate Status:
% 60.27/60.67 Generated: 236434
% 60.27/60.67 Kept: 45293
% 60.27/60.67 Inuse: 595
% 60.27/60.67 Deleted: 443
% 60.27/60.67 Deletedinuse: 9
% 60.27/60.67
% 60.27/60.67 Resimplifying inuse:
% 60.27/60.67 Done
% 60.27/60.67
% 60.27/60.67 Resimplifying inuse:
% 60.27/60.67 Done
% 60.27/60.67
% 60.27/60.67
% 60.27/60.67 Intermediate Status:
% 60.27/60.67 Generated: 245335
% 60.27/60.67 Kept: 47415
% 60.27/60.67 Inuse: 605
% 60.27/60.67 Deleted: 443
% 60.27/60.67 Deletedinuse: 9
% 60.27/60.67
% 60.27/60.67 Resimplifying inuse:
% 60.27/60.67 Done
% 60.27/60.67
% 60.27/60.67
% 60.27/60.67 Intermediate Status:
% 60.27/60.67 Generated: 253220
% 60.27/60.67 Kept: 49617
% 60.27/60.67 Inuse: 630
% 60.27/60.67 Deleted: 443
% 60.27/60.67 Deletedinuse: 9
% 60.27/60.67
% 60.27/60.67 Resimplifying inuse:
% 60.27/60.67 Done
% 60.27/60.67
% 60.27/60.67 Resimplifying inuse:
% 60.27/60.67 Done
% 60.27/60.67
% 60.27/60.67
% 60.27/60.67 Intermediate Status:
% 60.27/60.67 Generated: 260803
% 60.27/60.67 Kept: 51942
% 60.27/60.67 Inuse: 655
% 60.27/60.67 Deleted: 443
% 60.27/60.67 Deletedinuse: 9
% 60.27/60.67
% 60.27/60.67 Resimplifying inuse:
% 60.27/60.67 Done
% 60.27/60.67
% 60.27/60.67 Resimplifying inuse:
% 60.27/60.67 Done
% 60.27/60.67
% 60.27/60.67
% 60.27/60.67 Intermediate Status:
% 60.27/60.67 Generated: 267719
% 60.27/60.67 Kept: 54112
% 60.27/60.67 Inuse: 675
% 60.27/60.67 Deleted: 443
% 60.27/60.67 Deletedinuse: 9
% 60.27/60.67
% 60.27/60.67 Resimplifying inuse:
% 60.27/60.67 Done
% 60.27/60.67
% 60.27/60.67
% 60.27/60.67 Intermediate Status:
% 60.27/60.67 Generated: 275648
% 60.27/60.67 Kept: 56187
% 60.27/60.67 Inuse: 690
% 60.27/60.67 Deleted: 443
% 60.27/60.67 Deletedinuse: 9
% 60.27/60.67
% 60.27/60.67 Resimplifying inuse:
% 60.27/60.67 Done
% 60.27/60.67
% 60.27/60.67 Resimplifying inuse:
% 60.27/60.67 Done
% 60.27/60.67
% 60.27/60.67
% 60.27/60.67 Intermediate Status:
% 60.27/60.67 Generated: 286134
% 60.27/60.67 Kept: 59103
% 60.27/60.67 Inuse: 710
% 60.27/60.67 Deleted: 445
% 60.27/60.67 Deletedinuse: 11
% 60.27/60.67
% 60.27/60.67 Resimplifying inuse:
% 60.27/60.67 Done
% 60.27/60.67
% 60.27/60.67
% 60.27/60.67 Intermediate Status:
% 60.27/60.67 Generated: 311136
% 60.27/60.67 Kept: 61894
% 60.27/60.67 Inuse: 725
% 60.27/60.67 Deleted: 445
% 60.27/60.67 Deletedinuse: 11
% 60.27/60.67
% 60.27/60.67 Resimplifying inuse:
% 60.27/60.67 Done
% 60.27/60.67
% 60.27/60.67 Resimplifying clauses:
% 60.27/60.67 Done
% 60.27/60.67
% 60.27/60.67
% 60.27/60.67 Intermediate Status:
% 60.27/60.67 Generated: 332816
% 60.27/60.67 Kept: 64046
% 60.27/60.67 Inuse: 730
% 60.27/60.67 Deleted: 1135
% 60.27/60.67 Deletedinuse: 12
% 60.27/60.67
% 60.27/60.67 Resimplifying inuse:
% 60.27/60.67 Done
% 60.27/60.67
% 60.27/60.67 Resimplifying inuse:
% 60.27/60.67 Done
% 60.27/60.67
% 60.27/60.67
% 60.27/60.67 Intermediate Status:
% 60.27/60.67 Generated: 354116
% 60.27/60.67 Kept: 67544
% 60.27/60.67 Inuse: 739
% 60.27/60.67 Deleted: 1136
% 60.27/60.67 Deletedinuse: 12
% 60.27/60.67
% 60.27/60.67 Resimplifying inuse:
% 60.27/60.67 Done
% 60.27/60.67
% 60.27/60.67 Resimplifying inuse:
% 60.27/60.67 Done
% 60.27/60.67
% 60.27/60.67
% 60.27/60.67 Intermediate Status:
% 60.27/60.67 Generated: 364275
% 60.27/60.67 Kept: 70307
% 60.27/60.67 Inuse: 749
% 60.27/60.67 Deleted: 1136
% 141.68/142.03 Deletedinuse: 12
% 141.68/142.03
% 141.68/142.03 Resimplifying inuse:
% 141.68/142.03 Done
% 141.68/142.03
% 141.68/142.03 Resimplifying inuse:
% 141.68/142.03 Done
% 141.68/142.03
% 141.68/142.03
% 141.68/142.03 Intermediate Status:
% 141.68/142.03 Generated: 374371
% 141.68/142.03 Kept: 72578
% 141.68/142.03 Inuse: 764
% 141.68/142.03 Deleted: 1136
% 141.68/142.03 Deletedinuse: 12
% 141.68/142.03
% 141.68/142.03 Resimplifying inuse:
% 141.68/142.03 Done
% 141.68/142.03
% 141.68/142.03
% 141.68/142.03 Intermediate Status:
% 141.68/142.03 Generated: 381464
% 141.68/142.03 Kept: 74939
% 141.68/142.03 Inuse: 779
% 141.68/142.03 Deleted: 1136
% 141.68/142.03 Deletedinuse: 12
% 141.68/142.03
% 141.68/142.03 Resimplifying inuse:
% 141.68/142.03 Done
% 141.68/142.03
% 141.68/142.03 Resimplifying inuse:
% 141.68/142.03 Done
% 141.68/142.03
% 141.68/142.03
% 141.68/142.03 Intermediate Status:
% 141.68/142.03 Generated: 390388
% 141.68/142.03 Kept: 76993
% 141.68/142.03 Inuse: 794
% 141.68/142.03 Deleted: 1136
% 141.68/142.03 Deletedinuse: 12
% 141.68/142.03
% 141.68/142.03 Resimplifying inuse:
% 141.68/142.03 Done
% 141.68/142.03
% 141.68/142.03 Resimplifying inuse:
% 141.68/142.03 Done
% 141.68/142.03
% 141.68/142.03
% 141.68/142.03 Intermediate Status:
% 141.68/142.03 Generated: 408794
% 141.68/142.03 Kept: 80276
% 141.68/142.03 Inuse: 814
% 141.68/142.03 Deleted: 1136
% 141.68/142.03 Deletedinuse: 12
% 141.68/142.03
% 141.68/142.03 Resimplifying inuse:
% 141.68/142.03 Done
% 141.68/142.03
% 141.68/142.03 Resimplifying inuse:
% 141.68/142.03 Done
% 141.68/142.03
% 141.68/142.03
% 141.68/142.03 Intermediate Status:
% 141.68/142.03 Generated: 420730
% 141.68/142.03 Kept: 82880
% 141.68/142.03 Inuse: 829
% 141.68/142.03 Deleted: 1136
% 141.68/142.03 Deletedinuse: 12
% 141.68/142.03
% 141.68/142.03 Resimplifying inuse:
% 141.68/142.03 Done
% 141.68/142.03
% 141.68/142.03 Resimplifying clauses:
% 141.68/142.03 Done
% 141.68/142.03
% 141.68/142.03 Resimplifying inuse:
% 141.68/142.03 Done
% 141.68/142.03
% 141.68/142.03
% 141.68/142.03 Intermediate Status:
% 141.68/142.03 Generated: 428370
% 141.68/142.03 Kept: 85046
% 141.68/142.03 Inuse: 844
% 141.68/142.03 Deleted: 1737
% 141.68/142.03 Deletedinuse: 12
% 141.68/142.03
% 141.68/142.03 Resimplifying inuse:
% 141.68/142.03 Done
% 141.68/142.03
% 141.68/142.03 Resimplifying inuse:
% 141.68/142.03 Done
% 141.68/142.03
% 141.68/142.03
% 141.68/142.03 Intermediate Status:
% 141.68/142.03 Generated: 436437
% 141.68/142.03 Kept: 87307
% 141.68/142.03 Inuse: 864
% 141.68/142.03 Deleted: 1737
% 141.68/142.03 Deletedinuse: 12
% 141.68/142.03
% 141.68/142.03 Resimplifying inuse:
% 141.68/142.03 Done
% 141.68/142.03
% 141.68/142.03
% 141.68/142.03 Intermediate Status:
% 141.68/142.03 Generated: 446119
% 141.68/142.03 Kept: 89589
% 141.68/142.03 Inuse: 879
% 141.68/142.03 Deleted: 1737
% 141.68/142.03 Deletedinuse: 12
% 141.68/142.03
% 141.68/142.03 Resimplifying inuse:
% 141.68/142.03 Done
% 141.68/142.03
% 141.68/142.03 Resimplifying inuse:
% 141.68/142.03 Done
% 141.68/142.03
% 141.68/142.03
% 141.68/142.03 Intermediate Status:
% 141.68/142.03 Generated: 496407
% 141.68/142.03 Kept: 95266
% 141.68/142.03 Inuse: 899
% 141.68/142.03 Deleted: 1737
% 141.68/142.03 Deletedinuse: 12
% 141.68/142.03
% 141.68/142.03 Resimplifying inuse:
% 141.68/142.03 Done
% 141.68/142.03
% 141.68/142.03
% 141.68/142.03 Intermediate Status:
% 141.68/142.03 Generated: 507860
% 141.68/142.03 Kept: 98033
% 141.68/142.03 Inuse: 904
% 141.68/142.03 Deleted: 1737
% 141.68/142.03 Deletedinuse: 12
% 141.68/142.03
% 141.68/142.03 Resimplifying inuse:
% 141.68/142.03 Done
% 141.68/142.03
% 141.68/142.03 Resimplifying inuse:
% 141.68/142.03 Done
% 141.68/142.03
% 141.68/142.03
% 141.68/142.03 Intermediate Status:
% 141.68/142.03 Generated: 517142
% 141.68/142.03 Kept: 100512
% 141.68/142.03 Inuse: 924
% 141.68/142.03 Deleted: 1737
% 141.68/142.03 Deletedinuse: 12
% 141.68/142.03
% 141.68/142.03 Resimplifying inuse:
% 141.68/142.03 Done
% 141.68/142.03
% 141.68/142.03 Resimplifying inuse:
% 141.68/142.03 Done
% 141.68/142.03
% 141.68/142.03
% 141.68/142.03 Intermediate Status:
% 141.68/142.03 Generated: 530233
% 141.68/142.03 Kept: 104006
% 141.68/142.03 Inuse: 944
% 141.68/142.03 Deleted: 1737
% 141.68/142.03 Deletedinuse: 12
% 141.68/142.03
% 141.68/142.03 Resimplifying inuse:
% 141.68/142.03 Done
% 141.68/142.03
% 141.68/142.03 Resimplifying clauses:
% 141.68/142.03 Done
% 141.68/142.03
% 141.68/142.03 Resimplifying inuse:
% 141.68/142.03 Done
% 141.68/142.03
% 141.68/142.03
% 141.68/142.03 Intermediate Status:
% 141.68/142.03 Generated: 538406
% 141.68/142.03 Kept: 106081
% 141.68/142.03 Inuse: 959
% 141.68/142.03 Deleted: 1902
% 141.68/142.03 Deletedinuse: 13
% 141.68/142.03
% 141.68/142.03 Resimplifying inuse:
% 141.68/142.03 Done
% 141.68/142.03
% 141.68/142.03
% 141.68/142.03 Intermediate Status:
% 141.68/142.03 Generated: 548454
% 141.68/142.03 Kept: 108712
% 141.68/142.03 Inuse: 979
% 141.68/142.03 Deleted: 1902
% 141.68/142.03 Deletedinuse: 13
% 141.68/142.03
% 141.68/142.03 Resimplifying inuse:
% 141.68/142.03 Done
% 141.68/142.03
% 141.68/142.03 Resimplifying inuse:
% 141.68/142.03 Done
% 141.68/142.03
% 141.68/142.03
% 141.68/142.03 Intermediate Status:
% 141.68/142.03 Generated: 556322
% 141.68/142.03 Kept: 110942
% 141.68/142.03 Inuse: 994
% 141.68/142.03 Deleted: 1902
% 141.68/142.03 Deletedinuse: 13
% 141.68/142.03
% 141.68/142.03 Resimplifying inuse:
% 141.68/142.03 Done
% 141.68/142.03
% 141.68/142.03
% 141.68/142.03 Intermediate Status:
% 141.68/142.03 Generated: 573868
% 141.68/142.03 Kept: 115365
% 141.68/142.03 Inuse: 1009
% 141.68/142.03 Deleted: 1902
% 141.68/142.03 Deletedinuse: 13
% 141.68/142.03
% 141.68/142.03 Resimplifying inuse:
% 141.68/142.03 Done
% 141.68/142.03
% 141.68/142.03 Resimplifying inuse:
% 141.68/142.03 Done
% 141.68/142.03
% 141.68/142.03
% 141.68/142.03 Intermediate Status:
% 141.68/142.03 Generated: 587267
% 141.68/142.03 Kept: 117771
% 141.68/142.03 Inuse: 1039
% 141.68/142.03 Deleted: 1902
% 141.68/142.03 Deletedinuse: 13
% 141.68/142.03
% 141.68/142.03 Resimplifying inuse:
% 141.68/142.03 Done
% 141.68/142.03
% 141.68/142.03 Resimplifying inuse:
% 141.68/142.03 Done
% 141.68/142.03
% 141.68/142.03
% 141.68/142.03 Intermediate Status:
% 141.68/142.03 Generated: 599035
% 141.68/142.03 Kept: 120021
% 141.68/142.03 Inuse: 1054
% 141.68/142.03 Deleted: 1903
% 141.68/142.03 Deletedinuse: 14
% 141.68/142.03
% 141.68/142.03 Resimplifying inuse:
% 141.68/142.03 Done
% 141.68/142.03
% 141.68/142.03 Resimplifying inuse:
% 141.68/142.03 Done
% 141.68/142.03
% 141.68/142.03
% 141.68/142.03 Intermediate Status:
% 141.68/142.03 Generated: 609713
% 141.68/142.03 Kept: 122408
% 141.68/142.03 Inuse: 1074
% 141.68/142.03 Deleted: 1903
% 141.68/142.03 Deletedinuse: 14
% 141.68/142.03
% 141.68/142.03 Resimplifying inuse:
% 141.68/142.03 Done
% 141.68/142.03
% 141.68/142.03
% 141.68/142.03 Intermediate Status:
% 141.68/142.03 Generated: 617430
% 141.68/142.03 Kept: 124818
% 141.68/142.03 Inuse: 1080
% 141.68/142.03 Deleted: 1903
% 141.68/142.03 Deletedinuse: 14
% 141.68/142.03
% 141.68/142.03 Resimplifying inuse:
% 141.68/142.03 Done
% 141.68/142.03
% 141.68/142.03 Resimplifying clauses:
% 141.68/142.03 Done
% 141.68/142.03
% 141.68/142.03 Resimplifying inuse:
% 141.68/142.03 Done
% 141.68/142.03
% 141.68/142.03
% 141.68/142.03 Intermediate Status:
% 141.68/142.03 Generated: 629463
% 141.68/142.03 Kept: 127692
% 141.68/142.03 Inuse: 1094
% 141.68/142.03 Deleted: 2006
% 141.68/142.03 Deletedinuse: 14
% 141.68/142.03
% 141.68/142.03 Resimplifying inuse:
% 141.68/142.03 Done
% 141.68/142.03
% 141.68/142.03 Resimplifying inuse:
% 141.68/142.03 Done
% 141.68/142.03
% 141.68/142.03
% 141.68/142.03 Intermediate Status:
% 141.68/142.03 Generated: 639012
% 141.68/142.03 Kept: 129696
% 141.68/142.03 Inuse: 1106
% 141.68/142.03 Deleted: 2006
% 141.68/142.03 Deletedinuse: 14
% 141.68/142.03
% 141.68/142.03 Resimplifying inuse:
% 141.68/142.03 Done
% 141.68/142.03
% 141.68/142.03
% 141.68/142.03 Intermediate Status:
% 141.68/142.03 Generated: 647273
% 141.68/142.03 Kept: 131747
% 141.68/142.03 Inuse: 1114
% 141.68/142.03 Deleted: 2006
% 141.68/142.03 Deletedinuse: 14
% 141.68/142.03
% 141.68/142.03 Resimplifying inuse:
% 141.68/142.03 Done
% 141.68/142.03
% 141.68/142.03 Resimplifying inuse:
% 141.68/142.03 Done
% 141.68/142.03
% 141.68/142.03
% 141.68/142.03 Intermediate Status:
% 141.68/142.03 Generated: 659530
% 141.68/142.03 Kept: 134254
% 141.68/142.03 Inuse: 1129
% 141.68/142.03 Deleted: 2006
% 141.68/142.03 Deletedinuse: 14
% 141.68/142.03
% 141.68/142.03 Resimplifying inuse:
% 300.01/300.37 Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------