TSTP Solution File: LCL796-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : LCL796-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n004.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 : Sun Jul 17 07:58:06 EDT 2022
% Result : Timeout 300.01s 300.44s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : LCL796-1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.14 % Command : bliksem %s
% 0.14/0.35 % Computer : n004.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % DateTime : Sat Jul 2 16:17:23 EDT 2022
% 0.14/0.35 % CPUTime :
% 1.09/1.44 *** allocated 10000 integers for termspace/termends
% 1.09/1.44 *** allocated 10000 integers for clauses
% 1.09/1.44 *** allocated 10000 integers for justifications
% 1.09/1.44 *** allocated 15000 integers for termspace/termends
% 1.09/1.44 *** allocated 22500 integers for termspace/termends
% 1.09/1.44 *** allocated 33750 integers for termspace/termends
% 1.09/1.44 Bliksem 1.12
% 1.09/1.44
% 1.09/1.44
% 1.09/1.44 Automatic Strategy Selection
% 1.09/1.44
% 1.09/1.44 Clauses:
% 1.09/1.44 [
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.09/1.44 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.09/1.44 T, X ) ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), =(
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ),
% 1.09/1.44 T, X ), 'c_Orderings_Oord__class_Omin'( 'c_HOL_Ominus__class_Ominus'( Y,
% 1.09/1.44 T, X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X ), X ) ) ],
% 1.09/1.44 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_lessequals'( X, Y,
% 1.09/1.44 'tc_nat' ) ],
% 1.09/1.44 [ =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X, Y,
% 1.09/1.44 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.44 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.44 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.09/1.44 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.44 X ), 'c_HOL_Ominus__class_Ominus'( Y, U, X ) ), Z ) ), T ) ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.09/1.44 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 1.09/1.44 X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.09/1.44 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 1.09/1.44 X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.09/1.44 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 1.09/1.44 X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.09/1.44 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Z, X ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.09/1.44 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y, X ) ],
% 1.09/1.44 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_Suc'(
% 1.09/1.44 'v_sko__Nat__Xnat__Xinduct__1'( X ) ) ) ) ), ~( hBOOL( hAPP( X,
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.09/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.44 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.09/1.44 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.09/1.44 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.09/1.44 ), Y ), T ), Z, X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.09/1.44 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.09/1.44 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.09/1.44 T, X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.09/1.44 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.09/1.44 X ), Y ), Z ), X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y,
% 1.09/1.44 X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.09/1.44 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.09/1.44 'c_Suc'( Y ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_Suc'( Y
% 1.09/1.44 ) ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y
% 1.09/1.44 ) ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'( X ) )
% 1.09/1.44 , Y ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.09/1.44 Y ) ) ) ],
% 1.09/1.44 [ =( X, 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.44 'tc_nat' ), Z ), 'c_Suc'( X ) ), 'tc_nat' ) ), ~( 'c_lessequals'( hAPP(
% 1.09/1.44 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), Y, 'tc_nat' ) )
% 1.09/1.44 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z
% 1.09/1.44 , 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.44 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( T, Y, X
% 1.09/1.44 ) ), Z ) ), U ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.09/1.44 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), U ) ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.44 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Z ) ), T ), U, 'tc_nat'
% 1.09/1.44 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.44 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z
% 1.09/1.44 ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), U ), 'tc_nat' ) ),
% 1.09/1.44 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.44 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.09/1.44 ) ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ), 'tc_nat' ),
% 1.09/1.44 ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.44 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ) ), Y ) ), Z ), U, 'tc_nat'
% 1.09/1.44 ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.44 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ), T ) ), U ), 'tc_nat' )
% 1.09/1.44 , ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.44 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T
% 1.09/1.44 ) ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ), U ), 'tc_nat' ) ),
% 1.09/1.44 ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.44 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.09/1.44 ) ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ), 'tc_nat' ),
% 1.09/1.44 ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.44 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ) ), Y ) ), U ), 'tc_nat' )
% 1.09/1.44 ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.44 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.09/1.44 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( T, hAPP(
% 1.09/1.44 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( U, Y, X
% 1.09/1.44 ) ), Z ) ), W ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.44 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.09/1.44 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( hAPP(
% 1.09/1.44 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, U, X
% 1.09/1.44 ) ), Z ) ), T ), W ) ],
% 1.09/1.44 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Z,
% 1.09/1.44 'c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1'( X ), 'tc_nat' ) ),
% 1.09/1.44 ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.09/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.44 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.09/1.44 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ) ), 'c_Divides_Odiv__class_Omod'(
% 1.09/1.44 Z, Y, X ) ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 1.09/1.44 ) ],
% 1.09/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.44 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.09/1.44 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.09/1.44 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ), T ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), 'tc_nat' ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 1.09/1.44 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.09/1.44 ), Y ), Z, 'tc_nat' ), ~( 'c_lessequals'( X,
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.09/1.44 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ),
% 1.09/1.44 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.44 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat'
% 1.09/1.44 ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.09/1.44 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 1.09/1.44 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.09/1.44 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 1.09/1.44 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.09/1.44 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 1.09/1.44 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.09/1.44 'c_Orderings_Oord__class_Omax'( Y, Z, X ), X ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.09/1.44 'c_Orderings_Oord__class_Omax'( Z, Y, X ), X ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Obot'( X ) ), 'c_lessequals'(
% 1.09/1.44 'c_Orderings_Obot__class_Obot'( X ), Y, X ) ],
% 1.09/1.44 [ =( 'c_Nat_Onat_Onat__rec'( X, Y, 'c_Suc'( Z ), T ), hAPP( hAPP( Y, Z )
% 1.09/1.44 , 'c_Nat_Onat_Onat__rec'( X, Y, Z, T ) ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.09/1.44 'c_Groebner__Basis_Ogb__semiring'( U, W, X, V0, V1, V2 ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.09/1.44 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'( Y, Z, X )
% 1.09/1.44 , T, X ), 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'(
% 1.09/1.44 Y, T, X ), 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.09/1.44 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 1.09/1.44 X ), X ), 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'(
% 1.09/1.44 Y, Z, X ), 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.09/1.44 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.09/1.44 X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X )
% 1.09/1.44 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.09/1.44 ), ~( 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ) ],
% 1.09/1.44 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.44 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ) ), Y ),
% 1.09/1.44 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.09/1.44 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.09/1.44 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.09/1.44 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.09/1.44 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ],
% 1.09/1.44 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_Suc'(
% 1.09/1.44 'v_sko__List__Xupt__Xinduct__1'( X ) ) ) ) ), ~( hBOOL( hAPP( X,
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.09/1.44 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_Suc'(
% 1.09/1.44 'v_sko__List__Xreplicate__Xinduct__1'( X ) ) ) ) ), ~( hBOOL( hAPP( X,
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.09/1.44 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.09/1.44 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.09/1.44 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.44 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.09/1.44 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.44 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.09/1.44 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.44 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.44 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.09/1.44 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.44 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.09/1.44 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.09/1.44 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.09/1.44 'c_Power_Opower__class_Opower'( X ), Y ), T ), X ), ~( 'c_lessequals'( Y
% 1.09/1.44 , 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_lessequals'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( T, Z,
% 1.09/1.44 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.44 X ), U ), Z ) ), W ), X ), ~( 'c_lessequals'( T, hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.44 X ), 'c_HOL_Ominus__class_Ominus'( U, Y, X ) ), Z ) ), W ), X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'( Y
% 1.09/1.44 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X
% 1.09/1.44 ) ), U ) ), W ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.44 X ), T ), U ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.09/1.44 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ), W ), X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.44 X ), U ), Z ) ), W ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.44 X ), 'c_HOL_Ominus__class_Ominus'( Y, U, X ) ), Z ) ), T ), W, X ) ) ]
% 1.09/1.44 ,
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X
% 1.09/1.44 ) ), T ) ), U ), W, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.44 X ), Y ), T ) ), U ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.09/1.44 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), W ), X ) ) ],
% 1.09/1.44 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y
% 1.09/1.44 , X, 'tc_nat' ) ) ],
% 1.09/1.44 [ =( 'c_Lambda_Olift'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), Z ),
% 1.09/1.44 hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_Olift'( X, Z ) ),
% 1.09/1.44 'c_Lambda_Olift'( Y, Z ) ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.44 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.44 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.09/1.44 ), X ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP(
% 1.09/1.44 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ],
% 1.09/1.44 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 1.09/1.44 X, T, 'tc_nat' ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.09/1.44 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.09/1.44 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.09/1.44 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.09/1.44 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.09/1.44 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ), Y ),
% 1.09/1.44 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.09/1.44 'tc_nat' ) ) ],
% 1.09/1.44 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Y, 'tc_nat' ), X ),
% 1.09/1.44 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.09/1.44 'tc_nat' ) ) ],
% 1.09/1.44 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'(
% 1.09/1.44 X, Y, 'tc_nat' ) ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 1.09/1.44 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ),
% 1.09/1.44 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( =( 'c_List_Oreplicate'( X, Y, Z ), 'c_List_Oreplicate'( T, U, Z ) )
% 1.09/1.44 ), =( X, T ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.09/1.44 Y ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.09/1.44 Y ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.09/1.44 Y ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.09/1.44 Y ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.09/1.44 Y ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.09/1.44 Y ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.09/1.44 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.09/1.44 , Z ), T ), X ), ~( 'c_lessequals'( Y, T, X ) ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.09/1.44 ,
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.44 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ),
% 1.09/1.44 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.09/1.44 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.44 'c_Divides_Odiv__class_Odiv'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.09/1.44 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.44 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.09/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.44 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.09/1.44 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.09/1.44 Y, Z, 'tc_nat' ), ~( 'c_lessequals'( 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.09/1.44 Y, X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.09/1.44 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.09/1.44 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~( 'c_lessequals'( Y,
% 1.09/1.44 Z, 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_Lambda_Obeta'( 'c_Lambda_Osubst'( X, Y, Z ), 'c_Lambda_Osubst'( T,
% 1.09/1.44 Y, Z ) ), ~( 'c_Lambda_Obeta'( X, T ) ) ],
% 1.09/1.44 [ =( 'c_Lambda_OdB_OdB__case'( X, Y, Z, 'c_Lambda_OdB_OAbs'( T ), U ),
% 1.09/1.44 hAPP( Z, T ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.09/1.44 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.09/1.44 Z, X ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.09/1.44 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.44 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.09/1.44 ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.09/1.44 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.44 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.09/1.44 ) ) ],
% 1.09/1.44 [ =( 'c_Orderings_Oord__class_Omax'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 1.09/1.44 'tc_nat' ), 'c_Suc'( 'c_Orderings_Oord__class_Omax'( X, Y, 'tc_nat' ) ) )
% 1.09/1.44 ],
% 1.09/1.44 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.44 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.09/1.44 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.09/1.44 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.09/1.44 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~( 'c_lessequals'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.09/1.44 [ 'c_lessequals'( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), X,
% 1.09/1.44 'tc_nat' ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.09/1.44 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omin'( Y, Z,
% 1.09/1.44 X ), X ), 'c_Orderings_Oord__class_Omin'( Y, Z, X ) ) ],
% 1.09/1.44 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 1.09/1.44 'c_Lambda_OdB_OVar'( X ) ), =( X, Z ), 'c_HOL_Oord__class_Oless'( Z, X,
% 1.09/1.44 'tc_nat' ) ],
% 1.09/1.44 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ), 'tc_nat' ),
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( Z, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.44 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ) ), Y ) ), U ), 'tc_nat' )
% 1.09/1.44 ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 1.09/1.44 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ), 'tc_nat' ),
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.44 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ) ), Y ) ), Z ), U, 'tc_nat'
% 1.09/1.44 ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 1.09/1.44 ), Z ), Y ) ],
% 1.09/1.44 [ ~( hBOOL( hAPP( X, 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), Y, 'tc_nat' ) ) ) ),
% 1.09/1.44 hBOOL( hAPP( X, Z ) ) ],
% 1.09/1.44 [ ~( hBOOL( hAPP( X, 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), Y, 'tc_nat' ) ) ) ),
% 1.09/1.44 hBOOL( hAPP( X, Z ) ) ],
% 1.09/1.44 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 1.09/1.44 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ), =( 'c_Suc'(
% 1.09/1.44 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ],
% 1.09/1.44 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.09/1.44 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y )
% 1.09/1.44 , 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.44 'tc_nat' ), Y, 'tc_nat' ) ],
% 1.09/1.44 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.09/1.44 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z )
% 1.09/1.44 , 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.44 'tc_nat' ), X, 'tc_nat' ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.09/1.44 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.09/1.44 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.09/1.44 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_Suc'(
% 1.09/1.44 'v_sko__Nat__Xnat__Xinducts__1'( X ) ) ) ) ), ~( hBOOL( hAPP( X,
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.09/1.44 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ) ) ],
% 1.09/1.44 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.09/1.44 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.09/1.44 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.09/1.44 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.09/1.44 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.09/1.44 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ),
% 1.09/1.44 'tc_nat' ), ~( 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 1.09/1.44 Z, 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.09/1.44 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.09/1.44 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.09/1.44 ), Z ) ), Y ) ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.09/1.44 ), Z ) ) ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.09/1.44 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.09/1.44 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'c_lessequals'( X, X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X,
% 1.09/1.44 'c_Suc'( X ), 'tc_nat' ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ) ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~(
% 1.09/1.44 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.09/1.44 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.09/1.44 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.09/1.44 ), Z ) ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.09/1.44 ), T ) ) ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.09/1.44 ), T ) ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Z
% 1.09/1.44 ), T ) ) ) ],
% 1.09/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.44 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.09/1.44 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.09/1.44 ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.09/1.44 [ =( 'c_Lambda_OdB_OdB__case'( X, Y, Z, hAPP( hAPP( 'c_Lambda_OdB_OApp'
% 1.09/1.44 , T ), U ), W ), hAPP( hAPP( Y, T ), U ) ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.09/1.44 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.09/1.44 ), Y ), 'c_Suc'( Z ) ), 'c_HOL_Oone__class_Oone'( X ), X ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.09/1.44 ,
% 1.09/1.44 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.09/1.44 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.09/1.44 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.09/1.44 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Z ), ~( 'c_lessequals'( Y, Z,
% 1.09/1.44 X ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 1.09/1.44 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Z ) ), 'c_lessequals'( Y, Z, X
% 1.09/1.44 ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.09/1.44 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Y ), ~( 'c_lessequals'( Z, Y,
% 1.09/1.44 X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.44 X ), Y ), Z ) ), T ) ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.44 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.44 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.44 X ), Y ), Z ) ), T ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.44 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.09/1.44 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.44 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.09/1.44 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.44 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.09/1.44 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.09/1.44 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ) ],
% 1.09/1.44 [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X,
% 1.09/1.44 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.44 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ),
% 1.09/1.44 X ), 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X,
% 1.09/1.44 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.44 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.09/1.44 Y ), 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ],
% 1.09/1.44 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.09/1.44 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.09/1.44 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), X ), Y, 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.09/1.44 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.09/1.44 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.09/1.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 1.09/1.44 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 1.09/1.44 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.09/1.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y,
% 1.09/1.44 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y )
% 1.09/1.44 , 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.09/1.44 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y ), ~( 'c_lessequals'( Y, Z,
% 1.09/1.44 X ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 1.09/1.44 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y ) ), 'c_lessequals'( Y, Z, X
% 1.09/1.44 ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.09/1.44 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Z ), ~( 'c_lessequals'( Z, Y,
% 1.09/1.44 X ) ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), =(
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omax'( Y, Z, X ),
% 1.09/1.44 T, X ), 'c_Orderings_Oord__class_Omax'( 'c_HOL_Ominus__class_Ominus'( Y,
% 1.09/1.44 T, X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X ), X ) ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.09/1.44 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.09/1.44 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Y, X ) )
% 1.09/1.44 , ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ],
% 1.09/1.44 [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), Y,
% 1.09/1.44 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.44 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Osemigroup__add'( X ) ), =( 'c_List_Ofoldl'(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.44 X ), Y ), Z ), T, X, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.09/1.44 ), 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Z, T, X, X ) ) ) ]
% 1.09/1.44 ,
% 1.09/1.44 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( X )
% 1.09/1.44 , 'c_Power_Opower_Opower'( 'c_HOL_Oone__class_Oone'( X ),
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), X ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), 'c_Suc'( U ) )
% 1.09/1.44 , hAPP( hAPP( Y, T ), hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T )
% 1.09/1.44 , U ) ) ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.09/1.44 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.09/1.44 ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ],
% 1.09/1.44 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_Suc'(
% 1.09/1.44 'c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1'( X ) ) ) ) ), ~( hBOOL(
% 1.09/1.44 hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.09/1.44 [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 1.09/1.44 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.09/1.44 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ],
% 1.09/1.44 [ 'c_lessequals'( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.09/1.44 'c_Divides_Odiv__class_Odiv'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.09/1.44 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.44 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.09/1.44 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.44 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.09/1.44 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.09/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.44 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.09/1.44 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.09/1.44 ) ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.09/1.44 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.09/1.44 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.09/1.44 [ hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.09/1.44 ~( hBOOL( hAPP( X, T ) ) ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), 'c_Suc'( T ) ), 'tc_nat' )
% 1.09/1.44 ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.09/1.44 ), Z ), T ), Y, 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.09/1.44 'c_lessequals'( Y, T, X ), ~( 'c_lessequals'( Y,
% 1.09/1.44 'c_Orderings_Oord__class_Omax'( T, Z, X ), X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.09/1.44 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.09/1.44 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.09/1.44 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.09/1.44 [ 'c_lessequals'( 'c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1'(
% 1.09/1.44 X, Y ), Y, 'tc_nat' ), ~( hBOOL( hAPP( X, Y ) ) ), hBOOL( hAPP( X,
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, Z ), U ) )
% 1.09/1.44 , hAPP( hAPP( Y, Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.09/1.44 , T ), U ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, Y, V0, V1, V2
% 1.09/1.44 ) ) ],
% 1.09/1.44 [ =( 'c_Lambda_Oliftn'( 'c_Suc'( X ), Y, Z ), 'c_Lambda_Olift'(
% 1.09/1.44 'c_Lambda_Oliftn'( X, Y, Z ), Z ) ) ],
% 1.09/1.44 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Y
% 1.09/1.44 , X, 'tc_nat' ) ), Z ) ), T ) ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.09/1.44 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( T, Z, X ), X ) ) ]
% 1.09/1.44 ,
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.09/1.44 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ]
% 1.09/1.44 ,
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.09/1.44 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 1.09/1.44 T, X ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.09/1.44 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y,
% 1.09/1.44 T, X ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.09/1.44 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 1.09/1.44 T, X ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.09/1.44 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y,
% 1.09/1.44 T, X ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.09/1.44 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( T, Z, X ), X ) ) ]
% 1.09/1.44 ,
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.09/1.44 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ]
% 1.09/1.44 ,
% 1.09/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.44 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.09/1.44 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.09/1.44 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ),
% 1.09/1.44 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ) ), =( Z,
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.44 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.09/1.44 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.09/1.44 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ),
% 1.09/1.44 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ) ), =( T,
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.44 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.09/1.44 Y ) ) ],
% 1.09/1.44 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.09/1.44 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.09/1.44 'tc_nat' ), Y, 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat'
% 1.09/1.44 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.09/1.44 , Y, 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.44 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.09/1.44 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP(
% 1.09/1.44 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ), X ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( T, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.09/1.44 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( U, Y, X ) ), Z ) ), W ), X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.09/1.44 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( Z, T, X ) ), U ) ), W ), X ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), Y ), hAPP(
% 1.09/1.44 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ), W ), X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP(
% 1.09/1.44 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ), X ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( Y, U, X ) ), Z ) ), T ), W, X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( Y, Z, X ) ), T ) ), U ), W, X ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), U ), hAPP(
% 1.09/1.44 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), W ), X ) ) ],
% 1.09/1.44 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.09/1.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.09/1.44 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ) ), ~(
% 1.09/1.44 'c_lessequals'( T, X, 'tc_nat' ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X
% 1.09/1.44 , T, 'tc_nat' ) ), Y ) ), Z ), U ) ],
% 1.09/1.44 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ) ), ~(
% 1.09/1.44 'c_lessequals'( X, T, 'tc_nat' ) ), =( Z, hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( T
% 1.09/1.44 , X, 'tc_nat' ) ), Y ) ), U ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.09/1.44 'c_lessequals'( T, Z, X ), ~( 'c_lessequals'(
% 1.09/1.44 'c_Orderings_Oord__class_Omin'( T, Y, X ), Z, X ) ) ],
% 1.09/1.44 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Y
% 1.09/1.44 , X, 'tc_nat' ) ), Z ) ), T ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.44 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z
% 1.09/1.44 ) ), T ) ) ],
% 1.09/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.09/1.44 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.09/1.44 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.09/1.44 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.09/1.44 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.09/1.44 , U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), W ), T ), Z, X ) ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.09/1.44 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.09/1.44 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.09/1.44 ,
% 1.09/1.44 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.09/1.44 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.09/1.44 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.09/1.44 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.09/1.44 ,
% 1.09/1.44 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, 'c_Suc'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.09/1.44 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.09/1.44 ,
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.09/1.44 ,
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat'
% 1.09/1.44 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.09/1.44 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.44 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.09/1.44 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Ofoldl'(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ), Z, X, X
% 1.09/1.44 ) ), 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ) ) ]
% 1.09/1.44 ,
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.09/1.44 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( T, Y, X ), Z, X ) ) ]
% 1.09/1.44 ,
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.09/1.44 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( Y, T, X ), Z, X ) ) ]
% 1.09/1.44 ,
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.09/1.44 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 1.09/1.44 X ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.09/1.44 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z,
% 1.09/1.44 X ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.09/1.44 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 1.09/1.44 X ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.09/1.44 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z,
% 1.09/1.44 X ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.09/1.44 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( T, Y, X ), Z, X ) ) ]
% 1.09/1.44 ,
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.09/1.44 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( Y, T, X ), Z, X ) ) ]
% 1.09/1.44 ,
% 1.09/1.44 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.09/1.44 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'(
% 1.09/1.44 X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z,
% 1.09/1.44 'tc_nat' ), ~( 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.44 'tc_nat' ), Z ), Y ), 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.44 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.09/1.44 ,
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.09/1.44 , X ), 'c_HOL_Oord__class_Oless'( Y, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.44 Y, 'c_Orderings_Oord__class_Omax'( T, Z, X ), X ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), 'c_Suc'(
% 1.09/1.44 Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.09/1.44 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'( X )
% 1.09/1.44 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP(
% 1.09/1.44 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.09/1.44 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), =( Y,
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 1.09/1.44 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.44 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T
% 1.09/1.44 ) ), X ), Y, 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, T ) ) ],
% 1.09/1.44 [ 'c_InductTermi_OIT'( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 1.09/1.44 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ) ), Y ), Z, 'tc_Lambda_OdB'
% 1.09/1.44 , 'tc_Lambda_OdB' ) ), ~( 'c_InductTermi_OIT'( Y ) ), ~(
% 1.09/1.44 'c_InductTermi_OIT'( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 1.09/1.44 'c_Lambda_Osubst'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z,
% 1.09/1.44 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ],
% 1.09/1.44 [ ~( =( 'v_T____', 'c_Type_Otype_OFun'( X, Y ) ) ), 'c_InductTermi_OIT'(
% 1.09/1.44 'c_Lambda_Osubst'( Z, T, U ) ), ~( 'c_Type_Otyping'( W, T, X ) ), ~(
% 1.09/1.44 'c_InductTermi_OIT'( T ) ), ~( 'c_Type_Otyping'( 'c_Type_Oshift'( W, U, X
% 1.09/1.44 , 'tc_Type_Otype' ), Z, V0 ) ), ~( 'c_InductTermi_OIT'( Z ) ) ],
% 1.09/1.44 [ ~( =( 'v_T____', 'c_Type_Otype_OFun'( X, Y ) ) ), 'c_InductTermi_OIT'(
% 1.09/1.44 'c_Lambda_Osubst'( Z, T, U ) ), ~( 'c_Type_Otyping'( W, T, Y ) ), ~(
% 1.09/1.44 'c_InductTermi_OIT'( T ) ), ~( 'c_Type_Otyping'( 'c_Type_Oshift'( W, U, Y
% 1.09/1.44 , 'tc_Type_Otype' ), Z, V0 ) ), ~( 'c_InductTermi_OIT'( Z ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.44 [ 'c_InductTermi_OIT'( 'c_Lambda_Olift'( X, Y ) ), ~(
% 1.09/1.44 'c_InductTermi_OIT'( X ) ) ],
% 1.09/1.44 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( X ),
% 1.09/1.44 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 1.09/1.44 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T, 'tc_Lambda_OdB',
% 1.09/1.44 'tc_Lambda_OdB' ) ) ) ],
% 1.09/1.44 [ =( 'c_Nat_Onat_Onat__case'( X, Y, 'c_Suc'( Z ), T ), hAPP( Y, Z ) ) ]
% 1.09/1.44 ,
% 1.09/1.44 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OAbs'( Y ) ) ), =( X, Y
% 1.09/1.44 ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.44 X ), X ) ) ],
% 1.09/1.44 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Z ) ), T ), U, 'tc_nat'
% 1.09/1.44 ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.09/1.44 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), T ),
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), U ), 'tc_nat' ) ),
% 1.09/1.44 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ),
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ), 'tc_nat' ),
% 1.09/1.44 ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ) ), Y ) ), Z ), U, 'tc_nat'
% 1.09/1.44 ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.09/1.44 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ), T ) ), U ), 'tc_nat' )
% 1.09/1.44 , ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), X ),
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ), U ), 'tc_nat' ) ),
% 1.09/1.44 ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ),
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ), 'tc_nat' ),
% 1.09/1.44 ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.09/1.44 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ) ), Y ) ), U ), 'tc_nat' )
% 1.09/1.44 ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.09/1.44 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), X ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.09/1.44 Y, X ) ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ) ],
% 1.09/1.44 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ) ), Y, 'tc_nat'
% 1.09/1.44 ), 'c_Divides_Odiv__class_Omod'( 'c_Suc'( Z ), Y, 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.09/1.44 , X ), 'c_HOL_Oord__class_Oless'( T, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.44 'c_Orderings_Oord__class_Omin'( T, Y, X ), Z, X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.09/1.44 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.44 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.09/1.44 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.09/1.44 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.44 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.09/1.44 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.09/1.44 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.09/1.44 , Z ) ],
% 1.09/1.44 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.09/1.44 , Z ) ],
% 1.09/1.44 [ =( 'c_Nat_Osize__class_Osize'( X, 'tc_nat' ), X ) ],
% 1.09/1.44 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat'
% 1.09/1.44 ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Y
% 1.09/1.44 , X ), 'c_lessequals'( Y, Y, X ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.09/1.44 , Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.09/1.44 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.09/1.44 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.09/1.44 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.09/1.44 [ hBOOL( hAPP( X, Y ) ), 'c_HOL_Oord__class_Oless'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.09/1.44 'c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1'( X ), 'tc_nat' ),
% 1.09/1.44 ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), =( 'c_Lambda_Osubst'(
% 1.09/1.44 'c_Lambda_OdB_OVar'( X ), Y, X ), Y ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.09/1.44 'c_Nat_Osemiring__1__class_Oof__nat__aux'( Y, 'c_Suc'( Z ), T, X ),
% 1.09/1.44 'c_Nat_Osemiring__1__class_Oof__nat__aux'( Y, Z, hAPP( Y, T ), X ) ) ]
% 1.09/1.44 ,
% 1.09/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.44 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.09/1.44 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.09/1.44 ), Z ), T, X ) ) ],
% 1.09/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.44 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.09/1.44 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z, T
% 1.09/1.44 , X ) ), T, X ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.09/1.44 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 1.09/1.44 , T, X ), 'c_Orderings_Oord__class_Omin'( Y,
% 1.09/1.44 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.09/1.44 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 1.09/1.44 X ), X ), 'c_Orderings_Oord__class_Omin'( Z,
% 1.09/1.44 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ) ) ],
% 1.09/1.44 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.44 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ]
% 1.09/1.44 ,
% 1.09/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.09/1.44 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.09/1.44 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.09/1.44 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.09/1.44 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.09/1.44 'c_Power_Opower__class_Opower'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.09/1.44 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T,
% 1.09/1.44 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.09/1.44 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.09/1.44 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.09/1.44 'c_lessequals'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) )
% 1.09/1.44 , ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ),
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.09/1.44 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 1.09/1.44 ],
% 1.09/1.44 [ =( 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.44 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.09/1.44 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.09/1.44 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.09/1.44 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.09/1.44 ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.09/1.44 , T, X ) ) ), =( Y, Z ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.09/1.44 , T, X ) ) ), =( Z, T ) ],
% 1.09/1.44 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y
% 1.09/1.44 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), =( X, Z ) ]
% 1.09/1.44 ,
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.09/1.44 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Y, Z,
% 1.09/1.44 X ), X ), Y ) ],
% 1.09/1.44 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.09/1.44 'tc_nat' ) ), =( Y, Z ) ],
% 1.09/1.44 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, 'c_Suc'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.09/1.44 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.09/1.44 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.09/1.44 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Suc'( Y ), X ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.09/1.44 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'( X ) )
% 1.09/1.44 , Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_Suc'(
% 1.09/1.44 Y ) ) ) ],
% 1.09/1.44 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 1.09/1.44 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X )
% 1.09/1.44 , Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ),
% 1.09/1.44 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 1.09/1.44 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z )
% 1.09/1.44 , X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ),
% 1.09/1.44 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ), 'tc_nat' ) ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.09/1.44 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.09/1.44 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z )
% 1.09/1.44 , 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.09/1.44 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.44 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.09/1.44 ,
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.44 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.09/1.44 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.44 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.09/1.44 ,
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.44 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.09/1.44 'c_lessequals'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.09/1.44 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.09/1.44 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.44 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.09/1.44 Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.09/1.44 ) ), Y, 'tc_nat' ) ) ],
% 1.09/1.44 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ),
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ) ],
% 1.09/1.44 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.09/1.44 'c_Suc'( X ), 'tc_nat' ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.09/1.44 'c_Suc'( X ), 'tc_nat' ) ],
% 1.09/1.44 [ =( 'c_Nat_Osize__class_Osize'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y
% 1.09/1.44 ), 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.09/1.44 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.09/1.44 'c_Nat_Osize__class_Osize'( X, 'tc_Lambda_OdB' ) ),
% 1.09/1.44 'c_Nat_Osize__class_Osize'( Y, 'tc_Lambda_OdB' ) ) ), 'c_Suc'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.09/1.44 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.09/1.44 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.09/1.44 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.09/1.44 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.09/1.44 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omax'( Y, T
% 1.09/1.44 , X ), Z, X ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.09/1.44 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omax'( T, Y
% 1.09/1.44 , X ), Z, X ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.09/1.44 'c_Orderings_Oord__class_Omin'( Y, Z, X ), 'c_Orderings_Oord__class_Omin'(
% 1.09/1.44 Z, Y, X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.09/1.44 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.09/1.44 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.09/1.44 , Y, X ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ), T ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ), T ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.44 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), U ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.44 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ), U )
% 1.09/1.44 ) ],
% 1.09/1.44 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), X,
% 1.09/1.44 'tc_nat' ) ],
% 1.09/1.44 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 1.09/1.44 Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( 'c_Lambda_OdB_OAbs'( X )
% 1.09/1.44 , Y ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.09/1.44 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.44 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X
% 1.09/1.44 ), 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.09/1.44 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.44 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.09/1.44 ), 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.09/1.44 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.09/1.44 ,
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.09/1.44 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Z ),
% 1.09/1.44 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.09/1.44 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.09/1.44 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.44 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.09/1.44 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.44 X ), Z ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y )
% 1.09/1.44 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.44 [ ~( hBOOL( hAPP( X, 'c_Nat_Onat_Onat__case'( Y, Z, 'c_Suc'( T ), 't_a'
% 1.09/1.44 ) ) ) ), hBOOL( hAPP( X, hAPP( Z, T ) ) ) ],
% 1.09/1.44 [ ~( hBOOL( hAPP( X, 'c_Nat_Onat_Onat__case'( Y, Z, 'c_Suc'( T ), 't_a'
% 1.09/1.44 ) ) ) ), hBOOL( hAPP( X, hAPP( Z, T ) ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ),
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.44 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.09/1.44 ), X ), Z ), 'tc_nat' ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Z ),
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.44 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.09/1.44 ), Y ), Z ), 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.09/1.44 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.09/1.44 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.09/1.44 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omin'( Z
% 1.09/1.44 , T, X ), X ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.09/1.44 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omin'( T
% 1.09/1.44 , Z, X ), X ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.09/1.44 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.09/1.44 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.09/1.44 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.09/1.44 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 1.09/1.44 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.09/1.44 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.09/1.44 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.09/1.44 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.09/1.44 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.09/1.44 ), Z ) ), T ) ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.09/1.44 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.09/1.44 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z
% 1.09/1.44 , 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.44 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.44 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.09/1.44 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.09/1.44 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.09/1.44 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.09/1.44 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.09/1.44 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.09/1.44 , Y ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.44 [ =( 'c_Lambda_OdB_OdB__rec'( X, Y, Z, hAPP( hAPP( 'c_Lambda_OdB_OApp',
% 1.09/1.44 T ), U ), W ), hAPP( hAPP( hAPP( hAPP( Y, T ), U ),
% 1.09/1.44 'c_Lambda_OdB_OdB__rec'( X, Y, Z, T, W ) ), 'c_Lambda_OdB_OdB__rec'( X, Y
% 1.09/1.44 , Z, U, W ) ) ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.44 'tc_nat' ), 'c_Suc'( X ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.44 'tc_nat' ), 'c_Suc'( X ) ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.44 Y, Z, 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.44 'tc_nat' ), 'c_Suc'( Z ) ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.44 'tc_nat' ), 'c_Suc'( Z ) ), Y ), 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), =( 'c_Suc'( X
% 1.09/1.44 ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), ~( 'c_lessequals'( 'c_Suc'( Y )
% 1.09/1.44 , X, 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_lessequals'( Y, X,
% 1.09/1.44 'tc_nat' ) ],
% 1.09/1.44 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.09/1.44 ) ],
% 1.09/1.44 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), =( X, Z
% 1.09/1.44 ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.09/1.44 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.09/1.44 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.09/1.44 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.44 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.09/1.44 ), Y ), Z ), Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.44 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.09/1.44 ), Y ), Z ), Y, X ), Z ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.44 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.09/1.44 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) )
% 1.09/1.44 , 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.09/1.44 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 1.09/1.44 , 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.44 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.09/1.44 ],
% 1.09/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.09/1.44 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.09/1.44 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.09/1.44 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.09/1.44 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.09/1.44 ), U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), W ), T ), Z, X ) ) ],
% 1.09/1.44 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.09/1.44 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ), ~( 'c_lessequals'( Z
% 1.09/1.44 , Y, 'tc_nat' ) ) ],
% 1.09/1.44 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.09/1.44 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ), Y ) ), ~(
% 1.09/1.44 'c_lessequals'( Z, X, 'tc_nat' ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Suc'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Suc'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), U ) ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.09/1.44 ,
% 1.09/1.44 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.09/1.44 'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ) ),
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( Y, 'c_Divides_Odiv__class_Omod'( Y, X,
% 1.09/1.44 'tc_nat' ), 'tc_nat' ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.09/1.44 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ) ), Y ),
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( X, 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.09/1.44 'tc_nat' ), 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.44 X ), Y ), Z ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.09/1.44 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.09/1.44 ) ), Z ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.44 X ), Z ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ) ) ],
% 1.09/1.44 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z
% 1.09/1.44 , 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ), ~(
% 1.09/1.44 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.09/1.44 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.09/1.44 Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.09/1.44 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 1.09/1.44 ) ],
% 1.09/1.44 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 1.09/1.44 Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( 'c_Lambda_OdB_OVar'( X )
% 1.09/1.44 , Y ) ],
% 1.09/1.44 [ 'c_Lambda_Obeta'( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y,
% 1.09/1.44 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 1.09/1.44 , Z, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), ~( 'c_Lambda_Obeta'( X, Z )
% 1.09/1.44 ) ],
% 1.09/1.44 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_Suc'(
% 1.09/1.44 'v_sko__List__Xlexn__Xinduct__1'( X ) ) ) ) ), ~( hBOOL( hAPP( X,
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.09/1.44 [ =( 'c_Nat_Osize__class_Osize'( 'c_Suc'( X ), 'tc_nat' ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Nat_Osize__class_Osize'( X,
% 1.09/1.44 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ]
% 1.09/1.44 ,
% 1.09/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.44 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.44 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.09/1.44 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.44 'tc_nat' ) ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.09/1.44 , X ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.09/1.44 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 1.09/1.44 , X ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.09/1.44 , Y, X ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.09/1.44 , Y, X ) ) ],
% 1.09/1.44 [ ~( 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 1.09/1.44 ), Y ), X ), 'tc_nat' ) ), =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), X, 'tc_nat' ), Y ) ]
% 1.09/1.44 ,
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.09/1.44 'c_Orderings_Oord__class_Omin'( Y, Y, X ), Y ) ],
% 1.09/1.44 [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OVar'( Y ), Z ),
% 1.09/1.44 'c_Lambda_OdB_OVar'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.09/1.44 Y ), X ) ) ), 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ],
% 1.09/1.44 [ 'c_Lambda_Obeta'( hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 1.09/1.44 X ) ), Y ), 'c_Lambda_Osubst'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.09/1.44 ) ) ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.09/1.44 ,
% 1.09/1.44 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.09/1.44 , X ), Y ), 'tc_nat' ) ],
% 1.09/1.44 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.09/1.44 , Y ), X ), 'tc_nat' ) ],
% 1.09/1.44 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.09/1.44 , X ), Y ), 'tc_nat' ) ],
% 1.09/1.44 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Y ),
% 1.09/1.44 'c_Orderings_Oord__class_Omax'( X, Y, 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.09/1.44 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.44 X ), X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.09/1.44 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.09/1.44 ), =( Z, Y ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.09/1.44 ) ],
% 1.09/1.44 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_lessequals'( X
% 1.09/1.44 , Y, 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.09/1.44 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.09/1.44 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), 'c_HOL_Oord__class_Oless'( Y, Z,
% 1.09/1.44 'tc_nat' ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.09/1.44 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.09/1.44 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.09/1.44 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.09/1.44 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 1.09/1.44 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.09/1.44 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.09/1.44 ) ],
% 1.09/1.44 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.09/1.44 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.09/1.44 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.09/1.44 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.09/1.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.09/1.44 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( W, T,
% 1.09/1.44 X ), Z, X ) ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.09/1.44 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.44 , X ) ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.09/1.44 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.09/1.44 ,
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.09/1.44 'c_Orderings_Oord__class_Omax'( Y, Y, X ), Y ) ],
% 1.09/1.44 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP( hAPP(
% 1.09/1.44 'c_Lambda_OdB_OApp', Z ), T ) ) ), =( Y, T ) ],
% 1.09/1.44 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP( hAPP(
% 1.09/1.44 'c_Lambda_OdB_OApp', Z ), T ) ) ), =( X, Z ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.09/1.44 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.09/1.44 T, X ) ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.44 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.09/1.44 , Z ), T ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) )
% 1.09/1.44 , ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.09/1.44 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.09/1.44 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.09/1.44 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ),
% 1.09/1.44 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 1.09/1.44 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T, 'tc_Lambda_OdB',
% 1.09/1.44 'tc_Lambda_OdB' ) ) ), =( Y, T ) ],
% 1.09/1.44 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ),
% 1.09/1.44 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 1.09/1.44 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T, 'tc_Lambda_OdB',
% 1.09/1.44 'tc_Lambda_OdB' ) ) ), =( X, Z ) ],
% 1.09/1.44 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB',
% 1.09/1.44 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( Z ) ) ), =( X,
% 1.09/1.44 'c_Lambda_OdB_OAbs'( Z ) ) ],
% 1.09/1.44 [ 'c_Type_Otyping'( X, hAPP( hAPP( 'c_Lambda_OdB_OApp', Y ), Z ), T ),
% 1.09/1.44 ~( 'c_Type_Otyping'( X, Z, U ) ), ~( 'c_Type_Otyping'( X, Y,
% 1.09/1.44 'c_Type_Otype_OFun'( U, T ) ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.09/1.44 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), X ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.09/1.44 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ), 'tc_nat' ),
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.44 'tc_nat' ), X ), Z ), 'c_Suc'( Y ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y
% 1.09/1.44 , 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.44 , X ) ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.09/1.44 , X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.09/1.44 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.44 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.09/1.44 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.09/1.44 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.09/1.44 'c_lessequals'( Y, T, X ) ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.09/1.44 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.09/1.44 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.09/1.44 'c_lessequals'( Z, T, X ) ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.09/1.44 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.09/1.44 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.09/1.44 'c_lessequals'( Y, T, X ) ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.09/1.44 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.09/1.44 'c_lessequals'( Z, T, X ) ) ],
% 1.09/1.44 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.09/1.44 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ),
% 1.09/1.44 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), X ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.09/1.44 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ),
% 1.09/1.44 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.44 'c_HOL_Oone__class_Oone'( X ), X ) ],
% 1.09/1.44 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( Y, hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Y,
% 1.09/1.44 X, 'tc_nat' ) ), X ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ) ), Y ), ~( 'c_lessequals'(
% 1.09/1.44 X, Y, 'tc_nat' ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Y ), X ), ~(
% 1.09/1.44 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.09/1.44 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.09/1.44 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.09/1.44 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.09/1.44 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.44 'tc_nat' ), X ), 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ), Z,
% 1.09/1.44 'tc_nat' ) ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ), hAPP( hAPP( Z, Y ),
% 1.09/1.44 'c_Suc'( T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Z, W, V0,
% 1.09/1.44 V1 ) ) ],
% 1.09/1.44 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.09/1.44 ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.09/1.44 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 1.09/1.44 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =( hAPP(
% 1.09/1.44 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.09/1.44 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.09/1.44 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ],
% 1.09/1.44 [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X,
% 1.09/1.44 'tc_nat' ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.09/1.44 , =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.09/1.44 'c_Orderings_Oord__class_Omin'( Y, Z, X ) ), T ),
% 1.09/1.44 'c_Orderings_Oord__class_Omin'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.09/1.44 ), Y ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X )
% 1.09/1.44 ) ],
% 1.09/1.44 [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), Z, 'tc_nat' ), 'tc_nat'
% 1.09/1.44 ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), Z, X ), ~(
% 1.09/1.44 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.09/1.44 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.09/1.44 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), Y, X ), ~(
% 1.09/1.44 'c_lessequals'( Z, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.09/1.44 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.09/1.44 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.09/1.44 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.09/1.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 1.09/1.44 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 1.09/1.44 , T, X ), X ), T, X ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.09/1.44 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.09/1.44 'c_Groebner__Basis_Ogb__semiring'( W, Y, X, V0, V1, V2 ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( Z, hAPP(
% 1.09/1.44 hAPP( X, Y ), T ) ), hAPP( hAPP( X, Y ), U ) ) ), ~(
% 1.09/1.44 'c_Groebner__Basis_Ogb__semiring'( Z, X, W, V0, V1, V2 ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.09/1.44 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.09/1.44 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.09/1.44 , V0, V1, V2 ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.09/1.44 T, X, U, W, Y, V0 ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.09/1.44 T, X, U, Y, W, V0 ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.09/1.44 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.09/1.44 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.09/1.44 , V0, V1, V2 ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.09/1.44 X, T, U, Y, W, V0 ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.09/1.44 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.09/1.44 , V0, V1, V2 ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.09/1.44 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.09/1.44 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.09/1.44 , V0, V1, V2 ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.09/1.44 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.09/1.44 W, V0, V1, V2 ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.09/1.44 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.09/1.44 W, V0, V1, V2 ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.09/1.44 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.09/1.44 ~( 'c_Groebner__Basis_Ogb__semiring'( X, W, V0, V1, V2, V3 ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.09/1.44 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.09/1.44 W, V0, V1, V2 ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.09/1.44 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.09/1.44 , V0, V1, V2 ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.09/1.44 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.09/1.44 W, V0, V1, V2 ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.09/1.44 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.09/1.44 , V0, V1, V2 ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.09/1.44 , hAPP( hAPP( X, T ), hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), U ) ) ),
% 1.09/1.44 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.09/1.44 , hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), hAPP( hAPP( X, T ), U ) ) ) ),
% 1.09/1.44 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.09/1.44 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.09/1.44 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.09/1.44 T, X, U, W, Z, V0 ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.09/1.44 T, X, U, W, Y, V0 ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.09/1.44 T, X, U, Z, W, V0 ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.09/1.44 T, X, U, Y, W, V0 ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.09/1.44 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.09/1.44 'c_Groebner__Basis_Ogb__semiring'( Y, X, W, V0, V1, V2 ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.09/1.44 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.09/1.44 X, T, U, Z, W, V0 ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.09/1.44 X, T, U, Y, W, V0 ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, hAPP( hAPP( X, T ), T ) ),
% 1.09/1.44 Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, U, W, T, V0 ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ), hAPP( hAPP( Z, hAPP(
% 1.09/1.44 hAPP( X, T ), U ) ), Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, W
% 1.09/1.44 , V0, U, V1 ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ), hAPP( hAPP( Y, hAPP(
% 1.09/1.44 hAPP( X, Z ), U ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Y, W
% 1.09/1.44 , V0, U, V1 ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, U ), T ) )
% 1.09/1.44 , hAPP( hAPP( Y, hAPP( hAPP( X, Z ), U ) ), T ) ), ~(
% 1.09/1.44 'c_Groebner__Basis_Ogb__semiring'( X, Y, W, V0, V1, V2 ) ) ],
% 1.09/1.44 [ ~( =( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) )
% 1.09/1.44 , =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB',
% 1.09/1.44 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Z, Y,
% 1.09/1.44 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( X, Z ) ],
% 1.09/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.44 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.09/1.44 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.09/1.44 ) ), Z ), T, X ) ) ],
% 1.09/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.44 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.09/1.44 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z,
% 1.09/1.44 T, X ) ), T, X ) ) ],
% 1.09/1.44 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.09/1.44 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.09/1.44 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.09/1.44 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 1.09/1.44 X ), Y, 'tc_nat' ), 'c_Suc'( Z ), 'tc_nat' ),
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.09/1.44 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_lessequals'( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.09/1.44 'c_Divides_Odiv__class_Odiv'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.09/1.44 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.09/1.44 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.09/1.44 , Y, 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.09/1.44 'c_Suc'( X ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.09/1.44 , 'c_Suc'( X ) ), Z ), 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) )
% 1.09/1.44 ],
% 1.09/1.44 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'( Z ) ), X ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'( Z ) ), Y ), 'tc_nat' )
% 1.09/1.44 ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.44 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.09/1.44 ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.44 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.09/1.44 ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.44 [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OAbs'( X ) ), ~(
% 1.09/1.44 'c_InductTermi_OIT'( X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.44 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.09/1.44 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ],
% 1.09/1.44 [ 'c_Lambda_Obeta'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP(
% 1.09/1.44 hAPP( 'c_Lambda_OdB_OApp', X ), Z ) ), ~( 'c_Lambda_Obeta'( Y, Z ) ) ]
% 1.09/1.44 ,
% 1.09/1.44 [ 'c_Lambda_Obeta'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP(
% 1.09/1.44 hAPP( 'c_Lambda_OdB_OApp', Z ), Y ) ), ~( 'c_Lambda_Obeta'( X, Z ) ) ]
% 1.09/1.44 ,
% 1.09/1.44 [ =( 'c_Nat_Osize__class_Osize'( 'c_Lambda_OdB_OAbs'( X ),
% 1.09/1.44 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.09/1.44 'c_Nat_Osize__class_Osize'( X, 'tc_Lambda_OdB' ) ), 'c_Suc'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.09/1.44 'c_Orderings_Oord__class_Omax'( Y, Z, X ), 'c_Orderings_Oord__class_Omax'(
% 1.09/1.44 Z, Y, X ) ) ],
% 1.09/1.44 [ 'c_InductTermi_OIT'( 'v_u____' ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.09/1.44 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.09/1.44 'c_Power_Opower__class_Opower'( X ), T ), Z ) ) ), =( Y, T ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.09/1.44 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.09/1.44 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.09/1.44 [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OVar'( Y ), Z ),
% 1.09/1.44 'c_Lambda_OdB_OVar'( Y ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat'
% 1.09/1.44 ) ) ],
% 1.09/1.44 [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( X ), 'tc_nat' ) ],
% 1.09/1.44 [ =( 'c_List_Odrop'( X, 'c_List_Oreplicate'( Y, Z, T ), T ),
% 1.09/1.44 'c_List_Oreplicate'( 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), Z, T
% 1.09/1.44 ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.09/1.44 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 1.09/1.44 , 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ),
% 1.09/1.44 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 1.09/1.44 X ), X ), X ) ],
% 1.09/1.44 [ =( 'c_Lambda_Oliftn'( X, hAPP( hAPP( 'c_Lambda_OdB_OApp', Y ), Z ), T
% 1.09/1.44 ), hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_Oliftn'( X, Y, T ) ),
% 1.09/1.44 'c_Lambda_Oliftn'( X, Z, T ) ) ) ],
% 1.09/1.44 [ =( 'c_nat_Onat__size'( 'c_Suc'( X ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_nat_Onat__size'( X ) ),
% 1.09/1.44 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.09/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.09/1.44 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Y, Z,
% 1.09/1.44 X ), X ), Y ) ],
% 1.09/1.44 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.09/1.44 ), X ), X ), 'tc_nat' ) ],
% 1.09/1.44 [ =( 'c_Lambda_Osubst'( 'c_Lambda_Olift'( X, Y ), Z, Y ), X ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.09/1.44 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.09/1.44 ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.09/1.44 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.09/1.44 , Z ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X )
% 1.09/1.44 ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.09/1.44 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.09/1.44 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( X, Y
% 1.09/1.44 , 'tc_nat' ), 'tc_nat' ), Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 1.09/1.44 ,
% 1.09/1.44 [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OVar'( X ), Y ),
% 1.09/1.44 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat'
% 1.09/1.44 ) ) ],
% 1.09/1.44 [ 'c_Lambda_Obeta'( 'c_Lambda_Olift'( X, Y ), 'c_Lambda_Olift'( Z, Y ) )
% 1.09/1.44 , ~( 'c_Lambda_Obeta'( X, Z ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.09/1.44 , Y ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP(
% 1.09/1.44 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.09/1.44 ,
% 1.09/1.44 [ =( 'c_Orderings_Oord__class_Omin'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 1.09/1.44 'tc_nat' ), 'c_Suc'( 'c_Orderings_Oord__class_Omin'( X, Y, 'tc_nat' ) ) )
% 1.09/1.44 ],
% 1.09/1.44 [ =( X, 'c_Suc'( Y ) ), 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 1.09/1.44 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.09/1.44 X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.09/1.44 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.09/1.44 'c_Groebner__Basis_Ogb__semiring'( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), 'c_Power_Opower__class_Opower'( X ),
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.09/1.44 ,
% 1.09/1.44 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.09/1.44 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ),
% 1.09/1.44 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.44 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.09/1.44 ), X ), Z ), 'tc_nat' ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.09/1.44 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Z ),
% 1.09/1.44 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.44 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.09/1.44 ), Y ), Z ), 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.44 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.09/1.44 ), Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 1.09/1.44 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.09/1.44 , Y, 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.44 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.09/1.44 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 1.09/1.44 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.09/1.44 , X, 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.44 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.09/1.44 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.44 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.09/1.44 ), Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.44 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.09/1.44 ), Z ), Y ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.44 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.09/1.44 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 1.09/1.44 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.09/1.44 , X, 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.09/1.44 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.09/1.44 ,
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.09/1.44 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.09/1.44 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.44 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ), hAPP( hAPP( Y, Z ),
% 1.09/1.44 'c_Suc'( T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Y, W, V0,
% 1.09/1.44 V1 ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( X, Y ), 'c_Suc'( Z ) ), hAPP( hAPP( T, Y ), hAPP( hAPP(
% 1.09/1.44 X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1
% 1.09/1.44 ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( X, Y ), 'c_Suc'( Z ) ), hAPP( hAPP( T, Y ), hAPP( hAPP(
% 1.09/1.44 X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1
% 1.09/1.44 ) ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.44 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.09/1.44 ), Z ), Y ), 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.44 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.09/1.44 ), Y ), Z ), 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.09/1.44 , Y ), 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 1.09/1.44 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ),
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.44 'tc_nat' ), X ), Y ), Z, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat'
% 1.09/1.44 ) ) ],
% 1.09/1.44 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Z ),
% 1.09/1.44 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.44 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat'
% 1.09/1.44 ) ) ],
% 1.09/1.44 [ =( 'c_List_Odrop'( X, 'c_List_Odrop'( Y, Z, T ), T ), 'c_List_Odrop'(
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, T ) ) ]
% 1.09/1.44 ,
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.09/1.44 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.09/1.44 ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.09/1.44 'c_Suc'( T ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.09/1.44 'c_Suc'( T ) ), X ) ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.09/1.44 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.09/1.44 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.09/1.44 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), U ) ) ) ), =(
% 1.09/1.44 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.09/1.44 'c_Divides_Odiv__class_Omod'( T, Y, 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.44 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.09/1.44 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.09/1.44 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.44 , 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.09/1.44 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.09/1.44 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.09/1.44 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.09/1.44 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.09/1.44 ,
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.09/1.44 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.09/1.44 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.09/1.44 ,
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.09/1.44 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.09/1.44 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Z
% 1.09/1.44 , T ) ],
% 1.09/1.44 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.44 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.44 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.09/1.44 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.09/1.44 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.09/1.44 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.44 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.09/1.44 ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z )
% 1.09/1.44 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.44 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.44 'tc_nat' ) ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y ), 'tc_nat' ),
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.44 [ =( 'c_Lambda_OdB_OdB__rec'( X, Y, Z, 'c_Lambda_OdB_OAbs'( T ), U ),
% 1.09/1.44 hAPP( hAPP( Z, T ), 'c_Lambda_OdB_OdB__rec'( X, Y, Z, T, U ) ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.09/1.44 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.09/1.44 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.09/1.44 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.09/1.44 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ) ) ],
% 1.09/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.44 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.09/1.44 , Y ), Z ), Z, X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.09/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.44 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.09/1.44 , Y ), Z ), Y, X ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.44 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.09/1.44 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.44 X ), X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.44 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.09/1.44 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.44 X ), X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.44 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.44 X ), X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.44 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.44 X ), X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.09/1.44 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.09/1.44 ,
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.09/1.44 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.09/1.44 ,
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.09/1.44 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.09/1.44 ,
% 1.09/1.44 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.09/1.44 ), Z ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.09/1.44 hAPP( 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ) ) ],
% 1.09/1.44 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( X ), Y,
% 1.09/1.44 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ), ~( 'c_lessequals'( X, Y,
% 1.09/1.44 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.44 'tc_nat' ), Y ), X ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.09/1.44 ) ), X, 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.44 'tc_nat' ), X ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.09/1.44 ) ), X, 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'c_lessequals'( 'c_Suc'( X ), X, 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' )
% 1.09/1.44 , 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.09/1.44 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 1.09/1.44 ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.09/1.44 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.09/1.44 ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 1.09/1.44 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.09/1.44 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.09/1.44 ,
% 1.09/1.44 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), hAPP(
% 1.09/1.44 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ),
% 1.09/1.44 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.09/1.44 'tc_nat' ), Z, 'tc_nat' ) ) ), 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.09/1.44 'tc_nat' ) ) ) ],
% 1.09/1.44 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 1.09/1.44 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat'
% 1.09/1.44 ) ) ],
% 1.09/1.44 [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T,
% 1.09/1.44 'c_Lambda_OdB_OAbs'( U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( T, U ) ) )
% 1.09/1.44 ],
% 1.09/1.44 [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T,
% 1.09/1.44 'c_Lambda_OdB_OAbs'( U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( T, U ) ) )
% 1.09/1.44 ],
% 1.09/1.44 [ 'c_InductTermi_OIT'( 'c_Lambda_Osubst'( X, 'c_Lambda_OdB_OVar'( Y ), Z
% 1.09/1.44 ) ), ~( 'c_InductTermi_OIT'( X ) ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.09/1.44 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.44 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.09/1.44 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.09/1.44 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.09/1.44 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.09/1.44 X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.44 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.09/1.44 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.09/1.44 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.09/1.44 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X )
% 1.09/1.44 ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.44 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.09/1.44 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.09/1.44 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.44 'tc_nat' ), X ), Y ), X, 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.44 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =(
% 1.09/1.44 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ominus__class_Ominus'( Y, Z
% 1.09/1.44 , 'tc_nat' ), X ), 'c_HOL_Ominus__class_Ominus'(
% 1.09/1.44 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.09/1.44 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ), ~( 'c_lessequals'( Z
% 1.09/1.44 , Y, 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.09/1.44 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.09/1.44 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.09/1.44 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.09/1.44 [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), 'tc_nat' ),
% 1.09/1.44 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.09/1.44 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.44 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.09/1.44 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ) ), T ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( T, X, 'tc_nat' ) ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.09/1.44 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_lessequals'( Z,
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 1.09/1.44 ,
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.09/1.44 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'( Y,
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 1.09/1.44 ,
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'( hAPP(
% 1.09/1.44 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.09/1.44 ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'( hAPP(
% 1.09/1.44 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.09/1.44 ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), 'c_lessequals'( hAPP(
% 1.09/1.44 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.09/1.44 ],
% 1.09/1.44 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.09/1.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.09/1.44 'tc_nat' ), Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' )
% 1.09/1.44 ],
% 1.09/1.44 [ ~( =( 'c_Type_Otype_OFun'( X, Y ), 'c_Type_Otype_OFun'( Z, T ) ) ),
% 1.09/1.44 =( Y, T ) ],
% 1.09/1.44 [ ~( =( 'c_Type_Otype_OFun'( X, Y ), 'c_Type_Otype_OFun'( Z, T ) ) ),
% 1.09/1.44 =( X, Z ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.09/1.44 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ), =( T, U ), =( Z,
% 1.09/1.44 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.44 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.09/1.44 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ) ) ), =( Z, T ), =( Y
% 1.09/1.44 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.09/1.44 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.44 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.44 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.09/1.44 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.09/1.44 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.44 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.44 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.09/1.44 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.09/1.44 'tc_nat' ), Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~(
% 1.09/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.09/1.44 'tc_nat' ) ) ],
% 1.09/1.44 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.44 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.09/1.45 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.09/1.45 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.09/1.45 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.09/1.45 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 1.09/1.45 [ ~( =( 'c_Suc'( X ), X ) ) ],
% 1.09/1.45 [ ~( =( X, 'c_Suc'( X ) ) ) ],
% 1.09/1.45 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.09/1.45 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y
% 1.09/1.45 , 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.09/1.45 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.09/1.45 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.09/1.45 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.09/1.45 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.09/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.09/1.45 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.09/1.45 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ),
% 1.09/1.45 ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.09/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.09/1.45 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.45 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.09/1.45 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.09/1.45 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.09/1.45 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.09/1.45 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.09/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.09/1.45 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.09/1.45 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ),
% 1.09/1.45 ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.09/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.09/1.45 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.45 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 1.09/1.45 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.45 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.09/1.45 , Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 1.09/1.45 ],
% 1.09/1.45 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.09/1.45 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.45 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.09/1.45 , Z ), Y ), 'tc_nat' ) ) ],
% 1.09/1.45 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.45 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.09/1.45 , X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) )
% 1.09/1.45 ],
% 1.09/1.45 [ hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hBOOL(
% 1.09/1.45 hAPP( X, 'c_Suc'( 'c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1'( X ) ) )
% 1.09/1.45 ), ~( hBOOL( hAPP( X, Y ) ) ) ],
% 1.09/1.45 [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.09/1.45 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat'
% 1.09/1.45 ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.09/1.45 , Y, 'tc_nat' ) ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.45 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 1.09/1.45 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.09/1.45 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 1.09/1.45 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.09/1.45 ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X
% 1.09/1.45 ) ) ],
% 1.09/1.45 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.09/1.45 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X
% 1.09/1.45 ) ) ],
% 1.09/1.45 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.09/1.45 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.45 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.09/1.45 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.09/1.45 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 1.09/1.45 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( Z, Y, 'tc_nat' )
% 1.09/1.45 ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.09/1.45 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 1.09/1.45 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 1.09/1.45 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 1.09/1.45 ,
% 1.09/1.45 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.09/1.45 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_lessequals'( Y, T
% 1.09/1.45 , X ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.45 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.09/1.45 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.09/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.09/1.45 ,
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.45 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.09/1.45 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.09/1.45 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.45 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.09/1.45 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.09/1.45 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.09/1.45 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.09/1.45 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.09/1.45 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.09/1.45 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.09/1.45 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.45 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.09/1.45 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.09/1.45 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.45 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.09/1.45 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.09/1.45 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.45 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.45 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.09/1.45 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.09/1.45 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.09/1.45 , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.09/1.45 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.09/1.45 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.09/1.45 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.09/1.45 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.45 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.09/1.45 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.09/1.45 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.45 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.09/1.45 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.09/1.45 , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.45 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 1.09/1.45 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.09/1.45 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.09/1.45 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.09/1.45 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.09/1.45 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.09/1.45 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.09/1.45 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X,
% 1.09/1.45 Z, 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.09/1.45 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.45 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, Z, 'tc_nat' ) ),
% 1.09/1.45 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ), Z, 'tc_nat' ) ) ) ]
% 1.09/1.45 ,
% 1.09/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.09/1.45 , =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.09/1.45 'c_Orderings_Oord__class_Omax'( Y, Z, X ) ), T ),
% 1.09/1.45 'c_Orderings_Oord__class_Omax'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.09/1.45 ), Y ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X )
% 1.09/1.45 ) ],
% 1.09/1.45 [ 'c_InductTermi_OIT'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ),
% 1.09/1.45 'c_Lambda_OdB_OVar'( Y ) ) ), ~( 'c_InductTermi_OIT'( X ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.09/1.45 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.09/1.45 'c_Power_Opower__class_Opower'( X ), T ), 'c_Suc'( Z ) ) ) ), =( Y, T ),
% 1.09/1.45 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.09/1.45 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.09/1.45 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.45 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.09/1.45 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.09/1.45 ), 'c_Divides_Odiv__class_Odiv'( Z, T, X ) ), =( Y,
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.45 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.45 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.09/1.45 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.09/1.45 ), 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ), =( Z,
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.45 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.09/1.45 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), =( X,
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.45 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.09/1.45 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T )
% 1.09/1.45 , 'tc_nat' ), ~( 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X
% 1.09/1.45 , Z, 'tc_nat' ) ) ],
% 1.09/1.45 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.09/1.45 ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), X ) )
% 1.09/1.45 , 'tc_nat' ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.09/1.45 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_lessequals'(
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.09/1.45 , ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.09/1.45 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_lessequals'(
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.09/1.45 , ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.09/1.45 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.09/1.45 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omax'( Y, Z, X )
% 1.09/1.45 , T, X ), 'c_Orderings_Oord__class_Omax'( Y,
% 1.09/1.45 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ) ) ],
% 1.09/1.45 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.09/1.45 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 1.09/1.45 X ), X ), 'c_Orderings_Oord__class_Omax'( Z,
% 1.09/1.45 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.09/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.09/1.45 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 1.09/1.45 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.09/1.45 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), Y, 'tc_nat' )
% 1.09/1.45 , 'c_Divides_Odiv__class_Omod'( Z, Y, 'tc_nat' ) ) ],
% 1.09/1.45 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.45 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.09/1.45 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.09/1.45 , 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ],
% 1.09/1.45 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.45 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.09/1.45 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.09/1.45 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.45 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.45 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.09/1.45 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.09/1.45 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.09/1.45 X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), 'c_Suc'(
% 1.09/1.45 'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ) ) ), 'tc_nat' ) ],
% 1.09/1.45 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ) ), Y )
% 1.09/1.45 , 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z ), T,
% 1.09/1.45 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 1.09/1.45 , X ), X ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 1.09/1.45 , X ), X ) ],
% 1.09/1.45 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.45 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.09/1.45 , Y ), Z ), Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.09/1.45 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 1.09/1.45 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.45 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.45 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.09/1.45 , Y ), Z ), Z, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.09/1.45 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 1.09/1.45 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.09/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.45 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.09/1.45 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), X
% 1.09/1.45 ) ) ],
% 1.09/1.45 [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OAbs'( Y ) )
% 1.09/1.45 , ~( 'c_Lambda_Obeta'( X, Y ) ) ],
% 1.09/1.45 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.09/1.45 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omax'( Y, Z,
% 1.09/1.45 X ), X ), 'c_Orderings_Oord__class_Omax'( Y, Z, X ) ) ],
% 1.09/1.45 [ =( 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'(
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), X ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.45 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.45 X ), Y ), Z ), X ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.45 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.45 X ), Z ), Y ), X ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.45 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.45 X ), Y ), Z ), X ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.45 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.45 X ), Z ), Y ), X ) ) ],
% 1.09/1.45 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.09/1.45 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Y, 'tc_nat' ), X ) ]
% 1.09/1.45 ,
% 1.09/1.45 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.09/1.45 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ), Y ) ]
% 1.09/1.45 ,
% 1.09/1.45 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.09/1.45 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.09/1.45 , Y ), Z ), Z, X ), Y ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.09/1.45 Y, Z, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.09/1.45 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.09/1.45 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.09/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.09/1.45 Y, Z, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.09/1.45 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.09/1.45 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.09/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.09/1.45 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.09/1.45 'c_Power_Opower__class_Opower'( X ), Y ), T ), X ), ~( 'c_lessequals'( Z
% 1.09/1.45 , T, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.09/1.45 X ), Y, X ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.09/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.09/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~(
% 1.09/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.09/1.45 [ =( 'c_Nitpick_Onat__gcd'( X, Y ), 'c_Nitpick_Onat__gcd'( Y,
% 1.09/1.45 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ), =( Y,
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.45 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.45 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.09/1.45 ],
% 1.09/1.45 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), =( Y,
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 1.09/1.45 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.45 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T
% 1.09/1.45 ) ), X ), Y, 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, X ) ) ],
% 1.09/1.45 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.09/1.45 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.09/1.45 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.09/1.45 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.09/1.45 ,
% 1.09/1.45 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.09/1.45 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.09/1.45 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.09/1.45 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.09/1.45 ,
% 1.09/1.45 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.09/1.45 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.09/1.45 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.09/1.45 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ]
% 1.09/1.45 ,
% 1.09/1.45 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.09/1.45 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.09/1.45 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.09/1.45 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 1.09/1.45 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y
% 1.09/1.45 , 'tc_nat' ) ) ],
% 1.09/1.45 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.09/1.45 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 1.09/1.45 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 1.09/1.45 , 'tc_nat' ) ) ],
% 1.09/1.45 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.09/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.09/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 1.09/1.45 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.09/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~(
% 1.09/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.09/1.45 ,
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.09/1.45 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.09/1.45 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.09/1.45 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.09/1.45 ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 1.09/1.45 =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.09/1.45 ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.09/1.45 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.09/1.45 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.09/1.45 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.09/1.45 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.45 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.09/1.45 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.45 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.09/1.45 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.09/1.45 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.09/1.45 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.09/1.45 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.09/1.45 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.09/1.45 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.09/1.45 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 1.09/1.45 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.09/1.45 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.45 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.45 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.45 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.45 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.45 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.09/1.45 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.09/1.45 ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.09/1.45 X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y, X ),
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.45 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.09/1.45 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.45 ) ],
% 1.09/1.45 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.09/1.45 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.09/1.45 ) ],
% 1.09/1.45 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.09/1.45 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.45 ) ],
% 1.09/1.45 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.09/1.45 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.45 ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.09/1.45 X ) ), ~( =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) )
% 1.09/1.45 , =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.45 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.45 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.45 ) ],
% 1.09/1.45 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.45 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.09/1.45 ) ],
% 1.09/1.45 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.45 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.45 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.09/1.45 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.09/1.45 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.09/1.45 ,
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.09/1.45 X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 1.09/1.45 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.09/1.45 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.45 ) ), =( Y, Z ) ],
% 1.09/1.45 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.09/1.45 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.45 ) ), =( Y, Z ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.45 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.09/1.45 Y ) ],
% 1.09/1.45 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.09/1.45 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.09/1.45 Y ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.09/1.45 X ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.09/1.45 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.09/1.45 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.09/1.45 Y ) ],
% 1.09/1.45 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.09/1.45 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.09/1.45 Y ) ],
% 1.09/1.45 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.09/1.45 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.09/1.45 Y ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.45 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.09/1.45 Y ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.45 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.09/1.45 Y ) ],
% 1.09/1.45 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.09/1.45 , X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 1.09/1.45 , X ) ) ],
% 1.09/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.09/1.45 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 1.09/1.45 , X ), ~( 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.09/1.45 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ), X ) ) ],
% 1.09/1.45 [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T, hAPP( hAPP(
% 1.09/1.45 'c_Lambda_OdB_OApp', U ), W ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( hAPP(
% 1.09/1.45 Z, U ), W ) ) ) ],
% 1.09/1.45 [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T, hAPP( hAPP(
% 1.09/1.45 'c_Lambda_OdB_OApp', U ), W ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( hAPP(
% 1.09/1.45 Z, U ), W ) ) ) ],
% 1.09/1.45 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( X ),
% 1.09/1.45 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 1.09/1.45 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z ), T, 'tc_Lambda_OdB',
% 1.09/1.45 'tc_Lambda_OdB' ) ) ), =( Y, T ) ],
% 1.09/1.45 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( X ),
% 1.09/1.45 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 1.09/1.45 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( Z ), T, 'tc_Lambda_OdB',
% 1.09/1.45 'tc_Lambda_OdB' ) ) ), =( X, Z ) ],
% 1.09/1.45 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Y ),
% 1.09/1.45 Z ) ) ) ],
% 1.09/1.45 [ =( X, 'c_Type_Otype_OFun'( 'c_Type_Osko__Type__Xtyping__elims__3__1'(
% 1.09/1.45 X, Y, Z ), 'c_Type_Osko__Type__Xtyping__elims__3__2'( X, Y, Z ) ) ), ~(
% 1.09/1.45 'c_Type_Otyping'( Y, 'c_Lambda_OdB_OAbs'( Z ), X ) ) ],
% 1.09/1.45 [ =( 'c_Orderings_Oord__class_Omin'( 'c_HOL_Ominus__class_Ominus'( X, Y
% 1.09/1.45 , 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 1.09/1.45 , 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omin'( X, Z,
% 1.09/1.45 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.09/1.45 [ hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~(
% 1.09/1.45 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~( hBOOL( hAPP( X,
% 1.09/1.45 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ) ) ],
% 1.09/1.45 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Suc'(
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.09/1.45 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.09/1.45 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), Y ) ],
% 1.09/1.45 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.45 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.09/1.45 ), Y ), Z ), Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.45 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.45 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.09/1.45 ), Y ), Z ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.45 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ),
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.45 [ ~( hBOOL( hAPP( X, Y ) ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.09/1.45 'c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1'( X, Z ), 'tc_nat' )
% 1.09/1.45 ), ~( hBOOL( hAPP( X, Z ) ) ), hBOOL( hAPP( X,
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.09/1.45 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.09/1.45 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.09/1.45 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.09/1.45 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.09/1.45 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.09/1.45 T, X ) ) ],
% 1.09/1.45 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 1.09/1.45 , ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.09/1.45 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_Lambda_OdB_OAbs'(
% 1.09/1.45 Z ) ) ) ],
% 1.09/1.45 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.09/1.45 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X )
% 1.09/1.45 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.09/1.45 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ), Y ) ],
% 1.09/1.45 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.09/1.45 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y )
% 1.09/1.45 , 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.09/1.45 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.09/1.45 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z )
% 1.09/1.45 , 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.09/1.45 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.09/1.45 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z )
% 1.09/1.45 , 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.09/1.45 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.09/1.45 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y )
% 1.09/1.45 , 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.09/1.45 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.09/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.09/1.45 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.09/1.45 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.09/1.45 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.09/1.45 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ) ],
% 1.09/1.45 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.09/1.45 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 1.09/1.45 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.09/1.45 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( hAPP(
% 1.09/1.45 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.09/1.45 ,
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.45 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.09/1.45 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.09/1.45 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.45 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.45 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.45 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.09/1.45 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.09/1.45 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.45 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.45 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.09/1.45 [ =( 'c_Lambda_Osubst'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), Z, T
% 1.09/1.45 ), hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_Osubst'( X, Z, T ) ),
% 1.09/1.45 'c_Lambda_Osubst'( Y, Z, T ) ) ) ],
% 1.09/1.45 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'( X
% 1.09/1.45 ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'(
% 1.09/1.45 X ) ), Z ) ) ), =( Y, Z ) ],
% 1.09/1.45 [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ), X ), ~(
% 1.09/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.09/1.45 'tc_nat' ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.09/1.45 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( hAPP(
% 1.09/1.45 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), X ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Oplus__class_Oplus'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 1.09/1.45 , X ) ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ) ],
% 1.09/1.45 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.09/1.45 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.09/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.09/1.45 'tc_nat' ) ) ],
% 1.09/1.45 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.09/1.45 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 1.09/1.45 X ), X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 1.09/1.45 Y, Z, X ), 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ), X ) ],
% 1.09/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.09/1.45 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.09/1.45 , U, X ) ) ), 'c_lessequals'( U, T, X ), ~( 'c_lessequals'( Z, Y, X ) ) ]
% 1.09/1.45 ,
% 1.09/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.09/1.45 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.09/1.45 , U, X ) ) ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( U, T, X ) ) ]
% 1.09/1.45 ,
% 1.09/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.09/1.45 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.09/1.45 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( T, U, X ), ~(
% 1.09/1.45 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.09/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.09/1.45 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.09/1.45 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~(
% 1.09/1.45 'c_HOL_Oord__class_Oless'( T, U, X ) ) ],
% 1.09/1.45 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.09/1.45 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.09/1.45 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.09/1.45 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.45 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.09/1.45 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.09/1.45 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.09/1.45 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.45 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.09/1.45 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.09/1.45 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.09/1.45 , Y ), T ), Z, X ) ) ],
% 1.09/1.45 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.45 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.09/1.45 , Y ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ),
% 1.09/1.45 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.09/1.45 , Y ), Z ), T, X ) ) ],
% 1.09/1.45 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.09/1.45 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ) ), Y ),
% 1.09/1.45 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.09/1.45 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'( Y
% 1.09/1.45 ), 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.09/1.45 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.09/1.45 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.09/1.45 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.09/1.45 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.45 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.09/1.45 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 1.09/1.45 , T, X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 1.09/1.45 Y, T, X ), 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ) ) ],
% 1.09/1.45 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.09/1.45 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 1.09/1.45 X ), X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 1.09/1.45 Y, Z, X ), 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ) ) ],
% 1.09/1.45 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.09/1.45 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.09/1.45 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.09/1.45 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ) ) ],
% 1.09/1.45 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.09/1.45 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.45 X ), Y ), 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ) ),
% 1.09/1.45 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ), Z ) ],
% 1.09/1.45 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.09/1.45 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.45 X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.09/1.45 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), Y ) ],
% 1.09/1.45 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( Y, hAPP( hAPP(
% 1.09/1.45 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.45 X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.09/1.45 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ) ],
% 1.09/1.45 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.09/1.45 ), =( Z, Y ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.09/1.45 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.09/1.45 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Z, Y ) ],
% 1.09/1.45 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 1.09/1.45 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.09/1.45 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.09/1.45 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.09/1.45 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 1.09/1.45 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.09/1.45 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 1.09/1.45 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.09/1.45 ,
% 1.09/1.45 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.09/1.45 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.09/1.45 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.09/1.45 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.09/1.45 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.09/1.45 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Y, Z ) ],
% 1.09/1.45 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y
% 1.09/1.45 , Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 1.09/1.45 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.09/1.45 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.09/1.45 ,
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.09/1.45 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.45 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'( Z,
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.45 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.09/1.45 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), X ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.45 X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.45 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.09/1.45 ,
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.45 X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.45 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.09/1.45 ,
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.45 X ), Y ), Z ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.09/1.45 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.09/1.45 ,
% 1.09/1.45 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.09/1.45 X, 'tc_nat' ) ), 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.45 'tc_nat' ), X ), 'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ) ), Y,
% 1.09/1.45 'tc_nat' ) ],
% 1.09/1.45 [ =( 'c_Lambda_OdB_OdB__size'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y )
% 1.09/1.45 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Lambda_OdB_OdB__size'( X ) ),
% 1.09/1.45 'c_Lambda_OdB_OdB__size'( Y ) ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.45 'tc_nat' ) ) ) ) ],
% 1.09/1.45 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.45 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.09/1.45 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.09/1.45 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.09/1.45 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), Z ) ) ],
% 1.09/1.45 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.09/1.45 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.09/1.45 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.09/1.45 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.09/1.45 'c_Divides_Odiv__class_Omod'( Z, T, X ) ) ) ],
% 1.09/1.45 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( X ),
% 1.09/1.45 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.09/1.45 [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.09/1.45 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.09/1.45 [ =( 'c_Lambda_OdB_OdB__size'( 'c_Lambda_OdB_OAbs'( X ) ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Lambda_OdB_OdB__size'( X ) ),
% 1.09/1.45 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.09/1.45 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =( hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.09/1.45 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.45 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.09/1.45 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =( hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.09/1.45 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.09/1.45 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.09/1.45 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.09/1.45 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.09/1.45 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.09/1.45 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.09/1.45 ) ) ],
% 1.09/1.45 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.09/1.45 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.09/1.45 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.09/1.45 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.09/1.45 [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X, 'tc_nat' ) ]
% 1.09/1.45 ,
% 1.09/1.45 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.09/1.45 'c_lessequals'( Z, Y, X ) ],
% 1.09/1.45 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.09/1.45 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.09/1.45 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.09/1.45 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.09/1.45 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.09/1.45 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.09/1.45 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.45 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.09/1.45 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.09/1.45 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.09/1.45 ],
% 1.09/1.45 [ =( 'c_Nat_Osize__class_Osize'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.09/1.45 , 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.45 [ ~( hBOOL( hAPP( X, Y ) ) ), hBOOL( hAPP( X,
% 1.09/1.45 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.09/1.45 'tc_nat' ) ) ) ],
% 1.09/1.45 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Omod'( Y,
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.09/1.45 , Y ) ) ],
% 1.09/1.45 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.09/1.45 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ],
% 1.09/1.45 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.45 'tc_nat' ) ) ) ],
% 1.09/1.45 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.09/1.45 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.45 'tc_nat' ) ), Y ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.09/1.45 'c_Nat_Osemiring__1__class_Oof__nat__aux'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.45 'tc_nat' ), Z, X ), Z ) ],
% 1.09/1.45 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 1.09/1.45 'v_sko__List__Xlexn__Xinduct__1'( X ) ) ), ~( hBOOL( hAPP( X,
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.09/1.45 [ hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( hBOOL(
% 1.09/1.45 hAPP( X, 'c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1'( X ) ) ) ), ~(
% 1.09/1.45 hBOOL( hAPP( X, Y ) ) ) ],
% 1.09/1.45 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.09/1.45 [ =( 'c_Lambda_Oliftn'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, Y ),
% 1.09/1.45 X ) ],
% 1.09/1.45 [ hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ), ~( hBOOL( hAPP( X
% 1.09/1.45 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.09/1.45 [ ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), hBOOL(
% 1.09/1.45 hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.45 'tc_nat' ), 'tc_nat' ) ) ) ],
% 1.09/1.45 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.09/1.45 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.09/1.45 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.09/1.45 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.45 [ =( 'c_Nat_Onat_Onat__rec'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.09/1.45 ), Z ), X ) ],
% 1.09/1.45 [ hBOOL( hAPP( X, 'c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1'(
% 1.09/1.45 X, Y ) ) ), ~( hBOOL( hAPP( X, Y ) ) ), hBOOL( hAPP( X,
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.09/1.45 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.09/1.45 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.09/1.45 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 1.09/1.45 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ),
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ],
% 1.09/1.45 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.09/1.45 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 1.09/1.45 'c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1'( X ) ) ), ~( hBOOL( hAPP( X
% 1.09/1.45 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.09/1.45 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.45 'tc_nat' ) ) ],
% 1.09/1.45 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.45 'tc_nat' ) ) ],
% 1.09/1.45 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.45 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.45 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.45 [ =( 'c_Nat_Onat_Onat__case'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.09/1.45 ), Z ), X ) ],
% 1.09/1.45 [ =( 'c_Nat_Onat_Onat__case'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.09/1.45 ), Z ), X ) ],
% 1.09/1.45 [ =( 'c_Orderings_Oord__class_Omin'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.45 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.45 [ =( 'c_Orderings_Oord__class_Omin'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.45 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 1.09/1.45 ,
% 1.09/1.45 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.09/1.45 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), =( Y
% 1.09/1.45 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 1.09/1.45 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.09/1.45 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( X
% 1.09/1.45 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 1.09/1.45 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.09/1.45 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( Y
% 1.09/1.45 , Z ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.45 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.45 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.09/1.45 [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_nat' ),
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.45 [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 1.09/1.45 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.45 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X
% 1.09/1.45 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.45 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 1.09/1.45 'v_sko__List__Xreplicate__Xinduct__1'( X ) ) ), ~( hBOOL( hAPP( X,
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.09/1.45 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.09/1.45 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.09/1.45 [ ~( hBOOL( hAPP( X, 'c_Nat_Onat_Onat__case'( Y, Z,
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 't_a' ) ) ) ), hBOOL( hAPP( X, Y
% 1.09/1.45 ) ) ],
% 1.09/1.45 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, 'v_sko__Nat__Xnat__Xinducts__1'(
% 1.09/1.45 X ) ) ), ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) )
% 1.09/1.45 ],
% 1.09/1.45 [ =( 'c_Nitpick_Onat__gcd'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.09/1.45 , X ) ],
% 1.09/1.45 [ =( 'c_nat_Onat__size'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.45 [ =( 'c_String_Ochar_Ochar__size'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.45 'tc_nat' ) ) ],
% 1.09/1.45 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.45 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.45 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, 'v_sko__Nat__Xnat__Xinduct__1'(
% 1.09/1.45 X ) ) ), ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) )
% 1.09/1.45 ],
% 1.09/1.45 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.09/1.45 ), 'tc_nat' ) ) ],
% 1.09/1.45 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.09/1.45 ), 'tc_nat' ) ) ],
% 1.09/1.45 [ =( 'c_Orderings_Obot__class_Obot'( 'tc_nat' ),
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.45 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, 'v_sko__List__Xupt__Xinduct__1'(
% 1.09/1.45 X ) ) ), ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) )
% 1.09/1.45 ],
% 1.09/1.45 [ =( 'c_List_Odrop'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, Y ), X )
% 1.09/1.45 ],
% 1.09/1.45 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.09/1.45 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.45 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 1.09/1.45 'c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1'( X ) ) ) ), ~( hBOOL(
% 1.09/1.45 hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.09/1.45 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' )
% 1.09/1.45 ],
% 1.09/1.45 [ =( 'c_Nat_Osize__class_Osize'( X, 'tc_String_Ochar' ),
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.45 [ =( 'c_List_Oreplicate'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, Y )
% 1.09/1.45 , 'c_List_Oreplicate'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, Y ) ) ]
% 1.09/1.45 ,
% 1.09/1.45 [ =( 'c_Orderings_Oord__class_Omax'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.45 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.09/1.45 [ =( 'c_Orderings_Oord__class_Omax'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.45 'tc_nat' ), X, 'tc_nat' ), X ) ],
% 1.09/1.45 [ ~( =( 'c_List_Oreplicate'( X, Y, Z ), 'c_List_Oreplicate'( T, U, Z ) )
% 1.09/1.45 ), =( Y, U ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.45 [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.09/1.45 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ],
% 1.09/1.45 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.09/1.45 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ),
% 1.09/1.45 ~( 'c_Groebner__Basis_Ogb__semiring'( T, U, X, W, Z, V0 ) ) ],
% 1.09/1.45 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OVar'( Y ) ) ) ],
% 1.09/1.45 [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T,
% 1.09/1.45 'c_Lambda_OdB_OVar'( U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( Y, U ) ) )
% 1.09/1.45 ],
% 1.09/1.45 [ ~( hBOOL( hAPP( X, 'c_Lambda_OdB_OdB__case'( Y, Z, T,
% 1.09/1.45 'c_Lambda_OdB_OVar'( U ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( Y, U ) ) )
% 1.09/1.45 ],
% 1.09/1.45 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, X ), Y ) ],
% 1.09/1.45 [ ~( 'c_Lambda_Obeta'( 'c_Lambda_OdB_OVar'( X ), Y ) ) ],
% 1.09/1.45 [ =( 'c_Lambda_OdB_OdB__rec'( X, Y, Z, 'c_Lambda_OdB_OVar'( T ), U ),
% 1.09/1.45 hAPP( X, T ) ) ],
% 1.09/1.45 [ ~( =( 'c_Lambda_OdB_OVar'( X ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Y ),
% 1.09/1.45 Z ) ) ) ],
% 1.09/1.45 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OAbs'( Y ) ) ) ],
% 1.09/1.45 [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OVar'( X ) ) ],
% 1.09/1.45 [ =( 'c_Lambda_OdB_OdB__case'( X, Y, Z, 'c_Lambda_OdB_OVar'( T ), U ),
% 1.09/1.45 hAPP( X, T ) ) ],
% 1.09/1.45 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_Lambda_OdB_OVar'(
% 1.09/1.45 Z ) ) ) ],
% 1.09/1.45 [ =( X, Y ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'(
% 1.09/1.45 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( T ), U, 'tc_Lambda_OdB',
% 1.09/1.45 'tc_Lambda_OdB' ), Y ) ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'(
% 1.09/1.45 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OVar'( T ), U, 'tc_Lambda_OdB',
% 1.09/1.45 'tc_Lambda_OdB' ), X ) ) ],
% 1.09/1.45 [ 'c_Type_Otyping'( X, Y, Z ), ~( 'c_Lambda_Obeta'( T, Y ) ), ~(
% 1.09/1.45 'c_Type_Otyping'( X, T, Z ) ) ],
% 1.09/1.45 [ 'c_Type_Otyping'( 'c_Type_Oshift'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.45 'tc_nat' ), 'c_Type_Osko__Type__Xabs__typeE__1__1'( X, Y ),
% 1.09/1.45 'tc_Type_Otype' ), Y, 'c_Type_Osko__Type__Xabs__typeE__1__2'( X, Y ) ),
% 1.09/1.45 ~( 'c_Type_Otyping'( X, 'c_Lambda_OdB_OAbs'( Y ), Z ) ) ],
% 1.09/1.45 [ 'c_Type_Otyping'( 'c_Type_Oshift'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.45 'tc_nat' ), 'c_Type_Osko__Type__Xtyping__elims__3__1'( Y, X, Z ),
% 1.09/1.45 'tc_Type_Otype' ), Z, 'c_Type_Osko__Type__Xtyping__elims__3__2'( Y, X, Z
% 1.09/1.45 ) ), ~( 'c_Type_Otyping'( X, 'c_Lambda_OdB_OAbs'( Z ), Y ) ) ],
% 1.09/1.45 [ =( hAPP( 'c_Type_Oshift'( X, Y, Z, T ), U ), hAPP( X, U ) ), ~(
% 1.09/1.45 'c_HOL_Oord__class_Oless'( U, Y, 'tc_nat' ) ) ],
% 1.09/1.45 [ 'c_Type_Otyping'( 'v_e____', 'v_u____', 'v_T____' ) ],
% 1.09/1.45 [ 'c_Type_Otyping'( X, 'c_Lambda_OdB_OAbs'( Y ), 'c_Type_Otype_OFun'( Z
% 1.09/1.45 , T ) ), ~( 'c_Type_Otyping'( 'c_Type_Oshift'( X,
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_Type_Otype' ), Y, T ) ) ]
% 1.09/1.45 ,
% 1.09/1.45 [ 'c_Type_Otyping'( 'c_Type_Oshift'( 'v_e____', 'v_i____', 'v_T____',
% 1.09/1.45 'tc_Type_Otype' ), 'v_a____', 'v_T_H_H____' ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.09/1.45 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.09/1.45 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.09/1.45 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.09/1.45 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.09/1.45 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.09/1.45 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.09/1.45 ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.45 'tc_nat' ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.09/1.45 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.09/1.45 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.09/1.45 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.09/1.45 ) ) ],
% 1.09/1.45 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.09/1.45 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 1.09/1.45 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.09/1.45 [ =( 'c_Nat_Osize__class_Osize'( 'c_Lambda_OdB_OVar'( X ),
% 1.09/1.45 'tc_Lambda_OdB' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.45 [ =( 'c_Lambda_OdB_OdB__size'( 'c_Lambda_OdB_OVar'( X ) ),
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.09/1.45 [ =( 'c_Type_Oshift'( 'c_Type_Oshift'( X, Y, Z, T ),
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), U, T ), 'c_Type_Oshift'(
% 1.09/1.45 'c_Type_Oshift'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), U, T ),
% 1.09/1.45 'c_Suc'( Y ), Z, T ) ) ],
% 1.09/1.45 [ 'c_Type_Otyping'( 'c_Type_Oshift'( X, Y, Z, 'tc_Type_Otype' ),
% 1.09/1.45 'c_Lambda_Olift'( T, Y ), U ), ~( 'c_Type_Otyping'( X, T, U ) ) ],
% 1.09/1.45 [ ~( 'c_Type_Otyping'( X, Y, Z ) ), ~( 'c_Type_Otyping'( 'c_Type_Oshift'(
% 1.09/1.45 X, T, Z, 'tc_Type_Otype' ), U, W ) ), 'c_Type_Otyping'( X,
% 1.09/1.45 'c_Lambda_Osubst'( U, Y, T ), W ) ],
% 1.09/1.45 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OVar'( Y ) ) ), =( X, Y
% 1.09/1.45 ) ],
% 1.09/1.45 [ =( hAPP( 'c_Type_Oshift'( X, Y, Z, T ), Y ), Z ) ],
% 1.09/1.45 [ =( hAPP( X, Y ), Z ), ~( 'c_Type_Otyping'( X, 'c_Lambda_OdB_OVar'( Y )
% 1.09/1.45 , Z ) ) ],
% 1.09/1.45 [ 'c_Type_Otyping'( X, 'c_Lambda_OdB_OVar'( Y ), hAPP( X, Y ) ) ],
% 1.09/1.45 [ ~( 'c_Type_Otyping'( 'c_Type_Oshift'( 'v_e____',
% 1.09/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'v_T_H_H____', 'tc_Type_Otype' )
% 1.09/1.45 , 'c_Lambda_OdB_OVar'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.09/1.45 'v_T_H_H____' ) ) ],
% 1.09/1.45 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 1.09/1.45 'class_Orderings_Opreorder'( Y ) ) ],
% 1.09/1.45 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 1.09/1.45 'class_Orderings_Oorder'( Y ) ) ],
% 1.09/1.45 [ 'class_Orderings_Obot'( 'tc_fun'( X, Y ) ), ~( 'class_Orderings_Obot'(
% 1.09/1.45 Y ) ) ],
% 1.09/1.45 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 1.09/1.45 ],
% 1.09/1.45 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 1.09/1.45 ) ],
% 1.09/1.45 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 1.09/1.45 ],
% 1.09/1.45 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 1.09/1.45 ,
% 1.09/1.45 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 1.09/1.45 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 1.09/1.45 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 1.09/1.45 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 1.09/1.45 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 1.09/1.45 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 1.09/1.45 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 1.09/1.45 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 1.09/1.45 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 1.09/1.45 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 1.09/1.45 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 1.09/1.45 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 1.09/1.45 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 1.09/1.45 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 1.09/1.45 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 1.09/1.45 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 1.09/1.45 [ 'class_OrderedGroup_Osemigroup__add'( 'tc_nat' ) ],
% 1.09/1.45 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 1.09/1.45 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 1.09/1.45 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 1.09/1.45 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 1.09/1.45 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 1.09/1.45 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 1.09/1.45 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 1.09/1.45 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 1.09/1.45 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 1.09/1.45 [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ],
% 1.09/1.45 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 1.09/1.45 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 1.09/1.45 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 1.09/1.45 [ 'class_Orderings_Obot'( 'tc_nat' ) ],
% 1.09/1.45 [ 'class_Power_Opower'( 'tc_nat' ) ],
% 1.09/1.45 [ 'c_fequal'( X, X, Y ) ],
% 1.09/1.45 [ =( X, Y ), ~( 'c_fequal'( X, Y, Z ) ) ]
% 1.09/1.45 ] .
% 1.09/1.45
% 1.09/1.45
% 1.09/1.45 percentage equality = 0.269907, percentage horn = 0.895323
% 1.09/1.45 This is a problem with some equality
% 1.09/1.45
% 1.09/1.45
% 1.09/1.45
% 1.09/1.45 Options Used:
% 1.09/1.45
% 1.09/1.45 useres = 1
% 1.09/1.45 useparamod = 1
% 1.09/1.45 useeqrefl = 1
% 1.09/1.45 useeqfact = 1
% 1.09/1.45 usefactor = 1
% 1.09/1.45 usesimpsplitting = 0
% 1.09/1.45 usesimpdemod = 5
% 1.09/1.45 usesimpres = 3
% 1.09/1.45
% 1.09/1.45 resimpinuse = 1000
% 1.09/1.45 resimpclauses = 20000
% 1.09/1.45 substype = eqrewr
% 1.09/1.45 backwardsubs = 1
% 1.09/1.45 selectoldest = 5
% 1.09/1.45
% 1.09/1.45 litorderings [0] = split
% 1.09/1.45 litorderings [1] = extend the termordering, first sorting on arguments
% 1.09/1.45
% 1.09/1.45 termordering = kbo
% 1.09/1.45
% 1.09/1.45 litapriori = 0
% 1.09/1.45 termapriori = 1
% 1.09/1.45 litaposteriori = 0
% 1.09/1.45 termaposteriori = 0
% 1.09/1.45 demodaposteriori = 0
% 1.09/1.45 ordereqreflfact = 0
% 1.09/1.45
% 1.09/1.45 litselect = negord
% 1.09/1.45
% 1.09/1.45 maxweight = 15
% 1.09/1.45 maxdepth = 30000
% 1.09/1.45 maxlength = 115
% 1.09/1.45 maxnrvars = 195
% 1.09/1.45 excuselevel = 1
% 1.09/1.45 increasemaxweight = 1
% 1.09/1.45
% 1.09/1.45 maxselected = 10000000
% 1.09/1.45 maxnrclauses = 10000000
% 1.09/1.45
% 1.09/1.45 showgenerated = 0
% 1.09/1.45 showkept = 0
% 1.09/1.45 showselected = 0
% 1.09/1.45 showdeleted = 0
% 1.09/1.45 showresimp = 1
% 1.09/1.45 showstatus = 2000
% 1.09/1.45
% 1.09/1.45 prologoutput = 1
% 1.09/1.45 nrgoals = 5000000
% 1.09/1.45 totalproof = 1
% 1.09/1.45
% 1.09/1.45 Symbols occurring in the translation:
% 1.09/1.45
% 1.09/1.45 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.09/1.45 . [1, 2] (w:1, o:176, a:1, s:1, b:0),
% 1.09/1.45 ! [4, 1] (w:0, o:98, a:1, s:1, b:0),
% 1.09/1.45 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.09/1.45 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.09/1.45 'class_Orderings_Olinorder' [40, 1] (w:1, o:104, a:1, s:1, b:0),
% 1.09/1.45 'c_Orderings_Oord__class_Omax' [43, 3] (w:1, o:212, a:1, s:1, b:0),
% 1.09/1.45 'c_HOL_Oord__class_Oless' [45, 3] (w:1, o:213, a:1, s:1, b:0),
% 1.09/1.45 'class_OrderedGroup_Opordered__ab__group__add' [46, 1] (w:1, o:105
% 1.09/1.45 , a:1, s:1, b:0),
% 1.09/1.45 'c_Orderings_Oord__class_Omin' [47, 3] (w:1, o:214, a:1, s:1, b:0),
% 1.09/1.45 'c_HOL_Ominus__class_Ominus' [48, 3] (w:1, o:215, a:1, s:1, b:0),
% 1.09/1.45 'tc_nat' [51, 0] (w:1, o:27, a:1, s:1, b:0),
% 1.09/1.45 'c_HOL_Ozero__class_Ozero' [52, 1] (w:1, o:106, a:1, s:1, b:0),
% 1.09/1.45 'c_lessequals' [53, 3] (w:1, o:216, a:1, s:1, b:0),
% 1.09/1.45 'class_Ring__and__Field_Oordered__semidom' [54, 1] (w:1, o:110, a:1
% 1.09/1.45 , s:1, b:0),
% 1.09/1.45 'c_Power_Opower__class_Opower' [55, 1] (w:1, o:112, a:1, s:1, b:0),
% 1.09/1.45 hAPP [57, 2] (w:1, o:201, a:1, s:1, b:0),
% 1.09/1.45 'class_Ring__and__Field_Oring' [58, 1] (w:1, o:113, a:1, s:1, b:0),
% 1.09/1.45 'c_HOL_Oplus__class_Oplus' [59, 1] (w:1, o:115, a:1, s:1, b:0),
% 1.09/1.45 'c_HOL_Otimes__class_Otimes' [60, 1] (w:1, o:116, a:1, s:1, b:0),
% 1.09/1.45 hBOOL [66, 1] (w:1, o:117, a:1, s:1, b:0),
% 1.09/1.45 'v_sko__Nat__Xnat__Xinduct__1' [67, 1] (w:1, o:118, a:1, s:1, b:0),
% 1.09/1.45 'c_Suc' [68, 1] (w:1, o:120, a:1, s:1, b:0),
% 1.09/1.45 'class_Divides_Osemiring__div' [69, 1] (w:1, o:122, a:1, s:1, b:0),
% 1.09/1.45 'c_Divides_Odiv__class_Omod' [70, 3] (w:1, o:217, a:1, s:1, b:0),
% 1.09/1.45 'class_Ring__and__Field_Oordered__semiring__strict' [71, 1] (w:1, o:
% 1.09/1.45 123, a:1, s:1, b:0),
% 1.09/1.45 'c_HOL_Oone__class_Oone' [73, 1] (w:1, o:114, a:1, s:1, b:0),
% 1.09/1.72 'class_Ring__and__Field_Osemiring__0' [74, 1] (w:1, o:127, a:1, s:1
% 1.09/1.72 , b:0),
% 1.09/1.72 'class_Power_Opower' [75, 1] (w:1, o:148, a:1, s:1, b:0),
% 1.09/1.72 'c_Divides_Odiv__class_Odiv' [77, 3] (w:1, o:218, a:1, s:1, b:0),
% 1.09/1.72 'c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1' [81, 1] (w:1, o:
% 1.09/1.72 149, a:1, s:1, b:0),
% 1.09/1.72 'class_Orderings_Obot' [83, 1] (w:1, o:128, a:1, s:1, b:0),
% 1.09/1.72 'c_Orderings_Obot__class_Obot' [84, 1] (w:1, o:111, a:1, s:1, b:0),
% 1.09/1.72 'c_Nat_Onat_Onat__rec' [87, 4] (w:1, o:228, a:1, s:1, b:0),
% 1.09/1.72 'c_Groebner__Basis_Ogb__semiring' [94, 6] (w:1, o:235, a:1, s:1, b:0)
% 1.09/1.72 ,
% 1.09/1.72 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [96, 1]
% 1.09/1.72 (w:1, o:129, a:1, s:1, b:0),
% 1.09/1.72 'class_OrderedGroup_Ocomm__monoid__add' [97, 1] (w:1, o:130, a:1, s:1
% 1.09/1.72 , b:0),
% 1.09/1.72 'v_sko__List__Xupt__Xinduct__1' [98, 1] (w:1, o:150, a:1, s:1, b:0),
% 1.09/1.72
% 1.09/1.72 'v_sko__List__Xreplicate__Xinduct__1' [99, 1] (w:1, o:151, a:1, s:1
% 1.09/1.72 , b:0),
% 1.09/1.72 'class_Ring__and__Field_Opordered__ring' [100, 1] (w:1, o:155, a:1
% 1.09/1.72 , s:1, b:0),
% 1.09/1.72 'c_Lambda_OdB_OApp' [101, 0] (w:1, o:73, a:1, s:1, b:0),
% 1.09/1.72 'c_Lambda_Olift' [104, 2] (w:1, o:202, a:1, s:1, b:0),
% 1.09/1.72 'class_Ring__and__Field_Oordered__ring__strict' [105, 1] (w:1, o:109
% 1.09/1.72 , a:1, s:1, b:0),
% 1.09/1.72 'class_Ring__and__Field_Ocomm__semiring__1' [106, 1] (w:1, o:156, a:1
% 1.09/1.72 , s:1, b:0),
% 1.09/1.72 'c_List_Oreplicate' [108, 3] (w:1, o:219, a:1, s:1, b:0),
% 1.09/1.72 'class_OrderedGroup_Ocomm__monoid__mult' [109, 1] (w:1, o:131, a:1
% 1.09/1.72 , s:1, b:0),
% 1.09/1.72 'class_OrderedGroup_Omonoid__mult' [110, 1] (w:1, o:133, a:1, s:1, b:
% 1.09/1.72 0),
% 1.09/1.72 'c_Nat_Osemiring__1__class_Oof__nat' [111, 2] (w:1, o:203, a:1, s:1
% 1.09/1.72 , b:0),
% 1.09/1.72 'c_Lambda_Osubst' [113, 3] (w:1, o:220, a:1, s:1, b:0),
% 1.09/1.72 'c_Lambda_Obeta' [114, 2] (w:1, o:204, a:1, s:1, b:0),
% 1.09/1.72 'c_Lambda_OdB_OAbs' [117, 1] (w:1, o:157, a:1, s:1, b:0),
% 1.09/1.72 'c_Lambda_OdB_OdB__case' [118, 5] (w:1, o:232, a:1, s:1, b:0),
% 1.09/1.72 'class_Ring__and__Field_Oidom' [119, 1] (w:1, o:158, a:1, s:1, b:0),
% 1.09/1.72
% 1.09/1.72 'class_Int_Onumber__ring' [120, 1] (w:1, o:159, a:1, s:1, b:0),
% 1.09/1.72 'class_OrderedGroup_Olordered__ab__group__add' [121, 1] (w:1, o:132
% 1.09/1.72 , a:1, s:1, b:0),
% 1.09/1.72 'c_Lambda_OdB_OVar' [122, 1] (w:1, o:160, a:1, s:1, b:0),
% 1.09/1.72 'class_OrderedGroup_Ogroup__add' [123, 1] (w:1, o:134, a:1, s:1, b:0)
% 1.09/1.72 ,
% 1.09/1.72 'v_sko__Nat__Xnat__Xinducts__1' [124, 1] (w:1, o:161, a:1, s:1, b:0)
% 1.09/1.72 ,
% 1.09/1.72 'class_OrderedGroup_Opordered__ab__semigroup__add' [125, 1] (w:1, o:
% 1.09/1.72 135, a:1, s:1, b:0),
% 1.09/1.72 'c_Power_Opower_Opower' [126, 3] (w:1, o:221, a:1, s:1, b:0),
% 1.09/1.72 'class_OrderedGroup_Opordered__comm__monoid__add' [127, 1] (w:1, o:
% 1.09/1.72 136, a:1, s:1, b:0),
% 1.09/1.72 'class_Orderings_Opreorder' [130, 1] (w:1, o:138, a:1, s:1, b:0),
% 1.09/1.72 'class_Orderings_Oorder' [131, 1] (w:1, o:137, a:1, s:1, b:0),
% 1.09/1.72 'class_OrderedGroup_Oab__group__add' [132, 1] (w:1, o:139, a:1, s:1
% 1.09/1.72 , b:0),
% 1.09/1.72 'class_OrderedGroup_Oab__semigroup__add' [133, 1] (w:1, o:140, a:1
% 1.09/1.72 , s:1, b:0),
% 1.09/1.72 'class_Divides_Oring__div' [134, 1] (w:1, o:121, a:1, s:1, b:0),
% 1.09/1.72 'class_OrderedGroup_Osemigroup__add' [135, 1] (w:1, o:141, a:1, s:1
% 1.09/1.72 , b:0),
% 1.09/1.72 'c_List_Ofoldl' [137, 5] (w:1, o:233, a:1, s:1, b:0),
% 1.09/1.72 'c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1' [140, 1] (w:1, o:162
% 1.09/1.72 , a:1, s:1, b:0),
% 1.09/1.72 'class_Nat_Osemiring__char__0' [141, 1] (w:1, o:103, a:1, s:1, b:0),
% 1.09/1.72
% 1.09/1.72 'class_Ring__and__Field_Oordered__semiring' [142, 1] (w:1, o:152, a:1
% 1.09/1.72 , s:1, b:0),
% 1.09/1.72 'c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1' [143, 2] (w:1
% 1.09/1.72 , o:205, a:1, s:1, b:0),
% 1.09/1.72 'c_Lambda_Oliftn' [144, 3] (w:1, o:222, a:1, s:1, b:0),
% 1.09/1.72 'class_Ring__and__Field_Oordered__idom' [148, 1] (w:1, o:153, a:1, s:
% 1.09/1.72 1, b:0),
% 1.09/1.72 'class_OrderedGroup_Omonoid__add' [149, 1] (w:1, o:142, a:1, s:1, b:0
% 1.09/1.72 ),
% 1.09/1.72 'tc_Lambda_OdB' [151, 0] (w:1, o:78, a:1, s:1, b:0),
% 1.09/1.72 'c_InductTermi_OIT' [152, 1] (w:1, o:163, a:1, s:1, b:0),
% 1.09/1.72 'v_T____' [153, 0] (w:1, o:79, a:1, s:1, b:0),
% 1.09/1.72 'c_Type_Otype_OFun' [156, 2] (w:1, o:208, a:1, s:1, b:0),
% 13.56/13.92 'c_Type_Otyping' [157, 3] (w:1, o:225, a:1, s:1, b:0),
% 13.56/13.92 'tc_Type_Otype' [158, 0] (w:1, o:83, a:1, s:1, b:0),
% 13.56/13.92 'c_Type_Oshift' [159, 4] (w:1, o:229, a:1, s:1, b:0),
% 13.56/13.92 'c_Nat_Onat_Onat__case' [162, 4] (w:1, o:230, a:1, s:1, b:0),
% 13.56/13.92 'class_Ring__and__Field_Osemiring__1' [164, 1] (w:1, o:164, a:1, s:1
% 13.56/13.92 , b:0),
% 13.56/13.92 'c_Nat_Osize__class_Osize' [166, 2] (w:1, o:209, a:1, s:1, b:0),
% 13.56/13.92 'c_Nat_Osemiring__1__class_Oof__nat__aux' [168, 4] (w:1, o:231, a:1
% 13.56/13.92 , s:1, b:0),
% 13.56/13.92 'class_Ring__and__Field_Osemiring' [172, 1] (w:1, o:165, a:1, s:1, b:
% 13.56/13.92 0),
% 13.56/13.92 't_a' [173, 0] (w:1, o:85, a:1, s:1, b:0),
% 13.56/13.92 'class_Ring__and__Field_Opordered__cancel__semiring' [174, 1] (w:1
% 13.56/13.92 , o:166, a:1, s:1, b:0),
% 13.56/13.92 'c_Lambda_OdB_OdB__rec' [175, 5] (w:1, o:234, a:1, s:1, b:0),
% 13.56/13.92 'v_sko__List__Xlexn__Xinduct__1' [180, 1] (w:1, o:167, a:1, s:1, b:0)
% 13.56/13.92 ,
% 13.56/13.92 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [183, 1]
% 13.56/13.92 (w:1, o:143, a:1, s:1, b:0),
% 13.56/13.92 'class_OrderedGroup_Ocancel__ab__semigroup__add' [188, 1] (w:1, o:144
% 13.56/13.92 , a:1, s:1, b:0),
% 13.56/13.92 'class_OrderedGroup_Ocancel__semigroup__add' [189, 1] (w:1, o:145, a:
% 13.56/13.92 1, s:1, b:0),
% 13.56/13.92 'v_u____' [190, 0] (w:1, o:88, a:1, s:1, b:0),
% 13.56/13.92 'c_List_Odrop' [191, 3] (w:1, o:226, a:1, s:1, b:0),
% 13.56/13.92 'c_nat_Onat__size' [192, 1] (w:1, o:168, a:1, s:1, b:0),
% 13.56/13.92 'class_OrderedGroup_Oab__semigroup__idem__mult' [194, 1] (w:1, o:146
% 13.56/13.92 , a:1, s:1, b:0),
% 13.56/13.92 'class_Ring__and__Field_Oring__1' [196, 1] (w:1, o:124, a:1, s:1, b:0
% 13.56/13.92 ),
% 13.56/13.92 'class_Ring__and__Field_Omult__mono' [197, 1] (w:1, o:169, a:1, s:1
% 13.56/13.92 , b:0),
% 13.56/13.92 'class_Ring__and__Field_Omult__mono1' [198, 1] (w:1, o:170, a:1, s:1
% 13.56/13.92 , b:0),
% 13.56/13.92 'c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1' [203, 1] (w:1, o:171
% 13.56/13.92 , a:1, s:1, b:0),
% 13.56/13.92 'class_Ring__and__Field_Oordered__comm__semiring__strict' [204, 1]
% 13.56/13.92 (w:1, o:154, a:1, s:1, b:0),
% 13.56/13.92 'class_Ring__and__Field_Opordered__semiring' [205, 1] (w:1, o:172, a:
% 13.56/13.92 1, s:1, b:0),
% 13.56/13.92 'c_Nitpick_Onat__gcd' [206, 2] (w:1, o:210, a:1, s:1, b:0),
% 13.56/13.92 'class_Ring__and__Field_Ozero__neq__one' [207, 1] (w:1, o:173, a:1
% 13.56/13.92 , s:1, b:0),
% 13.56/13.92 'class_Ring__and__Field_Ono__zero__divisors' [208, 1] (w:1, o:108, a:
% 13.56/13.92 1, s:1, b:0),
% 13.56/13.92 'class_Ring__and__Field_Omult__zero' [209, 1] (w:1, o:107, a:1, s:1
% 13.56/13.92 , b:0),
% 13.56/13.92 'class_Ring__and__Field_Oring__1__no__zero__divisors' [210, 1] (w:1
% 13.56/13.92 , o:125, a:1, s:1, b:0),
% 13.56/13.92 'class_Ring__and__Field_Oring__no__zero__divisors' [211, 1] (w:1, o:
% 13.56/13.92 126, a:1, s:1, b:0),
% 13.56/13.92 'c_Type_Osko__Type__Xtyping__elims__3__1' [213, 3] (w:1, o:223, a:1
% 13.56/13.92 , s:1, b:0),
% 13.56/13.92 'c_Type_Osko__Type__Xtyping__elims__3__2' [214, 3] (w:1, o:224, a:1
% 13.56/13.92 , s:1, b:0),
% 13.56/13.92 'c_Lambda_OdB_OdB__size' [215, 1] (w:1, o:174, a:1, s:1, b:0),
% 13.56/13.92 'class_OrderedGroup_Oab__semigroup__mult' [216, 1] (w:1, o:147, a:1
% 13.56/13.92 , s:1, b:0),
% 13.56/13.92 'class_Ring__and__Field_Ocomm__semiring' [217, 1] (w:1, o:175, a:1
% 13.56/13.92 , s:1, b:0),
% 13.56/13.92 'c_String_Ochar_Ochar__size' [219, 1] (w:1, o:119, a:1, s:1, b:0),
% 13.56/13.92 'tc_String_Ochar' [220, 0] (w:1, o:82, a:1, s:1, b:0),
% 13.56/13.92 'c_Type_Osko__Type__Xabs__typeE__1__1' [223, 2] (w:1, o:206, a:1, s:1
% 13.56/13.92 , b:0),
% 13.56/13.92 'c_Type_Osko__Type__Xabs__typeE__1__2' [224, 2] (w:1, o:207, a:1, s:1
% 13.56/13.92 , b:0),
% 13.56/13.92 'v_e____' [225, 0] (w:1, o:90, a:1, s:1, b:0),
% 13.56/13.92 'v_i____' [226, 0] (w:1, o:91, a:1, s:1, b:0),
% 13.56/13.92 'v_a____' [227, 0] (w:1, o:92, a:1, s:1, b:0),
% 13.56/13.92 'v_T_H_H____' [228, 0] (w:1, o:93, a:1, s:1, b:0),
% 13.56/13.92 'tc_fun' [232, 2] (w:1, o:211, a:1, s:1, b:0),
% 13.56/13.92 'c_fequal' [233, 3] (w:1, o:227, a:1, s:1, b:0).
% 13.56/13.92
% 13.56/13.92
% 13.56/13.92 Starting Search:
% 13.56/13.92
% 13.56/13.92 Resimplifying inuse:
% 13.56/13.92 Done
% 13.56/13.92
% 13.56/13.92
% 13.56/13.92 Intermediate Status:
% 13.56/13.92 Generated: 4786
% 13.56/13.92 Kept: 2014
% 13.56/13.92 Inuse: 157
% 13.56/13.92 Deleted: 4
% 13.56/13.92 Deletedinuse: 0
% 13.56/13.92
% 13.56/13.92 Resimplifying inuse:
% 13.56/13.92 Done
% 13.56/13.92
% 13.56/13.92 Resimplifying inuse:
% 13.56/13.92 Done
% 13.56/13.92
% 13.56/13.92
% 13.56/13.92 Intermediate Status:
% 13.56/13.92 Generated: 9237
% 13.56/13.92 Kept: 4037
% 13.56/13.92 Inuse: 252
% 13.56/13.92 Deleted: 4
% 13.56/13.92 Deletedinuse: 0
% 13.56/13.92
% 13.56/13.92 Resimplifying inuse:
% 13.56/13.92 Done
% 13.56/13.92
% 13.56/13.92 Resimplifying inuse:
% 13.56/13.92 Done
% 13.56/13.92
% 13.56/13.92
% 13.56/13.92 Intermediate Status:
% 13.56/13.92 Generated: 16700
% 13.56/13.92 Kept: 6539
% 13.56/13.92 Inuse: 326
% 13.56/13.92 Deleted: 6
% 13.56/13.92 Deletedinuse: 1
% 45.28/45.63
% 45.28/45.63 Resimplifying inuse:
% 45.28/45.63 Done
% 45.28/45.63
% 45.28/45.63 Resimplifying inuse:
% 45.28/45.63 Done
% 45.28/45.63
% 45.28/45.63
% 45.28/45.63 Intermediate Status:
% 45.28/45.63 Generated: 22521
% 45.28/45.63 Kept: 8544
% 45.28/45.63 Inuse: 406
% 45.28/45.63 Deleted: 16
% 45.28/45.63 Deletedinuse: 7
% 45.28/45.63
% 45.28/45.63 Resimplifying inuse:
% 45.28/45.63 Done
% 45.28/45.63
% 45.28/45.63 Resimplifying inuse:
% 45.28/45.63 Done
% 45.28/45.63
% 45.28/45.63
% 45.28/45.63 Intermediate Status:
% 45.28/45.63 Generated: 28836
% 45.28/45.63 Kept: 10629
% 45.28/45.63 Inuse: 467
% 45.28/45.63 Deleted: 21
% 45.28/45.63 Deletedinuse: 7
% 45.28/45.63
% 45.28/45.63 Resimplifying inuse:
% 45.28/45.63 Done
% 45.28/45.63
% 45.28/45.63 Resimplifying inuse:
% 45.28/45.63 Done
% 45.28/45.63
% 45.28/45.63
% 45.28/45.63 Intermediate Status:
% 45.28/45.63 Generated: 34868
% 45.28/45.63 Kept: 12631
% 45.28/45.63 Inuse: 554
% 45.28/45.63 Deleted: 24
% 45.28/45.63 Deletedinuse: 8
% 45.28/45.63
% 45.28/45.63 Resimplifying inuse:
% 45.28/45.63 Done
% 45.28/45.63
% 45.28/45.63 Resimplifying inuse:
% 45.28/45.63 Done
% 45.28/45.63
% 45.28/45.63
% 45.28/45.63 Intermediate Status:
% 45.28/45.63 Generated: 42880
% 45.28/45.63 Kept: 14632
% 45.28/45.63 Inuse: 654
% 45.28/45.63 Deleted: 28
% 45.28/45.63 Deletedinuse: 8
% 45.28/45.63
% 45.28/45.63 Resimplifying inuse:
% 45.28/45.63 Done
% 45.28/45.63
% 45.28/45.63 Resimplifying inuse:
% 45.28/45.63 Done
% 45.28/45.63
% 45.28/45.63
% 45.28/45.63 Intermediate Status:
% 45.28/45.63 Generated: 50347
% 45.28/45.63 Kept: 16632
% 45.28/45.63 Inuse: 728
% 45.28/45.63 Deleted: 32
% 45.28/45.63 Deletedinuse: 10
% 45.28/45.63
% 45.28/45.63 Resimplifying inuse:
% 45.28/45.63 Done
% 45.28/45.63
% 45.28/45.63
% 45.28/45.63 Intermediate Status:
% 45.28/45.63 Generated: 59641
% 45.28/45.63 Kept: 18634
% 45.28/45.63 Inuse: 776
% 45.28/45.63 Deleted: 35
% 45.28/45.63 Deletedinuse: 12
% 45.28/45.63
% 45.28/45.63 Resimplifying inuse:
% 45.28/45.63 Done
% 45.28/45.63
% 45.28/45.63 Resimplifying clauses:
% 45.28/45.63 Done
% 45.28/45.63
% 45.28/45.63
% 45.28/45.63 Intermediate Status:
% 45.28/45.63 Generated: 68746
% 45.28/45.63 Kept: 20640
% 45.28/45.63 Inuse: 820
% 45.28/45.63 Deleted: 1528
% 45.28/45.63 Deletedinuse: 13
% 45.28/45.63
% 45.28/45.63 Resimplifying inuse:
% 45.28/45.63 Done
% 45.28/45.63
% 45.28/45.63 Resimplifying inuse:
% 45.28/45.63 Done
% 45.28/45.63
% 45.28/45.63
% 45.28/45.63 Intermediate Status:
% 45.28/45.63 Generated: 75627
% 45.28/45.63 Kept: 22695
% 45.28/45.63 Inuse: 858
% 45.28/45.63 Deleted: 1528
% 45.28/45.63 Deletedinuse: 13
% 45.28/45.63
% 45.28/45.63 Resimplifying inuse:
% 45.28/45.63 Done
% 45.28/45.63
% 45.28/45.63 Resimplifying inuse:
% 45.28/45.63 Done
% 45.28/45.63
% 45.28/45.63
% 45.28/45.63 Intermediate Status:
% 45.28/45.63 Generated: 85890
% 45.28/45.63 Kept: 24984
% 45.28/45.63 Inuse: 878
% 45.28/45.63 Deleted: 1528
% 45.28/45.63 Deletedinuse: 13
% 45.28/45.63
% 45.28/45.63 Resimplifying inuse:
% 45.28/45.63 Done
% 45.28/45.63
% 45.28/45.63
% 45.28/45.63 Intermediate Status:
% 45.28/45.63 Generated: 99333
% 45.28/45.63 Kept: 28167
% 45.28/45.63 Inuse: 888
% 45.28/45.63 Deleted: 1529
% 45.28/45.63 Deletedinuse: 14
% 45.28/45.63
% 45.28/45.63 Resimplifying inuse:
% 45.28/45.63 Done
% 45.28/45.63
% 45.28/45.63 Resimplifying inuse:
% 45.28/45.63 Done
% 45.28/45.63
% 45.28/45.63
% 45.28/45.63 Intermediate Status:
% 45.28/45.63 Generated: 110313
% 45.28/45.63 Kept: 31272
% 45.28/45.63 Inuse: 918
% 45.28/45.63 Deleted: 1529
% 45.28/45.63 Deletedinuse: 14
% 45.28/45.63
% 45.28/45.63 Resimplifying inuse:
% 45.28/45.63 Done
% 45.28/45.63
% 45.28/45.63 Resimplifying inuse:
% 45.28/45.63 Done
% 45.28/45.63
% 45.28/45.63
% 45.28/45.63 Intermediate Status:
% 45.28/45.63 Generated: 118694
% 45.28/45.63 Kept: 33344
% 45.28/45.63 Inuse: 977
% 45.28/45.63 Deleted: 1530
% 45.28/45.63 Deletedinuse: 14
% 45.28/45.63
% 45.28/45.63 Resimplifying inuse:
% 45.28/45.63 Done
% 45.28/45.63
% 45.28/45.63 Resimplifying inuse:
% 45.28/45.63 Done
% 45.28/45.63
% 45.28/45.63
% 45.28/45.63 Intermediate Status:
% 45.28/45.63 Generated: 125404
% 45.28/45.63 Kept: 35486
% 45.28/45.63 Inuse: 1032
% 45.28/45.63 Deleted: 1530
% 45.28/45.63 Deletedinuse: 14
% 45.28/45.63
% 45.28/45.63 Resimplifying inuse:
% 45.28/45.63 Done
% 45.28/45.63
% 45.28/45.63
% 45.28/45.63 Intermediate Status:
% 45.28/45.63 Generated: 141354
% 45.28/45.63 Kept: 39502
% 45.28/45.63 Inuse: 1071
% 45.28/45.63 Deleted: 1531
% 45.28/45.63 Deletedinuse: 14
% 45.28/45.63
% 45.28/45.63 Resimplifying inuse:
% 45.28/45.63 Done
% 45.28/45.63
% 45.28/45.63 Resimplifying clauses:
% 45.28/45.63 Done
% 45.28/45.63
% 45.28/45.63 Resimplifying inuse:
% 45.28/45.63 Done
% 45.28/45.63
% 45.28/45.63
% 45.28/45.63 Intermediate Status:
% 45.28/45.63 Generated: 149180
% 45.28/45.63 Kept: 41840
% 45.28/45.63 Inuse: 1096
% 45.28/45.63 Deleted: 1798
% 45.28/45.63 Deletedinuse: 14
% 45.28/45.63
% 45.28/45.63 Resimplifying inuse:
% 45.28/45.63 Done
% 45.28/45.63
% 45.28/45.63
% 45.28/45.63 Intermediate Status:
% 45.28/45.63 Generated: 182846
% 45.28/45.63 Kept: 45978
% 45.28/45.63 Inuse: 1116
% 45.28/45.63 Deleted: 1798
% 45.28/45.63 Deletedinuse: 14
% 45.28/45.63
% 45.28/45.63 Resimplifying inuse:
% 45.28/45.63 Done
% 45.28/45.63
% 45.28/45.63
% 45.28/45.63 Intermediate Status:
% 45.28/45.63 Generated: 216214
% 45.28/45.63 Kept: 49421
% 45.28/45.63 Inuse: 1121
% 45.28/45.63 Deleted: 1798
% 45.28/45.63 Deletedinuse: 14
% 45.28/45.63
% 45.28/45.63 Resimplifying inuse:
% 45.28/45.63 Done
% 45.28/45.63
% 45.28/45.63 Resimplifying inuse:
% 45.28/45.63 Done
% 45.28/45.63
% 45.28/45.63
% 45.28/45.63 Intermediate Status:
% 45.28/45.63 Generated: 226169
% 45.28/45.63 Kept: 51505
% 45.28/45.63 Inuse: 1181
% 45.28/45.63 Deleted: 1798
% 45.28/45.63 Deletedinuse: 14
% 45.28/45.63
% 45.28/45.63 Resimplifying inuse:
% 45.28/45.63 Done
% 45.28/45.63
% 45.28/45.63 Resimplifying inuse:
% 45.28/45.63 Done
% 45.28/45.63
% 45.28/45.63
% 45.28/45.63 Intermediate Status:
% 45.28/45.63 Generated: 243545
% 45.28/45.63 Kept: 53828
% 45.28/45.63 Inuse: 1206
% 45.28/45.63 Deleted: 1798
% 45.28/45.63 Deletedinuse: 14
% 45.28/45.63
% 45.28/45.63 Resimplifying inuse:
% 45.28/45.63 Done
% 45.28/45.63
% 45.28/45.63 Resimplifying inuse:
% 45.28/45.63 Done
% 45.28/45.63
% 45.28/45.63
% 45.28/45.63 Intermediate Status:
% 45.28/45.63 Generated: 253147
% 45.28/45.63 Kept: 55935
% 45.28/45.63 Inuse: 1250
% 45.28/45.63 Deleted: 1800
% 45.28/45.63 Deletedinuse: 15
% 45.28/45.63
% 45.28/45.63 Resimplifying inuse:
% 45.28/45.63 Done
% 45.28/45.63
% 45.28/45.63 Resimplifying inuse:
% 45.28/45.63 Done
% 45.28/45.63
% 45.28/45.63
% 45.28/45.63 Intermediate Status:
% 45.28/45.63 Generated: 261912
% 45.28/45.63 Kept: 57947
% 45.28/45.63 Inuse: 1291
% 45.28/45.63 Deleted: 1801
% 45.28/45.63 Deletedinuse: 16
% 45.28/45.63
% 45.28/45.63 Resimplifying inuse:
% 45.28/45.63 Done
% 45.28/45.63
% 45.28/45.63
% 45.28/45.63 Intermediate Status:
% 45.28/45.63 Generated: 272960
% 45.28/45.63 Kept: 60708
% 45.28/45.63 Inuse: 1315
% 45.28/45.63 Deleted: 1801
% 45.28/45.63 Deletedinuse: 16
% 45.28/45.63
% 45.28/45.63 Resimplifying inuse:
% 45.28/45.63 Done
% 45.28/45.63
% 45.28/45.63 Resimplifying clauses:
% 45.28/45.63 Done
% 45.28/45.63
% 45.28/45.63 Resimplifying inuse:
% 45.28/45.63 Done
% 45.28/45.63
% 45.28/45.63
% 45.28/45.63 Intermediate Status:
% 45.28/45.63 Generated: 289739
% 45.28/45.63 Kept: 63462
% 45.28/45.63 Inuse: 1338
% 45.28/45.63 Deleted: 2132
% 45.28/45.63 Deletedinuse: 23
% 45.28/45.63
% 45.28/45.63 Resimplifying inuse:
% 45.28/45.63 Done
% 45.28/45.63
% 45.28/45.63 Resimplifying inuse:
% 45.28/45.63 Done
% 45.28/45.63
% 45.28/45.63
% 45.28/45.63 Intermediate Status:
% 45.28/45.63 Generated: 298872
% 45.28/45.63 Kept: 65492
% 45.28/45.63 Inuse: 1349
% 45.28/45.63 Deleted: 2136
% 45.28/45.63 Deletedinuse: 23
% 45.28/45.63
% 45.28/45.63 Resimplifying inuse:
% 45.28/45.63 Done
% 45.28/45.63
% 45.28/45.63 Resimplifying inuse:
% 45.28/45.63 Done
% 45.28/45.63
% 45.28/45.63
% 45.28/45.63 Intermediate Status:
% 100.26/100.68 Generated: 307476
% 100.26/100.68 Kept: 67495
% 100.26/100.68 Inuse: 1391
% 100.26/100.68 Deleted: 2138
% 100.26/100.68 Deletedinuse: 23
% 100.26/100.68
% 100.26/100.68 Resimplifying inuse:
% 100.26/100.68 Done
% 100.26/100.68
% 100.26/100.68 Resimplifying inuse:
% 100.26/100.68 Done
% 100.26/100.68
% 100.26/100.68
% 100.26/100.68 Intermediate Status:
% 100.26/100.68 Generated: 317920
% 100.26/100.68 Kept: 69647
% 100.26/100.68 Inuse: 1407
% 100.26/100.68 Deleted: 2150
% 100.26/100.68 Deletedinuse: 35
% 100.26/100.68
% 100.26/100.68 Resimplifying inuse:
% 100.26/100.68 Done
% 100.26/100.68
% 100.26/100.68
% 100.26/100.68 Intermediate Status:
% 100.26/100.68 Generated: 328362
% 100.26/100.68 Kept: 71761
% 100.26/100.68 Inuse: 1417
% 100.26/100.68 Deleted: 2150
% 100.26/100.68 Deletedinuse: 35
% 100.26/100.68
% 100.26/100.68 Resimplifying inuse:
% 100.26/100.68 Done
% 100.26/100.68
% 100.26/100.68
% 100.26/100.68 Intermediate Status:
% 100.26/100.68 Generated: 343805
% 100.26/100.68 Kept: 76091
% 100.26/100.68 Inuse: 1418
% 100.26/100.68 Deleted: 2150
% 100.26/100.68 Deletedinuse: 35
% 100.26/100.68
% 100.26/100.68 Resimplifying inuse:
% 100.26/100.68 Done
% 100.26/100.68
% 100.26/100.68 Resimplifying inuse:
% 100.26/100.68 Done
% 100.26/100.68
% 100.26/100.68
% 100.26/100.68 Intermediate Status:
% 100.26/100.68 Generated: 354647
% 100.26/100.68 Kept: 78870
% 100.26/100.68 Inuse: 1437
% 100.26/100.68 Deleted: 2150
% 100.26/100.68 Deletedinuse: 35
% 100.26/100.68
% 100.26/100.68 Resimplifying inuse:
% 100.26/100.68 Done
% 100.26/100.68
% 100.26/100.68
% 100.26/100.68 Intermediate Status:
% 100.26/100.68 Generated: 370240
% 100.26/100.68 Kept: 81215
% 100.26/100.68 Inuse: 1452
% 100.26/100.68 Deleted: 2150
% 100.26/100.68 Deletedinuse: 35
% 100.26/100.68
% 100.26/100.68 Resimplifying inuse:
% 100.26/100.68 Done
% 100.26/100.68
% 100.26/100.68 Resimplifying clauses:
% 100.26/100.68 Done
% 100.26/100.68
% 100.26/100.68 Resimplifying inuse:
% 100.26/100.68 Done
% 100.26/100.68
% 100.26/100.68
% 100.26/100.68 Intermediate Status:
% 100.26/100.68 Generated: 385035
% 100.26/100.68 Kept: 83222
% 100.26/100.68 Inuse: 1461
% 100.26/100.68 Deleted: 3099
% 100.26/100.68 Deletedinuse: 35
% 100.26/100.68
% 100.26/100.68
% 100.26/100.68 Intermediate Status:
% 100.26/100.68 Generated: 395062
% 100.26/100.68 Kept: 85382
% 100.26/100.68 Inuse: 1472
% 100.26/100.68 Deleted: 3099
% 100.26/100.68 Deletedinuse: 35
% 100.26/100.68
% 100.26/100.68 Resimplifying inuse:
% 100.26/100.68 Done
% 100.26/100.68
% 100.26/100.68 Resimplifying inuse:
% 100.26/100.68 Done
% 100.26/100.68
% 100.26/100.68
% 100.26/100.68 Intermediate Status:
% 100.26/100.68 Generated: 416517
% 100.26/100.68 Kept: 91879
% 100.26/100.68 Inuse: 1482
% 100.26/100.68 Deleted: 3099
% 100.26/100.68 Deletedinuse: 35
% 100.26/100.68
% 100.26/100.68 Resimplifying inuse:
% 100.26/100.68 Done
% 100.26/100.68
% 100.26/100.68 Resimplifying inuse:
% 100.26/100.68 Done
% 100.26/100.68
% 100.26/100.68
% 100.26/100.68 Intermediate Status:
% 100.26/100.68 Generated: 427014
% 100.26/100.68 Kept: 93903
% 100.26/100.68 Inuse: 1510
% 100.26/100.68 Deleted: 3099
% 100.26/100.68 Deletedinuse: 35
% 100.26/100.68
% 100.26/100.68 Resimplifying inuse:
% 100.26/100.68 Done
% 100.26/100.68
% 100.26/100.68 Resimplifying inuse:
% 100.26/100.68 Done
% 100.26/100.68
% 100.26/100.68
% 100.26/100.68 Intermediate Status:
% 100.26/100.68 Generated: 436485
% 100.26/100.68 Kept: 96152
% 100.26/100.68 Inuse: 1527
% 100.26/100.68 Deleted: 3099
% 100.26/100.68 Deletedinuse: 35
% 100.26/100.68
% 100.26/100.68 Resimplifying inuse:
% 100.26/100.68 Done
% 100.26/100.68
% 100.26/100.68
% 100.26/100.68 Intermediate Status:
% 100.26/100.68 Generated: 447613
% 100.26/100.68 Kept: 98721
% 100.26/100.68 Inuse: 1542
% 100.26/100.68 Deleted: 3099
% 100.26/100.68 Deletedinuse: 35
% 100.26/100.68
% 100.26/100.68 Resimplifying inuse:
% 100.26/100.68 Done
% 100.26/100.68
% 100.26/100.68 Resimplifying inuse:
% 100.26/100.68 Done
% 100.26/100.68
% 100.26/100.68
% 100.26/100.68 Intermediate Status:
% 100.26/100.68 Generated: 458816
% 100.26/100.68 Kept: 100746
% 100.26/100.68 Inuse: 1578
% 100.26/100.68 Deleted: 3099
% 100.26/100.68 Deletedinuse: 35
% 100.26/100.68
% 100.26/100.68 Resimplifying inuse:
% 100.26/100.68 Done
% 100.26/100.68
% 100.26/100.68 Resimplifying clauses:
% 100.26/100.68 Done
% 100.26/100.68
% 100.26/100.68 Resimplifying inuse:
% 100.26/100.68 Done
% 100.26/100.68
% 100.26/100.68
% 100.26/100.68 Intermediate Status:
% 100.26/100.68 Generated: 468042
% 100.26/100.68 Kept: 102756
% 100.26/100.68 Inuse: 1611
% 100.26/100.68 Deleted: 3577
% 100.26/100.68 Deletedinuse: 36
% 100.26/100.68
% 100.26/100.68 Resimplifying inuse:
% 100.26/100.68 Done
% 100.26/100.68
% 100.26/100.68
% 100.26/100.68 Intermediate Status:
% 100.26/100.68 Generated: 483369
% 100.26/100.68 Kept: 104766
% 100.26/100.68 Inuse: 1617
% 100.26/100.68 Deleted: 3578
% 100.26/100.68 Deletedinuse: 37
% 100.26/100.68
% 100.26/100.68 Resimplifying inuse:
% 100.26/100.68 Done
% 100.26/100.68
% 100.26/100.68 Resimplifying inuse:
% 100.26/100.68 Done
% 100.26/100.68
% 100.26/100.68
% 100.26/100.68 Intermediate Status:
% 100.26/100.68 Generated: 514404
% 100.26/100.68 Kept: 109680
% 100.26/100.68 Inuse: 1627
% 100.26/100.68 Deleted: 3578
% 100.26/100.68 Deletedinuse: 37
% 100.26/100.68
% 100.26/100.68 Resimplifying inuse:
% 100.26/100.68 Done
% 100.26/100.68
% 100.26/100.68
% 100.26/100.68 Intermediate Status:
% 100.26/100.68 Generated: 531123
% 100.26/100.68 Kept: 112023
% 100.26/100.68 Inuse: 1632
% 100.26/100.68 Deleted: 3578
% 100.26/100.68 Deletedinuse: 37
% 100.26/100.68
% 100.26/100.68 Resimplifying inuse:
% 100.26/100.68 Done
% 100.26/100.68
% 100.26/100.68 Resimplifying inuse:
% 100.26/100.68 Done
% 100.26/100.68
% 100.26/100.68
% 100.26/100.68 Intermediate Status:
% 100.26/100.68 Generated: 549072
% 100.26/100.68 Kept: 114033
% 100.26/100.68 Inuse: 1642
% 100.26/100.68 Deleted: 3578
% 100.26/100.68 Deletedinuse: 37
% 100.26/100.68
% 100.26/100.68 Resimplifying inuse:
% 100.26/100.68 Done
% 100.26/100.68
% 100.26/100.68
% 100.26/100.68 Intermediate Status:
% 100.26/100.68 Generated: 567864
% 100.26/100.68 Kept: 116553
% 100.26/100.68 Inuse: 1662
% 100.26/100.68 Deleted: 3578
% 100.26/100.68 Deletedinuse: 37
% 100.26/100.68
% 100.26/100.68 Resimplifying inuse:
% 100.26/100.68 Done
% 100.26/100.68
% 100.26/100.68 Resimplifying inuse:
% 100.26/100.68 Done
% 100.26/100.68
% 100.26/100.68
% 100.26/100.68 Intermediate Status:
% 100.26/100.68 Generated: 584702
% 100.26/100.68 Kept: 118570
% 100.26/100.68 Inuse: 1668
% 100.26/100.68 Deleted: 3578
% 100.26/100.68 Deletedinuse: 37
% 100.26/100.68
% 100.26/100.68 Resimplifying inuse:
% 100.26/100.68 Done
% 100.26/100.68
% 100.26/100.68
% 100.26/100.68 Intermediate Status:
% 100.26/100.68 Generated: 607899
% 100.26/100.68 Kept: 121670
% 100.26/100.68 Inuse: 1692
% 100.26/100.68 Deleted: 3578
% 100.26/100.68 Deletedinuse: 37
% 100.26/100.68
% 100.26/100.68 Resimplifying inuse:
% 100.26/100.68 Done
% 100.26/100.68
% 100.26/100.68 Resimplifying clauses:
% 100.26/100.68 Done
% 100.26/100.68
% 100.26/100.68 Resimplifying inuse:
% 100.26/100.68 Done
% 100.26/100.68
% 100.26/100.68
% 100.26/100.68 Intermediate Status:
% 100.26/100.68 Generated: 625625
% 100.26/100.68 Kept: 123701
% 100.26/100.68 Inuse: 1700
% 100.26/100.68 Deleted: 3757
% 100.26/100.68 Deletedinuse: 37
% 100.26/100.68
% 100.26/100.68 Resimplifying inuse:
% 100.26/100.68 Done
% 100.26/100.68
% 100.26/100.68
% 100.26/100.68 Intermediate Status:
% 100.26/100.68 Generated: 636878
% 100.26/100.68 Kept: 125983
% 100.26/100.68 Inuse: 1725
% 100.26/100.68 Deleted: 3759
% 100.26/100.68 Deletedinuse: 37
% 100.26/100.68
% 100.26/100.68 Resimplifying inuse:
% 100.26/100.68 Done
% 100.26/100.68
% 100.26/100.68 Resimplifying inuse:
% 100.26/100.68 Done
% 100.26/100.68
% 100.26/100.68
% 100.26/100.68 Intermediate Status:
% 100.26/100.68 Generated: 642252
% 100.26/100.68 Kept: 128198
% 100.26/100.68 Inuse: 1731
% 100.26/100.68 Deleted: 3783
% 100.26/100.68 Deletedinuse: 37
% 100.26/100.68
% 100.26/100.68 Resimplifying inuse:
% 100.26/100.68 Done
% 100.26/100.68
% 100.26/100.68 Resimplifying inuse:
% 100.26/100.68 Done
% 100.26/100.68
% 100.26/100.68
% 100.26/100.68 Intermediate Status:
% 100.26/100.68 Generated: 650323
% 100.26/100.68 Kept: 130206
% 100.26/100.68 Inuse: 1747
% 100.26/100.68 Deleted: 3804
% 100.26/100.68 Deletedinuse: 37
% 100.26/100.68
% 100.26/100.68 Resimplifying inuse:
% 100.26/100.68 Done
% 100.26/100.68
% 100.26/100.68
% 100.26/100.68 Intermediate Status:
% 193.83/194.23 Generated: 671904
% 193.83/194.23 Kept: 133447
% 193.83/194.23 Inuse: 1760
% 193.83/194.23 Deleted: 3804
% 193.83/194.23 Deletedinuse: 37
% 193.83/194.23
% 193.83/194.23 Resimplifying inuse:
% 193.83/194.23 Done
% 193.83/194.23
% 193.83/194.23 Resimplifying inuse:
% 193.83/194.23 Done
% 193.83/194.23
% 193.83/194.23
% 193.83/194.23 Intermediate Status:
% 193.83/194.23 Generated: 690623
% 193.83/194.23 Kept: 135455
% 193.83/194.23 Inuse: 1769
% 193.83/194.23 Deleted: 3804
% 193.83/194.23 Deletedinuse: 37
% 193.83/194.23
% 193.83/194.23 Resimplifying inuse:
% 193.83/194.23 Done
% 193.83/194.23
% 193.83/194.23
% 193.83/194.23 Intermediate Status:
% 193.83/194.23 Generated: 723966
% 193.83/194.23 Kept: 139063
% 193.83/194.23 Inuse: 1775
% 193.83/194.23 Deleted: 3804
% 193.83/194.23 Deletedinuse: 37
% 193.83/194.23
% 193.83/194.23 Resimplifying inuse:
% 193.83/194.23 Done
% 193.83/194.23
% 193.83/194.23 Resimplifying inuse:
% 193.83/194.23 Done
% 193.83/194.23
% 193.83/194.23
% 193.83/194.23 Intermediate Status:
% 193.83/194.23 Generated: 738306
% 193.83/194.23 Kept: 141838
% 193.83/194.23 Inuse: 1795
% 193.83/194.23 Deleted: 3804
% 193.83/194.23 Deletedinuse: 37
% 193.83/194.23
% 193.83/194.23 Resimplifying inuse:
% 193.83/194.23 Done
% 193.83/194.23
% 193.83/194.23 Resimplifying clauses:
% 193.83/194.23 Done
% 193.83/194.23
% 193.83/194.23 Resimplifying inuse:
% 193.83/194.23 Done
% 193.83/194.23
% 193.83/194.23
% 193.83/194.23 Intermediate Status:
% 193.83/194.23 Generated: 749108
% 193.83/194.23 Kept: 144106
% 193.83/194.23 Inuse: 1810
% 193.83/194.23 Deleted: 4223
% 193.83/194.23 Deletedinuse: 37
% 193.83/194.23
% 193.83/194.23 Resimplifying inuse:
% 193.83/194.23 Done
% 193.83/194.23
% 193.83/194.23 Resimplifying inuse:
% 193.83/194.23 Done
% 193.83/194.23
% 193.83/194.23
% 193.83/194.23 Intermediate Status:
% 193.83/194.23 Generated: 760341
% 193.83/194.23 Kept: 146137
% 193.83/194.23 Inuse: 1829
% 193.83/194.23 Deleted: 4223
% 193.83/194.23 Deletedinuse: 37
% 193.83/194.23
% 193.83/194.23 Resimplifying inuse:
% 193.83/194.23 Done
% 193.83/194.23
% 193.83/194.23
% 193.83/194.23 Intermediate Status:
% 193.83/194.23 Generated: 769119
% 193.83/194.23 Kept: 148179
% 193.83/194.23 Inuse: 1840
% 193.83/194.23 Deleted: 4223
% 193.83/194.23 Deletedinuse: 37
% 193.83/194.23
% 193.83/194.23 Resimplifying inuse:
% 193.83/194.23 Done
% 193.83/194.23
% 193.83/194.23 Resimplifying inuse:
% 193.83/194.23 Done
% 193.83/194.23
% 193.83/194.23
% 193.83/194.23 Intermediate Status:
% 193.83/194.23 Generated: 783324
% 193.83/194.23 Kept: 150646
% 193.83/194.23 Inuse: 1855
% 193.83/194.23 Deleted: 4223
% 193.83/194.23 Deletedinuse: 37
% 193.83/194.23
% 193.83/194.23 Resimplifying inuse:
% 193.83/194.23 Done
% 193.83/194.23
% 193.83/194.23 Resimplifying inuse:
% 193.83/194.23 Done
% 193.83/194.23
% 193.83/194.23
% 193.83/194.23 Intermediate Status:
% 193.83/194.23 Generated: 796080
% 193.83/194.23 Kept: 152989
% 193.83/194.23 Inuse: 1870
% 193.83/194.23 Deleted: 4223
% 193.83/194.23 Deletedinuse: 37
% 193.83/194.23
% 193.83/194.23 Resimplifying inuse:
% 193.83/194.23 Done
% 193.83/194.23
% 193.83/194.23 Resimplifying inuse:
% 193.83/194.23 Done
% 193.83/194.23
% 193.83/194.23
% 193.83/194.23 Intermediate Status:
% 193.83/194.23 Generated: 806285
% 193.83/194.23 Kept: 155465
% 193.83/194.23 Inuse: 1885
% 193.83/194.23 Deleted: 4223
% 193.83/194.23 Deletedinuse: 37
% 193.83/194.23
% 193.83/194.23 Resimplifying inuse:
% 193.83/194.23 Done
% 193.83/194.23
% 193.83/194.23
% 193.83/194.23 Intermediate Status:
% 193.83/194.23 Generated: 816648
% 193.83/194.23 Kept: 158743
% 193.83/194.23 Inuse: 1895
% 193.83/194.23 Deleted: 4223
% 193.83/194.23 Deletedinuse: 37
% 193.83/194.23
% 193.83/194.23 Resimplifying inuse:
% 193.83/194.23 Done
% 193.83/194.23
% 193.83/194.23 Resimplifying inuse:
% 193.83/194.23 Done
% 193.83/194.23
% 193.83/194.23
% 193.83/194.23 Intermediate Status:
% 193.83/194.23 Generated: 824753
% 193.83/194.23 Kept: 160760
% 193.83/194.23 Inuse: 1905
% 193.83/194.23 Deleted: 4223
% 193.83/194.23 Deletedinuse: 37
% 193.83/194.23
% 193.83/194.23 Resimplifying inuse:
% 193.83/194.23 Done
% 193.83/194.23
% 193.83/194.23 Resimplifying clauses:
% 193.83/194.23 Done
% 193.83/194.23
% 193.83/194.23
% 193.83/194.23 Intermediate Status:
% 193.83/194.23 Generated: 844500
% 193.83/194.23 Kept: 162782
% 193.83/194.23 Inuse: 1911
% 193.83/194.23 Deleted: 4773
% 193.83/194.23 Deletedinuse: 37
% 193.83/194.23
% 193.83/194.23 Resimplifying inuse:
% 193.83/194.23 Done
% 193.83/194.23
% 193.83/194.23
% 193.83/194.23 Intermediate Status:
% 193.83/194.23 Generated: 867385
% 193.83/194.23 Kept: 167062
% 193.83/194.23 Inuse: 1935
% 193.83/194.23 Deleted: 4774
% 193.83/194.23 Deletedinuse: 38
% 193.83/194.23
% 193.83/194.23 Resimplifying inuse:
% 193.83/194.23 Done
% 193.83/194.23
% 193.83/194.23
% 193.83/194.23 Intermediate Status:
% 193.83/194.23 Generated: 879604
% 193.83/194.23 Kept: 169545
% 193.83/194.23 Inuse: 1940
% 193.83/194.23 Deleted: 4774
% 193.83/194.23 Deletedinuse: 38
% 193.83/194.23
% 193.83/194.23 Resimplifying inuse:
% 193.83/194.23 Done
% 193.83/194.23
% 193.83/194.23 Resimplifying inuse:
% 193.83/194.23 Done
% 193.83/194.23
% 193.83/194.23
% 193.83/194.23 Intermediate Status:
% 193.83/194.23 Generated: 896468
% 193.83/194.23 Kept: 171557
% 193.83/194.23 Inuse: 1974
% 193.83/194.23 Deleted: 4774
% 193.83/194.23 Deletedinuse: 38
% 193.83/194.23
% 193.83/194.23
% 193.83/194.23 Intermediate Status:
% 193.83/194.23 Generated: 919316
% 193.83/194.23 Kept: 173667
% 193.83/194.23 Inuse: 1975
% 193.83/194.23 Deleted: 4774
% 193.83/194.23 Deletedinuse: 38
% 193.83/194.23
% 193.83/194.23 Resimplifying inuse:
% 193.83/194.23 Done
% 193.83/194.23
% 193.83/194.23 Resimplifying inuse:
% 193.83/194.23 Done
% 193.83/194.23
% 193.83/194.23
% 193.83/194.23 Intermediate Status:
% 193.83/194.23 Generated: 932660
% 193.83/194.23 Kept: 175682
% 193.83/194.23 Inuse: 2002
% 193.83/194.23 Deleted: 4775
% 193.83/194.23 Deletedinuse: 39
% 193.83/194.23
% 193.83/194.23 Resimplifying inuse:
% 193.83/194.23 Done
% 193.83/194.23
% 193.83/194.23 Resimplifying inuse:
% 193.83/194.23 Done
% 193.83/194.23
% 193.83/194.23
% 193.83/194.23 Intermediate Status:
% 193.83/194.23 Generated: 944597
% 193.83/194.23 Kept: 177771
% 193.83/194.23 Inuse: 2020
% 193.83/194.23 Deleted: 4775
% 193.83/194.23 Deletedinuse: 39
% 193.83/194.23
% 193.83/194.23 Resimplifying inuse:
% 193.83/194.23 Done
% 193.83/194.23
% 193.83/194.23 Resimplifying inuse:
% 193.83/194.23 Done
% 193.83/194.23
% 193.83/194.23
% 193.83/194.23 Intermediate Status:
% 193.83/194.23 Generated: 957790
% 193.83/194.23 Kept: 179796
% 193.83/194.23 Inuse: 2044
% 193.83/194.23 Deleted: 4777
% 193.83/194.23 Deletedinuse: 41
% 193.83/194.23
% 193.83/194.23 Resimplifying inuse:
% 193.83/194.23 Done
% 193.83/194.23
% 193.83/194.23
% 193.83/194.23 Intermediate Status:
% 193.83/194.23 Generated: 973935
% 193.83/194.23 Kept: 183258
% 193.83/194.23 Inuse: 2055
% 193.83/194.23 Deleted: 4777
% 193.83/194.23 Deletedinuse: 41
% 193.83/194.23
% 193.83/194.23 Resimplifying inuse:
% 193.83/194.23 Done
% 193.83/194.23
% 193.83/194.23 Resimplifying clauses:
% 193.83/194.23 Done
% 193.83/194.23
% 193.83/194.23 Resimplifying inuse:
% 193.83/194.23 Done
% 193.83/194.23
% 193.83/194.23
% 193.83/194.23 Intermediate Status:
% 193.83/194.23 Generated: 989921
% 193.83/194.23 Kept: 185551
% 193.83/194.23 Inuse: 2080
% 193.83/194.23 Deleted: 5544
% 193.83/194.23 Deletedinuse: 41
% 193.83/194.23
% 193.83/194.23 Resimplifying inuse:
% 193.83/194.23 Done
% 193.83/194.23
% 193.83/194.23 Resimplifying inuse:
% 193.83/194.23 Done
% 193.83/194.23
% 193.83/194.23
% 193.83/194.23 Intermediate Status:
% 193.83/194.23 Generated: 999836
% 193.83/194.23 Kept: 187555
% 193.83/194.23 Inuse: 2094
% 193.83/194.23 Deleted: 5566
% 193.83/194.23 Deletedinuse: 61
% 193.83/194.23
% 193.83/194.23 Resimplifying inuse:
% 193.83/194.23 Done
% 193.83/194.23
% 193.83/194.23
% 193.83/194.23 Intermediate Status:
% 193.83/194.23 Generated: 1007399
% 193.83/194.23 Kept: 189587
% 193.83/194.23 Inuse: 2106
% 193.83/194.23 Deleted: 5568
% 193.83/194.23 Deletedinuse: 61
% 193.83/194.23
% 193.83/194.23 Resimplifying inuse:
% 193.83/194.23 Done
% 193.83/194.23
% 193.83/194.23 Resimplifying inuse:
% 193.83/194.23 Done
% 193.83/194.23
% 193.83/194.23
% 193.83/194.23 Intermediate Status:
% 193.83/194.23 Generated: 1017768
% 193.83/194.23 Kept: 191880
% 193.83/194.23 Inuse: 2126
% 193.83/194.23 Deleted: 5568
% 193.83/194.23 Deletedinuse: Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------