TSTP Solution File: LCL752-1 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : LCL752-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n017.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 07:57:31 EDT 2022
% Result : Timeout 300.02s 300.46s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL752-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Sat Jul 2 12:42:40 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.17/1.53 *** allocated 10000 integers for termspace/termends
% 1.17/1.53 *** allocated 10000 integers for clauses
% 1.17/1.53 *** allocated 10000 integers for justifications
% 1.17/1.53 *** allocated 15000 integers for termspace/termends
% 1.17/1.53 *** allocated 22500 integers for termspace/termends
% 1.17/1.53 *** allocated 33750 integers for termspace/termends
% 1.17/1.53 Bliksem 1.12
% 1.17/1.53
% 1.17/1.53
% 1.17/1.53 Automatic Strategy Selection
% 1.17/1.53
% 1.17/1.53 Clauses:
% 1.17/1.53 [
% 1.17/1.53 [ hBOOL( hAPP( 'c_lessequals'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.17/1.53 'tc_nat' ), 'tc_nat' ), X ) ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ) ) ],
% 1.17/1.53 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.53 'tc_nat' ), 'tc_nat' ), X ) ) ), 'c_Ring__and__Field_Odvd__class_Odvd'(
% 1.17/1.53 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.17/1.53 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X, 'tc_nat' ) ],
% 1.17/1.53 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.53 'tc_nat' ), 'tc_nat' ), X ) ) ), 'c_Ring__and__Field_Odvd__class_Odvd'(
% 1.17/1.53 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.17/1.53 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ), X, 'tc_nat' ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.17/1.53 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.53 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.17/1.53 ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.17/1.53 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.53 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.17/1.53 ) ) ],
% 1.17/1.53 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.17/1.53 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.17/1.53 [ =( 'c_Suc'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.17/1.53 ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 1.17/1.53 [ =( 'c_Suc'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.17/1.53 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ),
% 1.17/1.53 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( Y, 'tc_nat' ), Z ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( Y, 'tc_nat' ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.17/1.53 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ),
% 1.17/1.53 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ) ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.53 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.17/1.53 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.17/1.53 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Power_Opower__class_Opower'( Y,
% 1.17/1.53 Z, 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'(
% 1.17/1.53 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), Z, X ) ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.53 'c_Divides_Odiv__class_Odiv'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.17/1.53 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.17/1.53 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ),
% 1.17/1.53 'c_Int_Onumber__class_Onumber__of'( T, X ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.17/1.53 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.17/1.53 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), X ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Odvd'( X ) ),
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.17/1.53 Y ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.17/1.53 Y ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.17/1.53 Y ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.17/1.53 Y ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.17/1.53 Y ) ],
% 1.17/1.53 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.17/1.53 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ), X ) ],
% 1.17/1.53 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.17/1.53 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.17/1.53 Y ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.17/1.53 'c_Power_Opower__class_Opower'( Y, Z, X ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.17/1.53 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( X, hAPP( hAPP(
% 1.17/1.53 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ) ) ],
% 1.17/1.53 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( Y, 'tc_nat' ), Z ) ) ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( X, hAPP( hAPP(
% 1.17/1.53 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.53 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.17/1.53 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.53 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T
% 1.17/1.53 ) ) ) ],
% 1.17/1.53 [ =( 'c_Code__Numeral_Oof__nat'( 'c_Code__Numeral_Onat__of'( X ) ), X )
% 1.17/1.53 ],
% 1.17/1.53 [ =( 'c_Code__Numeral_Oof__nat'( 'c_Code__Numeral_Onat__of'( X ) ), X )
% 1.17/1.53 ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, X ) ) ],
% 1.17/1.53 [ 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.53 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.53 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.17/1.53 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.53 ), Y ), T ), Z, X ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.17/1.53 'c_Power_Opower__class_Opower'( Y, Z, X ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), X ), Y ) ) ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.53 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.17/1.53 , Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.17/1.53 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ), 'c_Divides_Odiv__class_Odiv'(
% 1.17/1.53 Z, T, X ) ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( T, Y, X ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.53 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Ominus__class_Ominus'( X ), T ), Y ) ), Z ) ), U ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.53 X ), T ), Z ) ), U ) ) ],
% 1.17/1.53 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ) ), T ),
% 1.17/1.53 'tc_nat' ), U ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), T ), 'tc_nat' ),
% 1.17/1.53 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), U ) ) ) ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( Y, 'tc_nat' ), X ) ) ) ],
% 1.17/1.53 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), 'tc_nat' ),
% 1.17/1.53 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ) ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.53 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP(
% 1.17/1.53 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), T ) ), Y ) ), Z ),
% 1.17/1.53 'tc_nat' ), U ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( T, 'tc_nat' ), X ) )
% 1.17/1.53 ) ],
% 1.17/1.53 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ), T ) ), U ) ) ), ~(
% 1.17/1.53 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), X ), 'tc_nat' ),
% 1.17/1.53 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ), U ) ) ) ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ) ],
% 1.17/1.53 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), 'tc_nat' ),
% 1.17/1.53 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ) ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), X ) ), Y ) ), U ) ) ) ),
% 1.17/1.53 ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), T ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.53 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.17/1.53 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( T, hAPP(
% 1.17/1.53 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Ominus__class_Ominus'( X ), U ), Y ) ), Z ) ), W ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.53 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.17/1.53 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( hAPP(
% 1.17/1.53 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T ), W ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.53 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.17/1.53 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ) ), 'c_Divides_Odiv__class_Omod'(
% 1.17/1.53 Z, Y, X ) ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 1.17/1.53 ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.53 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.17/1.53 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.17/1.53 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ), T ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ],
% 1.17/1.53 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.53 'tc_nat' ), X ), Y ), 'tc_nat' ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.17/1.53 X, 'tc_nat' ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z )
% 1.17/1.53 , Y ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ), Z ) ) ) ]
% 1.17/1.53 ,
% 1.17/1.53 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.17/1.53 Z ), 'tc_nat' ), Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, 'tc_nat' ),
% 1.17/1.53 Y ) ) ) ],
% 1.17/1.53 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X
% 1.17/1.53 , Y, 'tc_nat' ) ), Y ) ) ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.17/1.53 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z )
% 1.17/1.53 , T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ) ]
% 1.17/1.53 ,
% 1.17/1.53 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.17/1.53 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z )
% 1.17/1.53 , T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), Z ) ) ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ) ]
% 1.17/1.53 ,
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 1.17/1.53 , Z, X ), 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( Z, 'tc_nat' ), T ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, Z, X ), X ),
% 1.17/1.53 'c_Power_Opower__class_Opower'( Y, T, X ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ), ~(
% 1.17/1.53 hBOOL( hAPP( 'c_lessequals'( T, 'tc_nat' ), Z ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.53 X ), U ), Z ) ), W ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( T, X ), hAPP(
% 1.17/1.53 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Ominus__class_Ominus'( X ), U ), Y ) ), Z ) ), W ) ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.17/1.53 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), U ) ), W ) ) ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.17/1.53 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), Y ), X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.53 X ), Z ), U ) ), W ) ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.53 X ), U ), Z ) ), W ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.53 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T
% 1.17/1.53 ), X ), W ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ) ), U ), X ), W ) ),
% 1.17/1.53 ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.17/1.53 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), U ), X ),
% 1.17/1.53 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), W ) ) ) ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.17/1.53 , T, X ), X ) ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.17/1.53 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.17/1.53 , T, X ), X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ]
% 1.17/1.53 ,
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.17/1.53 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.17/1.53 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), X, 'tc_nat' ),
% 1.17/1.53 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat'
% 1.17/1.53 ), X ) ) ) ],
% 1.17/1.53 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 1.17/1.53 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.17/1.53 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.17/1.53 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.17/1.53 , X ) ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.17/1.53 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ) ) ) ],
% 1.17/1.53 [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OAbs'( X ), Y, Z ),
% 1.17/1.53 'c_Lambda_OdB_OAbs'( 'c_Lambda_Osubstn'( X, Y, hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), 'c_HOL_Oone__class_Oone'(
% 1.17/1.53 'tc_nat' ) ) ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.53 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.17/1.53 ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.17/1.53 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP(
% 1.17/1.53 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ),
% 1.17/1.53 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.17/1.53 ) ],
% 1.17/1.53 [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 1.17/1.53 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.17/1.53 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.53 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.17/1.53 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.53 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.53 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.17/1.53 ) ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), 'c_Power_Opower__class_Opower'( Y, Z,
% 1.17/1.53 X ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.17/1.53 'c_Power_Opower__class_Opower'( Y, Z, X ) ) ) ],
% 1.17/1.53 [ hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.17/1.53 ~( hBOOL( hAPP( X, T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y
% 1.17/1.53 , 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ),
% 1.17/1.53 'c_Suc'( T ) ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ), 'tc_nat' ), Y ) ) ) ]
% 1.17/1.53 ,
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), 'c_Power_Opower__class_Opower'( Y, Z,
% 1.17/1.53 X ) ), 'c_Power_Opower__class_Opower'( Y, T, X ) ),
% 1.17/1.53 'c_Power_Opower__class_Opower'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.53 'tc_nat' ), Z ), T ), X ) ) ],
% 1.17/1.53 [ =( 'c_Lambda_Oliftn'( 'c_Suc'( X ), Y, Z ), hAPP( hAPP(
% 1.17/1.53 'c_Lambda_Olift', 'c_Lambda_Oliftn'( X, Y, Z ) ), Z ) ) ],
% 1.17/1.53 [ ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ) ), Z ) ), T ) ) ) ]
% 1.17/1.53 ,
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.53 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.17/1.53 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.17/1.53 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ),
% 1.17/1.53 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ) ), =( Z,
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.53 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.17/1.53 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.17/1.53 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ),
% 1.17/1.53 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ) ), =( T,
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.53 [ =( 'c_Power_Opower__class_Opower'( X, Y, 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.17/1.53 'c_Power_Opower__class_Opower'( X, hAPP( hAPP(
% 1.17/1.53 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.17/1.53 'tc_nat' ) ), 'tc_nat' ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.17/1.53 ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.53 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.17/1.53 Y ) ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.17/1.53 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ), =( Z,
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.17/1.53 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ), =( Y,
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.53 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.17/1.53 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.17/1.53 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y
% 1.17/1.53 , 'tc_nat' ), X ) ) ) ],
% 1.17/1.53 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ) ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( T, 'tc_nat' ), X ) ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), T ) ), Y ) ), Z ), U ) ]
% 1.17/1.53 ,
% 1.17/1.53 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ) ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( X, 'tc_nat' ), T ) ) ), =( Z, hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), X ) ), Y ) ), U ) ) ],
% 1.17/1.53 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), X ) ), Y ) ), U ) ) ), ~(
% 1.17/1.53 hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), T ) ) ) ],
% 1.17/1.53 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), T ) ), Y ) ), Z ) ), U ) )
% 1.17/1.53 , ~( hBOOL( hAPP( 'c_lessequals'( T, 'tc_nat' ), X ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.17/1.53 'c_Power_Opower__class_Opower'( 'c_Power_Opower__class_Opower'( Y, Z, X )
% 1.17/1.53 , T, X ), 'c_Power_Opower__class_Opower'( Y, hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ), X ) ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.17/1.53 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), 'c_Power_Opower__class_Opower'( Y, Z,
% 1.17/1.53 X ) ), Y ) ) ],
% 1.17/1.53 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( Y,
% 1.17/1.53 'c_Suc'( Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.17/1.53 'c_Power_Opower__class_Opower'( Y, Z, X ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.17/1.53 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Power_Opower__class_Opower'( Y
% 1.17/1.53 , Z, X ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.17/1.53 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Power_Opower__class_Opower'( Y
% 1.17/1.53 , Z, X ) ) ) ],
% 1.17/1.53 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.53 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.53 'tc_nat' ), Z ), T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ),
% 1.17/1.53 T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Z ) ) ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ), hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z
% 1.17/1.53 ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ) ), ~(
% 1.17/1.53 hBOOL( hAPP( 'c_lessequals'( Z, X ), U ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.17/1.53 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.17/1.53 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ) ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.17/1.53 ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.53 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.17/1.53 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.17/1.53 ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ]
% 1.17/1.53 ,
% 1.17/1.53 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.17/1.53 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.17/1.53 'tc_nat' ) ) ), Y ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 1.17/1.53 ,
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.53 X ), Y ), Z ) ), T ) ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.17/1.53 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.17/1.53 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.53 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.17/1.53 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.53 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.17/1.53 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.53 X ), Y ), Z ) ), T ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.53 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.17/1.53 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.53 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.17/1.53 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.17/1.53 'c_Power_Opower__class_Opower'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.53 'tc_nat' ), Z ), T ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.53 , 'c_Power_Opower__class_Opower'( Y, Z, X ) ),
% 1.17/1.53 'c_Power_Opower__class_Opower'( Y, T, X ) ) ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ],
% 1.17/1.53 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( X, 'tc_nat' ), Z ) ) ) ],
% 1.17/1.53 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.17/1.53 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ),
% 1.17/1.53 X ), 'tc_nat' ), Y ) ) ) ],
% 1.17/1.53 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.17/1.53 Z ), 'tc_nat' ), Y ) ) ) ],
% 1.17/1.53 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( X, 'tc_nat' ), Z ) ) ) ],
% 1.17/1.53 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.17/1.53 [ =( hAPP( hAPP( 'c_Lambda_Olift', hAPP( 'c_Lambda_OdB_OVar', X ) ), Y )
% 1.17/1.53 , hAPP( 'c_Lambda_OdB_OVar', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.53 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ), hBOOL( hAPP(
% 1.17/1.53 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.17/1.53 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.17/1.53 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.17/1.53 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ),
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ),
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.53 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.17/1.53 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.17/1.53 ), Z ), T, X ) ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.53 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.17/1.53 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z, T
% 1.17/1.53 , X ) ), T, X ) ) ],
% 1.17/1.53 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.17/1.53 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 1.17/1.53 'tc_nat' ) ) ],
% 1.17/1.53 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.17/1.53 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( X, 'c_HOL_Oone__class_Oone'(
% 1.17/1.53 'tc_nat' ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, Z, X ), X ),
% 1.17/1.53 'c_Power_Opower__class_Opower'( Y, T, X ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), X ), Y ) ) ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( Z, 'tc_nat' ), T ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, Z, X ), X ),
% 1.17/1.53 'c_Power_Opower__class_Opower'( T, Z, X ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.17/1.53 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 1.17/1.53 ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.17/1.53 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.17/1.53 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.53 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.17/1.53 , X ) ), T ) ) ) ],
% 1.17/1.53 [ =( X, Y ), ~( 'c_List_Olist__all2'( 'c_fequal'( Z ), X, Y, Z, Z ) ) ]
% 1.17/1.53 ,
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.17/1.53 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Suc'( Y ), X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.17/1.53 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ) ],
% 1.17/1.53 [ ~( =( 'c_Code__Numeral_Onat__of'( X ), 'c_Code__Numeral_Onat__of'( Y )
% 1.17/1.53 ) ), =( X, Y ) ],
% 1.17/1.53 [ ~( =( 'c_Code__Numeral_Onat__of'( X ), 'c_Code__Numeral_Onat__of'( Y )
% 1.17/1.53 ) ), =( X, Y ) ],
% 1.17/1.53 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.17/1.53 ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.17/1.53 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =( Y, Z ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Finite__Set_Osetsum'( Z, T, U
% 1.17/1.53 , X ) ), 'c_Finite__Set_Osetsum'( hAPP( hAPP( 'c_COMBB'( X, X, U ), hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ) ), Z ), T, U, X ) ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( 'c_List_Olistsum'(
% 1.17/1.53 'c_List_Olist_ONil'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.53 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ), T ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ), T ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.53 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), U ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.53 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ), U )
% 1.17/1.53 ) ],
% 1.17/1.53 [ =( hAPP( hAPP( 'c_Lambda_Olift', hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 1.17/1.53 X ), Y ), Z ) ), T ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', hAPP( hAPP(
% 1.17/1.53 'c_Lambda_Olift', X ), T ) ), hAPP( hAPP( 'c_Lambda_Olift', Y ), T ) ),
% 1.17/1.53 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ),
% 1.17/1.53 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_HOL_Oord__class_Oless'( T, 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), 'c_HOL_Oone__class_Oone'(
% 1.17/1.53 'tc_nat' ) ) ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP(
% 1.17/1.53 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), X ),
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP(
% 1.17/1.53 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), X ),
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.53 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.17/1.53 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.17/1.53 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.17/1.53 ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ],
% 1.17/1.53 [ =( 'c_List_Ofilter'( X, 'c_List_Olist_ONil'( Y ), Y ),
% 1.17/1.53 'c_List_Olist_ONil'( Y ) ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X
% 1.17/1.53 ) ), T ), 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.17/1.53 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.17/1.53 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.17/1.53 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 1.17/1.53 , Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ]
% 1.17/1.53 ,
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 1.17/1.53 , Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ]
% 1.17/1.53 ,
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 1.17/1.53 , Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ]
% 1.17/1.53 ,
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 1.17/1.53 , Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ]
% 1.17/1.53 ,
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 1.17/1.53 , Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ) ]
% 1.17/1.53 ,
% 1.17/1.53 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'(
% 1.17/1.53 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ],
% 1.17/1.53 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.17/1.53 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.17/1.53 ) ],
% 1.17/1.53 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.17/1.53 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), =( X, Z
% 1.17/1.53 ) ],
% 1.17/1.53 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.17/1.53 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.17/1.53 ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.17/1.53 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 1.17/1.53 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =( hAPP(
% 1.17/1.53 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.17/1.53 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.17/1.53 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ],
% 1.17/1.53 [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'c_Lambda_OdB_OAbs'( X ) ), Y
% 1.17/1.53 ), Z ), 'c_Lambda_OdB_OAbs'( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ),
% 1.17/1.53 hAPP( hAPP( 'c_Lambda_Olift', Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.17/1.53 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ),
% 1.17/1.53 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ) ) ],
% 1.17/1.53 [ hBOOL( hAPP( 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.17/1.53 'tc_nat' ), 'tc_nat' ), X ) ) ],
% 1.17/1.53 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), Z ) ) ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.17/1.53 X ), Y ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ),
% 1.17/1.53 'c_HOL_Oone__class_Oone'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.17/1.53 X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.17/1.53 'c_HOL_Oone__class_Oone'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 1.17/1.53 , Z, X ), 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.53 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.53 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.17/1.53 ) ), Z ), T, X ) ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.53 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.53 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z,
% 1.17/1.53 T, X ) ), T, X ) ) ],
% 1.17/1.53 [ hBOOL( hAPP( 'c_lessequals'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.17/1.53 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( Z, Y, 'tc_nat' ) )
% 1.17/1.53 ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Z ) ) ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Divides_Odiv__class_Odiv'( Y, T
% 1.17/1.53 , X ), 'c_Divides_Odiv__class_Odiv'( Z, T, X ), X ) ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( T, Y, X ) ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Divides_Odiv__class_Odiv'( Y, Z
% 1.17/1.53 , X ), 'c_Divides_Odiv__class_Odiv'( T, Z, X ), X ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, X ) ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.17/1.53 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.53 'tc_nat' ), 'c_Suc'( X ) ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'( X ) ), Z ) ) ), ~(
% 1.17/1.53 hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ), Z ) ) ) ],
% 1.17/1.53 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.17/1.53 'c_Suc'( Z ) ), X ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.53 'tc_nat' ), 'c_Suc'( Z ) ), Y ) ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.53 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.17/1.53 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ],
% 1.17/1.53 [ =( 'c_Nat_Osize__class_Osize'( 'c_Lambda_OdB_OAbs'( X ),
% 1.17/1.53 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.17/1.53 'c_Nat_Osize__class_Osize'( X, 'tc_Lambda_OdB' ) ), 'c_Suc'(
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.17/1.53 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), X ) ) ) ],
% 1.17/1.53 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.17/1.53 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.17/1.53 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X
% 1.17/1.53 ) ), Z ), Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ]
% 1.17/1.53 ,
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Divides_Odiv__class_Odiv'( Z,
% 1.17/1.53 Y, X ) ), Z ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ]
% 1.17/1.53 ,
% 1.17/1.53 [ 'c_Lambda_Obeta'( hAPP( hAPP( 'c_Lambda_Olift', X ), Y ), hAPP( hAPP(
% 1.17/1.53 'c_Lambda_Olift', Z ), Y ) ), ~( 'c_Lambda_Obeta'( X, Z ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.53 , Y ), 'c_Power_Opower__class_Opower'( Y, Z, X ) ), X ),
% 1.17/1.53 'c_Power_Opower__class_Opower'( Y, Z, X ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ),
% 1.17/1.53 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.53 ), X ), Y ) ) ) ],
% 1.17/1.53 [ =( hAPP( hAPP( 'c_Lambda_Olift', hAPP( hAPP( hAPP( 'c_Lambda_Osubst',
% 1.17/1.53 X ), Y ), Z ) ), T ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', hAPP( hAPP(
% 1.17/1.53 'c_Lambda_Olift', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.17/1.53 , T ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ), hAPP( hAPP(
% 1.17/1.53 'c_Lambda_Olift', Y ), T ) ), Z ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), 'c_HOL_Oone__class_Oone'(
% 1.17/1.53 'tc_nat' ) ) ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.17/1.53 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.17/1.53 X ), Y ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.17/1.53 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.17/1.53 X ), Y ) ],
% 1.17/1.53 [ ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ) ), Z ) ), T ) ), hAPP(
% 1.17/1.53 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), T ) ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.17/1.53 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.17/1.53 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.17/1.53 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.17/1.53 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.17/1.53 , U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), W ), T ), Z, X ) ) ],
% 1.17/1.53 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X )
% 1.17/1.53 , Z ), 'tc_nat' ), Y ) ) ) ],
% 1.17/1.53 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.17/1.53 'tc_nat' ), X ), Y ), 'tc_nat' ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.17/1.53 X, 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y
% 1.17/1.53 ) ) ) ) ],
% 1.17/1.53 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), 'c_Suc'(
% 1.17/1.53 Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.17/1.53 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.17/1.53 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'( X )
% 1.17/1.53 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP(
% 1.17/1.53 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.17/1.53 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ), =(
% 1.17/1.53 Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 1.17/1.53 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.53 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T
% 1.17/1.53 ) ), X ), Y, 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, T ) ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.53 'c_Power_Opower__class_Opower'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ),
% 1.17/1.53 T, X ), 'c_Divides_Odiv__class_Odiv'( 'c_Power_Opower__class_Opower'( Y,
% 1.17/1.53 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.17/1.53 [ =( hAPP( 'c_Type_Oshift'( X, Y, Z, T ), Y ), Z ) ],
% 1.17/1.53 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OAbs'( Y ) ) ), =( X, Y
% 1.17/1.53 ) ],
% 1.17/1.53 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.53 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP(
% 1.17/1.53 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ) ), T ),
% 1.17/1.53 'tc_nat' ), U ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), T ), 'tc_nat' ),
% 1.17/1.53 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), U ) ) ) ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( Y, 'tc_nat' ), X ) ) ) ],
% 1.17/1.53 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.53 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.17/1.53 ) ), Z ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.17/1.53 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) )
% 1.17/1.53 ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), T ) ), Y ) ), Z ),
% 1.17/1.53 'tc_nat' ), U ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( T, 'tc_nat' ), X ) )
% 1.17/1.53 ) ],
% 1.17/1.53 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ), T ) ), U ) ) ), ~(
% 1.17/1.53 hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.53 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T
% 1.17/1.53 ) ), X ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.17/1.53 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ), U ) )
% 1.17/1.53 ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ) ],
% 1.17/1.53 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.53 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.17/1.53 ) ), Z ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.17/1.53 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) )
% 1.17/1.53 ), ~( hBOOL( hAPP( 'c_lessequals'( Z, 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), X ) ), Y ) ), U ) ) ) ),
% 1.17/1.53 ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), T ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.17/1.53 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.17/1.53 Y, X ) ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ) ],
% 1.17/1.53 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ) ), Y, 'tc_nat'
% 1.17/1.53 ), 'c_Divides_Odiv__class_Omod'( 'c_Suc'( Z ), Y, 'tc_nat' ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.17/1.53 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.53 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.17/1.53 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.17/1.53 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.53 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.17/1.53 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.17/1.53 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.17/1.53 , Z ) ],
% 1.17/1.53 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.17/1.53 , Z ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.53 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.53 ), Y ), Z ), Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.53 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.53 ), Y ), Z ), Y, X ), Z ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.53 [ ~( =( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.17/1.53 ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.17/1.53 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ) ) ), X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.17/1.53 ) ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.17/1.53 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.17/1.53 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.17/1.53 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.17/1.53 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.53 ), U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), W ), T ), Z, X ) ) ],
% 1.17/1.53 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ) ],
% 1.17/1.53 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ), Y ) ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( Z, 'tc_nat' ), X ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), U ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.17/1.53 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.17/1.53 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.17/1.53 'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ),
% 1.17/1.53 'c_Divides_Odiv__class_Omod'( Y, X, 'tc_nat' ) ) ) ],
% 1.17/1.53 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.17/1.53 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ) ), Y ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ),
% 1.17/1.53 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.53 X ), Y ), Z ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.17/1.53 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.17/1.53 ) ), Z ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.53 X ), Z ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ) ) ],
% 1.17/1.53 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP(
% 1.17/1.53 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.17/1.53 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ),
% 1.17/1.53 'c_Int_Onumber__class_Onumber__of'( T, X ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.53 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.17/1.53 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.53 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.53 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( X, hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.17/1.53 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 1.17/1.53 [ ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), X ), Y ) ],
% 1.17/1.53 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.17/1.53 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ) ],
% 1.17/1.53 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Power_Opower__class_Opower'( Y
% 1.17/1.53 , Z, X ) ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.17/1.53 'c_HOL_Oone__class_Oone'( X ), X ), Y ) ) ) ],
% 1.17/1.53 [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OAbs'( Y ), Z ),
% 1.17/1.53 'c_Lambda_OdB_OAbs'( 'c_Lambda_Oliftn'( X, Y, hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), 'c_HOL_Oone__class_Oone'(
% 1.17/1.53 'tc_nat' ) ) ) ) ) ],
% 1.17/1.53 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 1.17/1.53 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 1.17/1.53 [ =( X, Y ), ~( hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ), X ) ) ), ~(
% 1.17/1.53 hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.17/1.53 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 1.17/1.53 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 1.17/1.53 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), =( Y, X
% 1.17/1.53 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 1.17/1.53 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 1.17/1.53 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 1.17/1.53 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 1.17/1.53 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 1.17/1.53 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), =( Y, X
% 1.17/1.53 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 1.17/1.53 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ), =( Y, X ) ]
% 1.17/1.53 ,
% 1.17/1.53 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( Z, X ), Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.17/1.53 Z ) ) ) ],
% 1.17/1.53 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( Z, X ), Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.17/1.53 Z ) ) ) ],
% 1.17/1.53 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( Y, X ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ),
% 1.17/1.53 Y ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Y, X ) ],
% 1.17/1.53 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, X, 'tc_nat' ) ],
% 1.17/1.53 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ),
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ),
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 1.17/1.53 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.17/1.53 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ) ), X ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.17/1.53 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ) ), Z ), X ) ],
% 1.17/1.53 [ 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.53 'tc_nat' ) ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y ), 'tc_nat' ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.17/1.53 , hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.17/1.53 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z )
% 1.17/1.53 ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.17/1.53 , hBOOL( hAPP( 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X
% 1.17/1.53 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.17/1.53 , hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.17/1.53 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T )
% 1.17/1.53 ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), T ) ) ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.17/1.53 , hBOOL( hAPP( 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), X
% 1.17/1.53 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ) ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ), hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z
% 1.17/1.53 ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), ~(
% 1.17/1.53 hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ), hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z
% 1.17/1.53 ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), ~(
% 1.17/1.53 hBOOL( hAPP( 'c_lessequals'( Z, X ), T ) ) ) ],
% 1.17/1.53 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.53 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.53 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ),
% 1.17/1.53 Z ) ) ) ],
% 1.17/1.53 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ),
% 1.17/1.53 X ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z )
% 1.17/1.53 , Y ) ) ) ) ],
% 1.17/1.53 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.53 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.53 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ),
% 1.17/1.53 Z ) ) ) ],
% 1.17/1.53 [ ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ), =( Y, hAPP(
% 1.17/1.53 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ) ), X ) ) ],
% 1.17/1.53 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ) ), Y ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.17/1.53 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Y ), X ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( Y, 'tc_nat' ), X ) ) ) ],
% 1.17/1.53 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.17/1.53 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.17/1.53 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.17/1.53 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.53 'tc_nat' ), X ), 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ), Z,
% 1.17/1.53 'tc_nat' ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.53 X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ) ) ) ],
% 1.17/1.53 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ) ],
% 1.17/1.53 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( Y, 'tc_nat' ), X ) ) ) ],
% 1.17/1.53 [ =( X, 'c_List_Olist_ONil'( Y ) ), ~( 'c_List_Olist__all2'( Z,
% 1.17/1.53 'c_List_Olist_ONil'( T ), X, T, Y ) ) ],
% 1.17/1.53 [ =( X, 'c_List_Olist_ONil'( Y ) ), ~( 'c_List_Olist__all2'( Z, X,
% 1.17/1.53 'c_List_Olist_ONil'( T ), Y, T ) ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.17/1.53 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X
% 1.17/1.53 ) ), 'c_Divides_Odiv__class_Odiv'( T, U, X ) ),
% 1.17/1.53 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.53 ), Y ), T ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ), X
% 1.17/1.53 ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( U, T, X ) ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.17/1.53 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.17/1.53 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), U ) ) ) ), =(
% 1.17/1.53 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.17/1.53 'c_Divides_Odiv__class_Omod'( T, Y, 'tc_nat' ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ), Y,
% 1.17/1.53 X ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =(
% 1.17/1.53 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.17/1.53 Y, T, X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.17/1.53 'c_HOL_Oone__class_Oone'( X ), X ), Y ) ) ), =( Z, T ) ],
% 1.17/1.53 [ =( 'c_Power_Opower__class_Opower'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.53 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.17/1.53 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( Y,
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( X
% 1.17/1.53 ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.17/1.53 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.17/1.53 , X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.17/1.53 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.17/1.53 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.17/1.53 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.17/1.53 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.17/1.53 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ) ],
% 1.17/1.53 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.17/1.53 hBOOL( hAPP( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.17/1.53 X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), hBOOL( hAPP(
% 1.17/1.53 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ), X
% 1.17/1.53 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.17/1.53 [ ~( 'class_Int_Onumber'( X ) ), ~( 'class_Divides_Osemiring__div'( X )
% 1.17/1.53 ), =( 'c_Divides_Odiv__class_Omod'( 'c_Int_Onumber__class_Onumber__of'(
% 1.17/1.53 Y, X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Int_Onumber__class_Onumber__of'(
% 1.17/1.53 Z, X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.17/1.53 [ ~( 'class_Int_Onumber'( X ) ), ~( 'class_Divides_Osemiring__div'( X )
% 1.17/1.53 ), ~( =( 'c_Divides_Odiv__class_Omod'(
% 1.17/1.53 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.17/1.53 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Int_Onumber__class_Onumber__of'(
% 1.17/1.53 Z, X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.53 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.53 ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z )
% 1.17/1.53 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.53 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.53 'tc_nat' ) ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y ), 'tc_nat' ),
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.53 [ =( hAPP( hAPP( 'c_Lambda_Olift', hAPP( hAPP( 'c_Lambda_Olift', X ), Y
% 1.17/1.53 ) ), 'c_Suc'( Z ) ), hAPP( hAPP( 'c_Lambda_Olift', hAPP( hAPP(
% 1.17/1.53 'c_Lambda_Olift', X ), Z ) ), Y ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), 'c_HOL_Oone__class_Oone'(
% 1.17/1.53 'tc_nat' ) ) ) ) ) ],
% 1.17/1.53 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.17/1.53 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ),
% 1.17/1.53 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.53 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.17/1.53 ), X ), Z ), 'tc_nat' ) ) ],
% 1.17/1.53 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.17/1.53 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Z ),
% 1.17/1.53 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.53 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.17/1.53 ), Y ), Z ), 'tc_nat' ) ) ],
% 1.17/1.53 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.17/1.53 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X,
% 1.17/1.53 Z, 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.17/1.53 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.53 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, Z, 'tc_nat' ) ),
% 1.17/1.53 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ), Z, 'tc_nat' ) ) ) ]
% 1.17/1.53 ,
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.53 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.53 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.17/1.53 ), 'c_Divides_Odiv__class_Odiv'( Z, T, X ) ), =( Y,
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.53 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.53 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.17/1.53 ), 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ), =( Z,
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.53 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.17/1.53 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), =( X,
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.53 [ ~( 'c_Type_Otyping'( X, Y, Z ) ), ~( 'c_Type_Otyping'( 'c_Type_Oshift'(
% 1.17/1.53 X, T, Z, 'tc_Type_Otype' ), U, W ) ), 'c_Type_Otyping'( X, hAPP( hAPP(
% 1.17/1.53 hAPP( 'c_Lambda_Osubst', U ), Y ), T ), W ) ],
% 1.17/1.53 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat'
% 1.17/1.53 ), Z ) ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'(
% 1.17/1.53 'c_Power_Opower__class_Opower'( Z, X, 'tc_nat' ),
% 1.17/1.53 'c_Power_Opower__class_Opower'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.17/1.53 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.53 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( Y, 'tc_nat' ), T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( X
% 1.17/1.53 , 'tc_nat' ), Z ) ) ) ],
% 1.17/1.53 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), X ) ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.17/1.53 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), ~(
% 1.17/1.53 hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) )
% 1.17/1.53 ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.17/1.53 , T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), U ) ) ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.17/1.53 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), ~(
% 1.17/1.53 hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) )
% 1.17/1.53 ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.17/1.53 , Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), U ) ) ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.17/1.53 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), Y, 'tc_nat' )
% 1.17/1.53 , 'c_Divides_Odiv__class_Omod'( Z, Y, 'tc_nat' ) ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.53 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.17/1.53 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.17/1.53 , 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.53 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.17/1.53 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.17/1.53 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.53 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.17/1.53 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.17/1.53 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), =( Z,
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ), 'tc_nat' ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.17/1.53 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.17/1.53 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.53 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.17/1.53 , Y ), Z ), Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.17/1.53 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 1.17/1.53 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.53 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.17/1.53 , Y ), Z ), Z, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.17/1.53 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 1.17/1.53 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.53 [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OAbs'( Y ) )
% 1.17/1.53 , ~( 'c_Lambda_Obeta'( X, Y ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( Y, 'tc_nat' ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.17/1.53 'c_Power_Opower__class_Opower'( T, Y, X ), X ),
% 1.17/1.53 'c_Power_Opower__class_Opower'( T, Z, X ) ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), T ) ) ) ]
% 1.17/1.53 ,
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( Y, 'tc_nat' ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.17/1.53 'c_Power_Opower__class_Opower'( T, Y, X ), X ),
% 1.17/1.53 'c_Power_Opower__class_Opower'( T, Z, X ) ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), T ) ) ) ]
% 1.17/1.53 ,
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, Z, X ), X ),
% 1.17/1.53 'c_Power_Opower__class_Opower'( Y, T, X ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( Z, 'tc_nat' ), T ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), Y ) ) ) ]
% 1.17/1.53 ,
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), Z ) ) ),
% 1.17/1.53 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.17/1.53 , X ), Y ) ) ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.53 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.17/1.53 ],
% 1.17/1.53 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ), =(
% 1.17/1.53 Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 1.17/1.53 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.53 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T
% 1.17/1.53 ) ), X ), Y, 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, X ) ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.17/1.53 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_HOL_Oord__class_Oless'( Z, X ), U ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.17/1.53 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( Z, X ), U ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.17/1.53 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ),
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 1.17/1.53 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ),
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.17/1.53 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.17/1.53 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.17/1.53 ), ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.53 ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 1.17/1.53 =( 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.53 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.17/1.53 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.17/1.53 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.17/1.53 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.17/1.53 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.17/1.53 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.17/1.53 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.53 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.17/1.53 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.17/1.53 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.17/1.53 , X ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.17/1.53 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.17/1.53 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.53 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.17/1.53 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.53 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 1.17/1.53 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.53 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.53 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.53 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.17/1.53 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.53 ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.17/1.53 X ) ), ~( =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) )
% 1.17/1.53 , =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.53 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.17/1.53 ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.53 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.17/1.53 ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.53 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.17/1.53 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.17/1.53 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.17/1.53 ,
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( Y,
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.17/1.53 , X ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.17/1.53 Y ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.17/1.53 Y ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.17/1.53 X ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.17/1.53 Y ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.17/1.53 Y ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.17/1.53 Y ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.17/1.53 Y ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.17/1.53 Y ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.17/1.53 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.53 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U
% 1.17/1.53 ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.53 X ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.53 X ), X ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), U )
% 1.17/1.53 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.17/1.53 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.53 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U
% 1.17/1.53 ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.53 X ), Z ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_HOL_Oord__class_Oless'( Z, X ), U ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.17/1.53 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.53 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U
% 1.17/1.53 ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( Z, X ), U ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.17/1.53 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.53 X ), Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.17/1.53 ) ) ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.17/1.53 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.53 X ), Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.17/1.53 , ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.17/1.53 ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.53 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP(
% 1.17/1.53 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), X ),
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, T, X ), X )
% 1.17/1.53 , 'c_Power_Opower__class_Opower'( Z, T, X ) ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.53 , T ), Y ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.17/1.53 ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.53 , Y ), T ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T )
% 1.17/1.53 ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.17/1.53 hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.53 X ), T ), Y ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z
% 1.17/1.53 ) ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.17/1.53 hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.53 X ), Y ), T ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T
% 1.17/1.53 ) ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.17/1.53 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.53 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U
% 1.17/1.53 ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.53 X ), Z ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_HOL_Oord__class_Oless'( Z, X ), U ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.17/1.53 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.53 X ), Z ), T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ), ~(
% 1.17/1.53 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.53 X ), Z ) ) ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.17/1.53 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.53 X ), Z ), T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), T )
% 1.17/1.53 ) ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.17/1.53 ), Z ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_HOL_Oord__class_Oless'( T, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.17/1.53 ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.17/1.53 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~(
% 1.17/1.53 hBOOL( hAPP( 'c_lessequals'( T, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.17/1.53 ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) )
% 1.17/1.53 ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.17/1.53 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~(
% 1.17/1.53 hBOOL( hAPP( 'c_lessequals'( Z, X ), T ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) )
% 1.17/1.53 ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) )
% 1.17/1.53 , ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) )
% 1.17/1.53 , ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.17/1.53 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.17/1.53 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.17/1.53 , ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.17/1.53 ) ) ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.17/1.53 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.17/1.53 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.17/1.53 ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.17/1.53 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ) ), =( Y,
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.17/1.53 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ) ), =( Z,
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.17/1.53 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.17/1.53 'c_HOL_Oone__class_Oone'( X ) ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.17/1.53 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ) ) ],
% 1.17/1.53 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), hBOOL( hAPP(
% 1.17/1.53 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.17/1.53 Y, X ), Z ) ) ) ],
% 1.17/1.53 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( Y, X ), Z ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.17/1.53 Y, X ), Z ) ) ],
% 1.17/1.53 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.17/1.53 Y, X ), Z ) ) ), =( Y, Z ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Power_Opower__class_Opower'( Y
% 1.17/1.53 , Z, X ) ), 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), 'c_Power_Opower__class_Opower'( Y, Z,
% 1.17/1.53 X ) ), Y ), 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ) ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.53 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.17/1.53 , Y ), Z ), Z, X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.53 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.17/1.53 , Y ), Z ), Y, X ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 1.17/1.53 , Z, X ), 'c_Power_Opower__class_Opower'( T, U, X ), X ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( Z, 'tc_nat' ), U ) ) ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z )
% 1.17/1.53 , Y ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 1.17/1.53 , Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z )
% 1.17/1.53 , Y ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 1.17/1.53 , Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), Z, X ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.17/1.53 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), hAPP(
% 1.17/1.53 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ),
% 1.17/1.53 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.17/1.53 'tc_nat' ), Z, 'tc_nat' ) ) ), 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.17/1.53 'tc_nat' ) ) ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.53 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T
% 1.17/1.53 , X ), 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X
% 1.17/1.53 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.17/1.53 Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y
% 1.17/1.53 ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.17/1.53 [ ~( =( 'c_Code__Numeral_Oof__nat'( X ), 'c_Code__Numeral_Oof__nat'( Y )
% 1.17/1.53 ) ), =( X, Y ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ), X )
% 1.17/1.53 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.17/1.53 'c_Power_Opower__class_Opower'( Y, Z, X ) ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), Y ) ) ) ]
% 1.17/1.53 ,
% 1.17/1.53 [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), 'tc_nat' ),
% 1.17/1.53 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.17/1.53 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Z, U, X ) ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.17/1.53 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.17/1.53 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ) ), T ), 'tc_nat' ), hAPP(
% 1.17/1.53 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_HOL_Oord__class_Oless'( T, 'tc_nat' ), X ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.53 'tc_nat' ), Z ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.17/1.53 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), ~(
% 1.17/1.53 hBOOL( hAPP( 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.17/1.53 ), ~( hBOOL( hAPP( 'c_lessequals'( T, X ), Y ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.17/1.53 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~(
% 1.17/1.53 hBOOL( hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.17/1.53 ), ~( hBOOL( hAPP( 'c_lessequals'( T, X ), Z ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.17/1.53 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), ~(
% 1.17/1.53 hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) )
% 1.17/1.53 ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.17/1.53 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~(
% 1.17/1.53 hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) )
% 1.17/1.53 ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), T ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.17/1.53 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~(
% 1.17/1.53 hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) )
% 1.17/1.53 ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), T ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.17/1.53 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ), =( T, U ), =( Z,
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.53 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.17/1.53 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ) ) ), =( Z, T ), =( Y
% 1.17/1.53 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.17/1.53 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.53 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.17/1.53 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.53 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.53 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X
% 1.17/1.53 ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( T, X ), Z ) ) ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z
% 1.17/1.53 ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ]
% 1.17/1.53 ,
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 1.17/1.53 , Z, X ), T, X ), ~( hBOOL( hAPP( 'c_lessequals'( Z, 'tc_nat' ), U ) ) )
% 1.17/1.53 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'(
% 1.17/1.53 'c_Power_Opower__class_Opower'( Y, U, X ), T, X ) ) ],
% 1.17/1.53 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y
% 1.17/1.53 , X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( T, X ), Z ) ) ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.17/1.53 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), X ) ) ],
% 1.17/1.53 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( X
% 1.17/1.53 , 'tc_nat' ), Z ) ) ) ],
% 1.17/1.53 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), X ) ) ],
% 1.17/1.53 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X
% 1.17/1.53 ), Y ) ) ],
% 1.17/1.53 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y
% 1.17/1.53 , X ), Y ) ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z )
% 1.17/1.53 , T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( U, X ), T ) ) ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.17/1.53 , Z ), U ) ) ) ) ],
% 1.17/1.53 [ 'c_Type_Otyping'( X, Y, Z ), ~( 'c_Lambda_Obeta'( T, Y ) ), ~(
% 1.17/1.53 'c_Type_Otyping'( X, T, Z ) ) ],
% 1.17/1.53 [ =( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), Y, 'tc_nat' ) ), ~(
% 1.17/1.53 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.53 'tc_nat' ), 'tc_nat' ), Y ) ) ) ],
% 1.17/1.53 [ =( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ), ~(
% 1.17/1.53 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.53 'tc_nat' ), 'tc_nat' ), Y ) ) ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.17/1.53 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), Y ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.53 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.53 ), Y ), Z ), Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.53 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.53 ), Y ), Z ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.53 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ),
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.53 [ =( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Oone__class_Oone'(
% 1.17/1.53 'tc_nat' ), 'tc_nat' ) ) ],
% 1.17/1.53 [ =( 'c_Code__Numeral_Onat__of'( 'c_Code__Numeral_Oof__nat'( X ) ), X )
% 1.17/1.53 ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X )
% 1.17/1.53 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.17/1.53 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ), Y ) ],
% 1.17/1.53 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.53 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( X, 'tc_nat' ), Z ) ) ) ],
% 1.17/1.53 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.53 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( Y, 'tc_nat' ), Z ) ) ) ],
% 1.17/1.53 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.53 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( Y, 'tc_nat' ), Z ) ) ) ],
% 1.17/1.53 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.53 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( X, 'tc_nat' ), Z ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( hAPP(
% 1.17/1.53 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.17/1.53 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.17/1.53 ,
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.17/1.53 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 1.17/1.53 , X ) ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ) ],
% 1.17/1.53 [ 'c_List_Olist__all2'( X, 'c_List_Olist_ONil'( Y ), 'c_List_Olist_ONil'(
% 1.17/1.53 Z ), Y, Z ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.17/1.53 'c_Power_Opower__class_Opower'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.53 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.17/1.53 'c_Power_Opower__class_Opower'( Y, T, X ) ),
% 1.17/1.53 'c_Power_Opower__class_Opower'( Z, T, X ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.17/1.53 'c_Power_Opower__class_Opower'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.53 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.17/1.53 'c_Power_Opower__class_Opower'( Y, T, X ) ),
% 1.17/1.53 'c_Power_Opower__class_Opower'( Z, T, X ) ) ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.53 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.17/1.53 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.17/1.53 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.17/1.53 , Y ), T ), Z, X ) ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.53 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.17/1.53 , Y ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ),
% 1.17/1.53 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.17/1.53 , Y ), Z ), T, X ) ) ],
% 1.17/1.53 [ 'c_List_Olist__all2'( 'c_fequal'( X ), Y, Y, X, X ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 1.17/1.53 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.17/1.53 X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), W ) ) ), T
% 1.17/1.53 ), X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, W, X ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 1.17/1.53 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.17/1.53 X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), W
% 1.17/1.53 ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), Z ), W ), X ) ), ~(
% 1.17/1.53 'c_Ring__and__Field_Odvd__class_Odvd'( Y, U, X ) ) ],
% 1.17/1.53 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.17/1.53 'c_Power_Opower__class_Opower'( Y, hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ), X ),
% 1.17/1.53 'c_Power_Opower__class_Opower'( 'c_Power_Opower__class_Opower'( Y, Z, X )
% 1.17/1.53 , T, X ) ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.53 X ), Y ), 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ) ),
% 1.17/1.53 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ), Z ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.53 X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.17/1.53 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), Y ) ],
% 1.17/1.53 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( Y, hAPP( hAPP(
% 1.17/1.53 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.53 X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.17/1.53 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ) ],
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ]
% 1.17/1.53 ,
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.17/1.53 hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ]
% 1.17/1.53 ,
% 1.17/1.53 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.17/1.53 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.53 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.17/1.54 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.17/1.54 hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.17/1.54 hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.17/1.54 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 'tc_nat' ), 'tc_nat' ), X ) ) ), hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.17/1.54 'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ) ), 'tc_nat' ), Y ) ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.54 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.54 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.17/1.54 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.17/1.54 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), Z ) ) ],
% 1.17/1.54 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.54 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.54 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.17/1.54 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.17/1.54 'c_Divides_Odiv__class_Omod'( Z, T, X ) ) ) ],
% 1.17/1.54 [ =( hAPP( hAPP( 'c_Lambda_Olift', 'c_Lambda_OdB_OAbs'( X ) ), Y ),
% 1.17/1.54 'c_Lambda_OdB_OAbs'( hAPP( hAPP( 'c_Lambda_Olift', X ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.17/1.54 'tc_nat' ) ) ) ) ) ],
% 1.17/1.54 [ =( 'c_Lambda_OdB_OdB__size'( 'c_Lambda_OdB_OAbs'( X ) ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Lambda_OdB_OdB__size'( X ) ),
% 1.17/1.54 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.17/1.54 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.17/1.54 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.17/1.54 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), =( Y,
% 1.17/1.54 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.17/1.54 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.17/1.54 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.54 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.17/1.54 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.54 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.17/1.54 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.17/1.54 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.17/1.54 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.17/1.54 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.54 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.17/1.54 ) ) ],
% 1.17/1.54 [ 'c_Type_Otyping'( 'c_Type_Oshift'( X, Y, Z, 'tc_Type_Otype' ), hAPP(
% 1.17/1.54 hAPP( 'c_Lambda_Olift', T ), Y ), U ), ~( 'c_Type_Otyping'( X, T, U ) ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), hBOOL( hAPP(
% 1.17/1.54 'c_lessequals'( Y, 'tc_nat' ), X ) ) ],
% 1.17/1.54 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ),
% 1.17/1.54 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ), ~(
% 1.17/1.54 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ), ~(
% 1.17/1.54 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 1.17/1.54 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.17/1.54 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ),
% 1.17/1.54 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ), ~(
% 1.17/1.54 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 1.17/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y
% 1.17/1.54 , X ), Z ) ), hBOOL( hAPP( 'c_lessequals'( Z, X ), Y ) ) ],
% 1.17/1.54 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), =( Y, Z ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_lessequals'( Y, X ), Z ) ) ) ],
% 1.17/1.54 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), =( Y, Z ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_lessequals'( Y, X ), Z ) ) ) ],
% 1.17/1.54 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.17/1.54 Y, X ), Z ) ) ) ],
% 1.17/1.54 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.17/1.54 Y, X ), Z ) ) ), =( Z, Y ) ],
% 1.17/1.54 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), =( Z, Y ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_lessequals'( Y, X ), Z ) ) ) ],
% 1.17/1.54 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.17/1.54 T, X ), Z ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), T ) )
% 1.17/1.54 ) ],
% 1.17/1.54 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( T, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.17/1.54 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_lessequals'( T, X ), Z ) ) ) ],
% 1.17/1.54 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.17/1.54 Y, X ), T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ), Z ) )
% 1.17/1.54 ) ],
% 1.17/1.54 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.17/1.54 , hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T
% 1.17/1.54 ), Y ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ) )
% 1.17/1.54 ],
% 1.17/1.54 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.17/1.54 , hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Z, X ), T ) ) ) ],
% 1.17/1.54 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.17/1.54 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Z, X ), T ) ) ) ],
% 1.17/1.54 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.17/1.54 , hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.17/1.54 ), T ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) )
% 1.17/1.54 ],
% 1.17/1.54 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.17/1.54 , hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.17/1.54 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.17/1.54 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.17/1.54 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y
% 1.17/1.54 , X ), Z ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) )
% 1.17/1.54 ],
% 1.17/1.54 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X
% 1.17/1.54 ), Z ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.17/1.54 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Z, X ), U ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.17/1.54 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP( 'c_lessequals'( Z
% 1.17/1.54 , X ), Y ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), Z ) ) ) ],
% 1.17/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP( 'c_lessequals'( Z
% 1.17/1.54 , X ), Y ) ) ],
% 1.17/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.17/1.54 Y, X ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Y ) )
% 1.17/1.54 ) ],
% 1.17/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), Y ) ), hBOOL( hAPP( 'c_lessequals'( Y
% 1.17/1.54 , X ), Y ) ) ],
% 1.17/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_lessequals'( Z, X ), Y ) ) ) ],
% 1.17/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y
% 1.17/1.54 , X ), Z ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.17/1.54 Y, X ), Z ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), Y ) )
% 1.17/1.54 ) ],
% 1.17/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP( 'c_lessequals'( Z
% 1.17/1.54 , X ), Y ) ) ],
% 1.17/1.54 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.17/1.54 Y, X ), Z ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), Y ) )
% 1.17/1.54 ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.54 , T ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y )
% 1.17/1.54 ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.54 , Z ), T ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.17/1.54 ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.17/1.54 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ) ), U ), X ), W ) ),
% 1.17/1.54 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.54 X ), Y ), T ) ), U ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.17/1.54 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), W ) ) ) ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.17/1.54 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), X ), hAPP(
% 1.17/1.54 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.17/1.54 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T ), X ), W ) ) ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.54 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), U ) ), W ) ) ), ~( hBOOL(
% 1.17/1.54 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.54 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), Y ), X )
% 1.17/1.54 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ), W ) ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.17/1.54 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), X ), hAPP(
% 1.17/1.54 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.54 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( X ), U ), Y ) ), Z ) ), W ) ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.17/1.54 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.54 X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.17/1.54 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.17/1.54 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), hBOOL( hAPP(
% 1.17/1.54 'c_lessequals'( Z, X ), Y ) ), ~( hBOOL( hAPP( 'c_lessequals'( U, X ), T
% 1.17/1.54 ) ) ) ],
% 1.17/1.54 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.17/1.54 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), hBOOL( hAPP(
% 1.17/1.54 'c_lessequals'( U, X ), T ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), Y
% 1.17/1.54 ) ) ) ],
% 1.17/1.54 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.17/1.54 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.17/1.54 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.17/1.54 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.17/1.54 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.17/1.54 ), U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( X ), W ), T ), Z, X ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.17/1.54 'c_Ring__and__Field_Odvd__class_Odvd'( Y, hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ), X ), ~(
% 1.17/1.54 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.17/1.54 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.17/1.54 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.17/1.54 X ), Y ), Z ) ), Z ), Y ) ],
% 1.17/1.54 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.17/1.54 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), T, X ),
% 1.17/1.54 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.17/1.54 ), 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), Z ), T, X ) ) ],
% 1.17/1.54 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.17/1.54 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), T, X ),
% 1.17/1.54 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.17/1.54 ), Y ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.17/1.54 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.17/1.54 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), T, X ),
% 1.17/1.54 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.17/1.54 ), 'c_Divides_Odiv__class_Omod'( Y, T, X ) ),
% 1.17/1.54 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.17/1.54 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.54 X ), Y ), Z ) ), Z ), Y ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( T, Y, X ), X )
% 1.17/1.54 , 'c_Power_Opower__class_Opower'( T, Z, X ) ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), T ) ) ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ), X )
% 1.17/1.54 , 'c_Power_Opower__class_Opower'( Y, T, X ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), Y ) ) ),
% 1.17/1.54 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' ), T ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( T, Y, X ), X )
% 1.17/1.54 , 'c_Power_Opower__class_Opower'( T, Z, X ) ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), T ) ) ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ), X )
% 1.17/1.54 , 'c_Power_Opower__class_Opower'( Y, T, X ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' ), T ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), Y ) ) ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( T ), X ), X )
% 1.17/1.54 , 'c_Power_Opower__class_Opower'( Z, 'c_Suc'( T ), X ) ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =(
% 1.17/1.54 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 1.17/1.54 'c_Power_Opower__class_Opower'( T, 'c_Suc'( Z ), X ) ) ), =( Y, T ), ~(
% 1.17/1.54 hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) )
% 1.17/1.54 ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.17/1.54 , Y ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.17/1.54 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), Y ) ) ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), =( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( X ), 'c_Finite__Set_Osetsum'( Y, Z, T, X )
% 1.17/1.54 ), U ), 'c_Finite__Set_Osetsum'( 'c_COMBC'( hAPP( hAPP( 'c_COMBB'( X,
% 1.17/1.54 'tc_fun'( X, X ), T ), 'c_HOL_Otimes__class_Otimes'( X ) ), Y ), U, T, X
% 1.17/1.54 , X ), Z, T, X ) ) ],
% 1.17/1.54 [ ~( hBOOL( hAPP( X, Y ) ) ), hBOOL( hAPP( X,
% 1.17/1.54 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.54 'tc_nat' ) ) ) ],
% 1.17/1.54 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Omod'( Y,
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.17/1.54 , Y ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.54 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.17/1.54 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 'tc_nat' ) ) ) ],
% 1.17/1.54 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 'tc_nat' ) ), Y ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 1.17/1.54 'v_sko__List__Xlexn__Xinduct__1'( X ) ) ), ~( hBOOL( hAPP( X,
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( hBOOL(
% 1.17/1.54 hAPP( X, 'c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1'( X ) ) ) ), ~(
% 1.17/1.54 hBOOL( hAPP( X, Y ) ) ) ],
% 1.17/1.54 [ =( 'c_Lambda_Oliftn'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, Y ),
% 1.17/1.54 X ) ],
% 1.17/1.54 [ hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ), ~( hBOOL( hAPP( X
% 1.17/1.54 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.17/1.54 [ ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), hBOOL(
% 1.17/1.54 hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 'tc_nat' ), 'tc_nat' ) ) ) ],
% 1.17/1.54 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.17/1.54 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.17/1.54 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_lessequals'( X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) )
% 1.17/1.54 ) ],
% 1.17/1.54 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 'tc_nat' ) ) ],
% 1.17/1.54 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 'tc_nat' ) ) ],
% 1.17/1.54 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.54 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.54 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.54 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.17/1.54 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), =( Y
% 1.17/1.54 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 1.17/1.54 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.17/1.54 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( X
% 1.17/1.54 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 1.17/1.54 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.17/1.54 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( Y
% 1.17/1.54 , Z ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.54 [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 1.17/1.54 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.54 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X
% 1.17/1.54 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.54 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.54 'tc_nat' ), X ) ) ],
% 1.17/1.54 [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.17/1.54 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ],
% 1.17/1.54 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.54 'tc_nat' ), Y ) ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y,
% 1.17/1.54 'tc_nat' ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.17/1.54 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Power_Opower__class_Opower'(
% 1.17/1.54 Y, Z, X ), X ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), Z ) ) ) ],
% 1.17/1.54 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.17/1.54 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.54 'tc_nat' ), X ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Odiv'(
% 1.17/1.54 X, Y, 'tc_nat' ), 'tc_nat' ), X ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.54 'tc_nat' ), X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.17/1.54 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), Y ) ) ) ],
% 1.17/1.54 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~( hBOOL(
% 1.17/1.54 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.54 'tc_nat' ), Z ) ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ), 'tc_nat' ) ) ],
% 1.17/1.54 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.17/1.54 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ), 'tc_nat' ) ), ~(
% 1.17/1.54 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 'tc_nat' ), 'tc_nat' ), Z ) ) ) ],
% 1.17/1.54 [ 'c_Ring__and__Field_Odvd__class_Odvd'( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ), ~(
% 1.17/1.54 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.54 'tc_nat' ), X ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_lessequals'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.17/1.54 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X, Z, 'tc_nat' ) )
% 1.17/1.54 ), ~( hBOOL( hAPP( 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ), ~( hBOOL(
% 1.17/1.54 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.54 'tc_nat' ), Z ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.17/1.54 'tc_nat' ), 'tc_nat' ), Y ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), Y ) ) ) ],
% 1.17/1.54 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ), Y ),
% 1.17/1.54 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 'tc_nat' ), 'tc_nat' ), X ) ) ) ],
% 1.17/1.54 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Y, 'tc_nat' ), X ),
% 1.17/1.54 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 'tc_nat' ), 'tc_nat' ), Y ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_lessequals'( X, 'tc_nat' ), Y ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.54 'tc_nat' ), Z ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.54 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.54 'tc_nat' ), Y ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.54 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.54 'tc_nat' ), X ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.54 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ), hAPP(
% 1.17/1.54 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.54 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), 'tc_nat' ), hAPP(
% 1.17/1.54 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z )
% 1.17/1.54 , X ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.17/1.54 Z ), Y ) ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), Z ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.54 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_lessequals'( Y, 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.54 'tc_nat' ), X ) ) ) ],
% 1.17/1.54 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.17/1.54 'c_Finite__Set_Osetsum'( 'c_COMBS'( hAPP( hAPP( 'c_COMBB'( X, 'tc_fun'( X
% 1.17/1.54 , X ), Y ), 'c_HOL_Oplus__class_Oplus'( X ) ), Z ), T, Y, X, X ), U, Y, X
% 1.17/1.54 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_Finite__Set_Osetsum'(
% 1.17/1.54 Z, U, Y, X ) ), 'c_Finite__Set_Osetsum'( T, U, Y, X ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 'tc_nat' ) ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.54 'tc_nat' ), X ), Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_Suc'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), Y ) ) ), ~( hBOOL(
% 1.17/1.54 hAPP( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.17/1.54 'tc_nat' ), X ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 'tc_nat' ) ), 'tc_nat' ), 'c_Power_Opower__class_Opower'( X, Y, 'tc_nat'
% 1.17/1.54 ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_Suc'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), X ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 'tc_nat' ) ), 'tc_nat' ), X ) ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_Suc'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ) ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =(
% 1.17/1.54 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.17/1.54 T, Z, X ) ) ), =( Y, T ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), Z ) ) ), ~( hBOOL(
% 1.17/1.54 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~(
% 1.17/1.54 hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) )
% 1.17/1.54 ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.17/1.54 'c_Power_Opower__class_Opower'( Y, Z, X ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.54 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.17/1.54 'c_HOL_Oone__class_Oone'( X ), X ), Y ) ) ) ],
% 1.17/1.54 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 'tc_nat' ), 'tc_nat' ), X ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.17/1.54 Y, 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X )
% 1.17/1.54 , 'c_Suc'( 'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ) ) ) ) ) ],
% 1.17/1.54 [ =( 'c_Nat_Osize__class_Osize'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y
% 1.17/1.54 ), 'tc_Lambda_OdB' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.17/1.54 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.17/1.54 'c_Nat_Osize__class_Osize'( X, 'tc_Lambda_OdB' ) ),
% 1.17/1.54 'c_Nat_Osize__class_Osize'( Y, 'tc_Lambda_OdB' ) ) ), 'c_Suc'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.17/1.54 [ =( 'c_Lambda_OdB_OdB__size'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y )
% 1.17/1.54 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Lambda_OdB_OdB__size'( X ) ),
% 1.17/1.54 'c_Lambda_OdB_OdB__size'( Y ) ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 'tc_nat' ) ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), =( 'c_List_Olistsum'(
% 1.17/1.54 'c_List_Omap'( 'c_COMBC'( hAPP( hAPP( 'c_COMBB'( X, 'tc_fun'( X, X ), Y )
% 1.17/1.54 , 'c_HOL_Otimes__class_Otimes'( X ) ), Z ), T, Y, X, X ), U, Y, X ), X )
% 1.17/1.54 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_List_Olistsum'(
% 1.17/1.54 'c_List_Omap'( Z, U, Y, X ), X ) ), T ) ) ],
% 1.17/1.54 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.17/1.54 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.17/1.54 'tc_nat' ) ) ), Y ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.17/1.54 'c_List_Olistsum'( 'c_List_Omap'( 'c_COMBS'( hAPP( hAPP( 'c_COMBB'( X,
% 1.17/1.54 'tc_fun'( X, X ), Y ), 'c_HOL_Oplus__class_Oplus'( X ) ), Z ), T, Y, X, X
% 1.17/1.54 ), U, Y, X ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.17/1.54 'c_List_Olistsum'( 'c_List_Omap'( Z, U, Y, X ), X ) ), 'c_List_Olistsum'(
% 1.17/1.54 'c_List_Omap'( T, U, Y, X ), X ) ) ) ],
% 1.17/1.54 [ 'c_Lambda_Obeta'( hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 1.17/1.54 X ) ), Y ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Y ),
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), X ) ), =(
% 1.17/1.54 'c_Lambda_Osubstn'( hAPP( 'c_Lambda_OdB_OVar', X ), Y, X ),
% 1.17/1.54 'c_Lambda_Oliftn'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ =( 'c_Lambda_Osubstn'( hAPP( 'c_Lambda_OdB_OVar', X ), Y, Z ), hAPP(
% 1.17/1.54 'c_Lambda_OdB_OVar', hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' )
% 1.17/1.54 , X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' ), X ) ) ) ],
% 1.17/1.54 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.17/1.54 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) )
% 1.17/1.54 ],
% 1.17/1.54 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ),
% 1.17/1.54 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.54 ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ) ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 1.17/1.54 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) )
% 1.17/1.54 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), T ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.54 , Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.17/1.54 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ), Y ) ) ), ~(
% 1.17/1.54 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.54 , Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.17/1.54 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ), ~(
% 1.17/1.54 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.54 X ), Z ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.17/1.54 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.54 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z
% 1.17/1.54 ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.54 , Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.17/1.54 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( T, X ), Y ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.54 , Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.17/1.54 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ), Z ) ) ), ~(
% 1.17/1.54 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.54 , Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.17/1.54 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), T ) ) ), ~(
% 1.17/1.54 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.54 X ), Y ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.17/1.54 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.54 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.17/1.54 ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Z, X ), T ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.54 , Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.17/1.54 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( T, X ), Z ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.54 , Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.17/1.54 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), T ) ) ), ~(
% 1.17/1.54 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.54 X ), Y ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.54 , T ), Y ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.17/1.54 ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.54 , Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.17/1.54 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ), Z ) ) ), ~(
% 1.17/1.54 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.54 , T ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y )
% 1.17/1.54 ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ),
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.17/1.54 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.54 X ), Y ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), X ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.17/1.54 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.54 X ), Y ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.17/1.54 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( hBOOL(
% 1.17/1.54 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.54 X ), Y ), Y ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.17/1.54 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.17/1.54 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.54 X ), Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.17/1.54 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.17/1.54 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.17/1.54 ), Y ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.17/1.54 ],
% 1.17/1.54 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.17/1.54 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ),
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.17/1.54 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ),
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.17/1.54 ), Y ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.17/1.54 ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.17/1.54 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.17/1.54 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.17/1.54 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.17/1.54 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.17/1.54 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.17/1.54 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.17/1.54 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.17/1.54 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL(
% 1.17/1.54 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z
% 1.17/1.54 ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.17/1.54 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.17/1.54 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.17/1.54 'c_Power_Opower__class_Opower'( Y, Z, X ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) )
% 1.17/1.54 ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.17/1.54 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.17/1.54 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.17/1.54 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.17/1.54 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 X ), X ), Y ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.17/1.54 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.17/1.54 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.54 X ), Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.17/1.54 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 X ), X ), Z ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.17/1.54 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.54 X ), Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.17/1.54 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 X ), X ), Y ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.17/1.54 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.54 X ), Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.17/1.54 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.54 X ), Z ), T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), T )
% 1.17/1.54 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.17/1.54 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), T ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.54 , Z ), Y ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y )
% 1.17/1.54 ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ),
% 1.17/1.54 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.17/1.54 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), T ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.54 , Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.17/1.54 ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ),
% 1.17/1.54 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ) ) ) ],
% 1.17/1.54 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), X ),
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.17/1.54 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ),
% 1.17/1.54 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.17/1.54 Y, X ), Z ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.17/1.54 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.17/1.54 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.17/1.54 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.17/1.54 ), ~( =( 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.17/1.54 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.17/1.54 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.17/1.54 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.17/1.54 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.17/1.54 ), =( 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.17/1.54 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ), X )
% 1.17/1.54 , 'c_Power_Opower__class_Opower'( T, Z, X ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.54 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.17/1.54 X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.17/1.54 X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.17/1.54 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( X ), 'c_Suc'( Y ), X ),
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 'tc_nat' ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 1.17/1.54 ), X ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 'tc_nat' ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 1.17/1.54 ), X ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), Y ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 'tc_nat' ), 'tc_nat' ), 'c_Power_Opower__class_Opower'( X,
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.17/1.54 hAPP( 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Z, X,
% 1.17/1.54 'tc_nat' ), 'tc_nat' ), 'c_Power_Opower__class_Opower'( Z, Y, 'tc_nat' )
% 1.17/1.54 ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), Z ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP(
% 1.17/1.54 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL(
% 1.17/1.54 hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.54 'tc_nat' ), X ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.17/1.54 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.54 'tc_nat' ), Z ), X ), 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.54 'tc_nat' ), Z ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP(
% 1.17/1.54 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL(
% 1.17/1.54 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.54 'tc_nat' ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X,
% 1.17/1.54 'tc_nat' ), Z ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP(
% 1.17/1.54 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL(
% 1.17/1.54 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.54 'tc_nat' ), X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y,
% 1.17/1.54 'tc_nat' ), Z ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP(
% 1.17/1.54 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL(
% 1.17/1.54 hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.54 'tc_nat' ), X ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP(
% 1.17/1.54 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL(
% 1.17/1.54 hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.54 'tc_nat' ), Y ) ) ) ],
% 1.17/1.54 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 'tc_nat' ), 'tc_nat' ), X ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 'tc_nat' ), 'tc_nat' ), X ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ) ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 'tc_nat' ), 'tc_nat' ), X ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.17/1.54 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat'
% 1.17/1.54 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ) )
% 1.17/1.54 ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 'tc_nat' ), 'tc_nat' ), X ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.17/1.54 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), 'tc_nat'
% 1.17/1.54 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ) ) ) )
% 1.17/1.54 ],
% 1.17/1.54 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.17/1.54 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~(
% 1.17/1.54 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 'tc_nat' ), 'tc_nat' ), X ) ) ), =( Y, Z ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'(
% 1.17/1.54 X, Y, 'tc_nat' ), 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.54 'tc_nat' ), Y ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 'tc_nat' ), 'tc_nat' ), X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.54 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X )
% 1.17/1.54 ) ) ) ],
% 1.17/1.54 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.54 'tc_nat' ), Y ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 'tc_nat' ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.54 'tc_nat' ), X ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), Y ) ) ), ~( hBOOL(
% 1.17/1.54 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.54 'tc_nat' ), X ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 'tc_nat' ), 'tc_nat' ), 'c_Power_Opower__class_Opower'( X, Y, 'tc_nat' )
% 1.17/1.54 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ) ) ],
% 1.17/1.54 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), ~( hBOOL(
% 1.17/1.54 hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), X ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.54 'tc_nat' ), Y ) ) ) ],
% 1.17/1.54 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.54 'tc_nat' ), Y ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 1.17/1.54 'c_Power_Opower__class_Opower'( Y, X, 'tc_nat' ) ) ) ) ],
% 1.17/1.54 [ =( 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), X ) ],
% 1.17/1.54 [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~(
% 1.17/1.54 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_Suc'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.17/1.54 [ =( 'c_Power_Opower__class_Opower'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 'tc_nat' ) ), X, 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 'tc_nat' ) ) ) ],
% 1.17/1.54 [ =( 'c_Power_Opower__class_Opower'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 'tc_nat' ) ), X, 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 'tc_nat' ) ) ) ],
% 1.17/1.54 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.17/1.54 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.17/1.54 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.17/1.54 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.54 [ ~( =( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) )
% 1.17/1.54 , =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.54 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.17/1.54 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, 'c_Suc'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.54 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Suc'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ],
% 1.17/1.54 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.17/1.54 [ =( 'c_Power_Opower__class_Opower'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 'tc_nat' ), 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.17/1.54 ) ],
% 1.17/1.54 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.17/1.54 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.17/1.54 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.17/1.54 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.17/1.54 [ =( 'c_Type_Oshift'( 'c_Type_Oshift'( X, Y, Z, T ),
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), U, T ), 'c_Type_Oshift'(
% 1.17/1.54 'c_Type_Oshift'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), U, T ),
% 1.17/1.54 'c_Suc'( Y ), Z, T ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 'tc_nat' ) ), 'tc_nat' ), X ) ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_Suc'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ) ],
% 1.17/1.54 [ =( X, 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), 'c_Suc'( X ) ) ) ) ), ~(
% 1.17/1.54 hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.54 'tc_nat' ), Z ), X ), 'tc_nat' ), Y ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.54 'tc_nat' ), Z ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), =( X, Y
% 1.17/1.54 ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.17/1.54 [ =( X, Y ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y )
% 1.17/1.54 ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), =( X, Y
% 1.17/1.54 ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.17/1.54 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.54 'tc_nat' ), Z ), X ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.54 'tc_nat' ), Z ), Y ) ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Z ) ) ) ],
% 1.17/1.54 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), Y ) ) ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), X ) ) ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ =( hAPP( 'c_Type_Oshift'( X, Y, Z, T ), U ), hAPP( X, U ) ), ~( hBOOL(
% 1.17/1.54 hAPP( 'c_HOL_Oord__class_Oless'( U, 'tc_nat' ), Y ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.17/1.54 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.54 'tc_nat' ), X ), Z ), 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.17/1.54 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.54 'tc_nat' ), Z ), X ), 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), T ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Z ) ) ) ],
% 1.17/1.54 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ) ],
% 1.17/1.54 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.17/1.54 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.17/1.54 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' ), Y ) ) ), hBOOL(
% 1.17/1.54 hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), T ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Z ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.17/1.54 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.54 'tc_nat' ), X ), Z ), 'tc_nat' ), Y ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Z ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_lessequals'( 'c_Suc'( X ), 'tc_nat' ), 'c_Suc'( Y ) )
% 1.17/1.54 ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_lessequals'( 'c_Suc'( X ), 'tc_nat' ), 'c_Suc'( Y ) ) ) ) ],
% 1.17/1.54 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'( X
% 1.17/1.54 ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'(
% 1.17/1.54 X ) ), Z ) ) ), =( Y, Z ) ],
% 1.17/1.54 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.17/1.54 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y
% 1.17/1.54 , 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.17/1.54 [ ~( hBOOL( hAPP( 'c_lessequals'( 'c_Suc'( X ), 'tc_nat' ), X ) ) ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), 'c_Suc'( Y ) ) ), ~( hBOOL(
% 1.17/1.54 hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_lessequals'( 'c_Suc'( X ), 'tc_nat' ), Y ) ) ) ],
% 1.17/1.54 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'( X ) )
% 1.17/1.54 , Y ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.17/1.54 Y ) ) ) ],
% 1.17/1.54 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_Suc'( Y
% 1.17/1.54 ) ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y
% 1.17/1.54 ) ) ) ],
% 1.17/1.54 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 1.17/1.54 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ), =( 'c_Suc'(
% 1.17/1.54 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ],
% 1.17/1.54 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'( X ) )
% 1.17/1.54 , Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_Suc'(
% 1.17/1.54 Y ) ) ) ],
% 1.17/1.54 [ ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_lessequals'( 'c_Suc'( Y ), 'tc_nat' ), X ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_lessequals'( 'c_Suc'( X ), 'tc_nat' ), Y ) ), hBOOL(
% 1.17/1.54 hAPP( 'c_lessequals'( Y, 'tc_nat' ), X ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_lessequals'( 'c_Suc'( X ), 'tc_nat' ), 'c_Suc'( X ) )
% 1.17/1.54 ) ],
% 1.17/1.54 [ =( X, 'c_Suc'( Y ) ), hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y )
% 1.17/1.54 ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), 'c_Suc'( Y ) ) ) ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( 'c_List_Olistsum'( Y,
% 1.17/1.54 X ), 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( X ), Y, X, X ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), =( 'c_List_Olistsum'(
% 1.17/1.54 'c_List_Omap'( hAPP( hAPP( 'c_COMBB'( X, X, Y ), hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( X ), Z ) ), T ), U, Y, X ), X ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( X ), Z ), 'c_List_Olistsum'( 'c_List_Omap'(
% 1.17/1.54 T, U, Y, X ), X ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =(
% 1.17/1.54 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ), X ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.17/1.54 Y, X ) ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), ~( hBOOL(
% 1.17/1.54 hAPP( 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.17/1.54 Y ), Z ) ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z
% 1.17/1.54 ), 'c_ATP__Linkup_Osko__Nat__Xnat__diff__split__1__1'( X, Y, Z ) ) ),
% 1.17/1.54 ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.17/1.54 Y ), Z ) ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z
% 1.17/1.54 ), 'c_ATP__Linkup_Osko__Nat__Xnat__diff__split__asm__1__1'( X, Y, Z ) )
% 1.17/1.54 ), ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_Lambda_OdB_OAbs'(
% 1.17/1.54 Z ) ) ) ],
% 1.17/1.54 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Y ),
% 1.17/1.54 Z ) ) ) ],
% 1.17/1.54 [ =( hAPP( hAPP( 'c_Lambda_Olift', hAPP( hAPP( 'c_Lambda_OdB_OApp', X )
% 1.17/1.54 , Y ) ), Z ), hAPP( hAPP( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 1.17/1.54 'c_Lambda_Olift', X ), Z ) ), hAPP( hAPP( 'c_Lambda_Olift', Y ), Z ) ) )
% 1.17/1.54 ],
% 1.17/1.54 [ 'c_Lambda_Obeta'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP(
% 1.17/1.54 hAPP( 'c_Lambda_OdB_OApp', X ), Z ) ), ~( 'c_Lambda_Obeta'( Y, Z ) ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ 'c_Lambda_Obeta'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP(
% 1.17/1.54 hAPP( 'c_Lambda_OdB_OApp', Z ), Y ) ), ~( 'c_Lambda_Obeta'( X, Z ) ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ =( 'c_Lambda_Oliftn'( X, hAPP( hAPP( 'c_Lambda_OdB_OApp', Y ), Z ), T
% 1.17/1.54 ), hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_Oliftn'( X, Y, T ) ),
% 1.17/1.54 'c_Lambda_Oliftn'( X, Z, T ) ) ) ],
% 1.17/1.54 [ =( 'c_Lambda_Osubstn'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), Z, T
% 1.17/1.54 ), hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_Osubstn'( X, Z, T ) ),
% 1.17/1.54 'c_Lambda_Osubstn'( Y, Z, T ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.17/1.54 Y ), Z ) ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z
% 1.17/1.54 ), 'c_ATP__Linkup_Osko__Nat__Xnat__diff__split__asm__1__1'( X, Y, Z ) )
% 1.17/1.54 ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ) ],
% 1.17/1.54 [ =( hAPP( 'c_Type_Oshift'( X, Y, Z, T ), U ), hAPP( X, hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), U ), 'c_HOL_Oone__class_Oone'(
% 1.17/1.54 'tc_nat' ) ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat'
% 1.17/1.54 ), U ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.17/1.54 Y ), Z ) ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z
% 1.17/1.54 ), 'c_ATP__Linkup_Osko__Nat__Xnat__diff__split__1__1'( X, Y, Z ) ) ),
% 1.17/1.54 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ) ],
% 1.17/1.54 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), 'c_Suc'(
% 1.17/1.54 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ), hAPP(
% 1.17/1.54 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), 'c_Suc'( Y ) ) ), ~(
% 1.17/1.54 hBOOL( hAPP( 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ) ],
% 1.17/1.54 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), 'c_Suc'( hAPP(
% 1.17/1.54 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ) ), Z ), hAPP(
% 1.17/1.54 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), 'c_Suc'( X ) ), hAPP(
% 1.17/1.54 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL(
% 1.17/1.54 hAPP( 'c_lessequals'( Y, 'tc_nat' ), X ) ) ) ],
% 1.17/1.54 [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', hAPP( hAPP( hAPP(
% 1.17/1.54 'c_Lambda_Osubst', X ), hAPP( hAPP( 'c_Lambda_Olift', Y ), Z ) ), 'c_Suc'(
% 1.17/1.54 T ) ) ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst', U ), Y ), T ) ), Z ), hAPP(
% 1.17/1.54 hAPP( hAPP( 'c_Lambda_Osubst', hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ),
% 1.17/1.54 U ), Z ) ), Y ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z,
% 1.17/1.54 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ),
% 1.17/1.54 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ) ) ],
% 1.17/1.54 [ =( 'c_Lambda_Osubstn'( X, Y, Z ), hAPP( hAPP( hAPP( 'c_Lambda_Osubst'
% 1.17/1.54 , X ), 'c_Lambda_Oliftn'( Z, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.17/1.54 ), Z ) ) ],
% 1.17/1.54 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~(
% 1.17/1.54 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ), ~(
% 1.17/1.54 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 1.17/1.54 [ ~( hBOOL( hAPP( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.17/1.54 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), Y ) )
% 1.17/1.54 ) ), hBOOL( hAPP( X, Z ) ) ],
% 1.17/1.54 [ ~( hBOOL( hAPP( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.17/1.54 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), Y ) )
% 1.17/1.54 ) ), hBOOL( hAPP( X, Z ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.17/1.54 Y ), Z ) ) ), ~( hBOOL( hAPP( X,
% 1.17/1.54 'c_ATP__Linkup_Osko__Nat__Xzero__induct__lemma__1__1'( X ) ) ) ), ~(
% 1.17/1.54 hBOOL( hAPP( X, Y ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.17/1.54 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.17/1.54 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_lessequals'( X, 'tc_nat' ), Z ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.17/1.54 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_lessequals'( X, 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y
% 1.17/1.54 , 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ), X )
% 1.17/1.54 ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X )
% 1.17/1.54 , Z ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.17/1.54 Y ), Z ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ),
% 1.17/1.54 ~( hBOOL( hAPP( 'c_lessequals'( Z, 'tc_nat' ), X ) ) ) ],
% 1.17/1.54 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.17/1.54 [ ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ),
% 1.17/1.54 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ) ), ~(
% 1.17/1.54 hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_lessequals'( Y, 'tc_nat' ), X ) ) ), =( X, Z ) ],
% 1.17/1.54 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ) ],
% 1.17/1.54 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.17/1.54 'tc_nat' ), X ), Y ), 'tc_nat' ), X ) ) ],
% 1.17/1.54 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.17/1.54 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.17/1.54 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.17/1.54 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_lessequals'( Y, 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y
% 1.17/1.54 , 'tc_nat' ), X ) ) ) ],
% 1.17/1.54 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP(
% 1.17/1.54 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Y ), ~( hBOOL(
% 1.17/1.54 hAPP( 'c_lessequals'( Y, 'tc_nat' ), X ) ) ) ],
% 1.17/1.54 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Y ), X ) ],
% 1.17/1.54 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), X ), Y ) ],
% 1.17/1.54 [ =( 'c_Lambda_Oliftn'( X, hAPP( 'c_Lambda_OdB_OVar', Y ), Z ), hAPP(
% 1.17/1.54 'c_Lambda_OdB_OVar', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.17/1.54 Y ), X ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z )
% 1.17/1.54 ) ],
% 1.17/1.54 [ ~( =( 'c_List_Omap'( X, Y, Z, T ), 'c_List_Olist_ONil'( T ) ) ), =( Y
% 1.17/1.54 , 'c_List_Olist_ONil'( Z ) ) ],
% 1.17/1.54 [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Omap'( Y, Z, T, X ) ) ), =( Z
% 1.17/1.54 , 'c_List_Olist_ONil'( T ) ) ],
% 1.17/1.54 [ =( 'c_List_Omap'( X, 'c_List_Olist_ONil'( Y ), Y, Z ),
% 1.17/1.54 'c_List_Olist_ONil'( Z ) ) ],
% 1.17/1.54 [ =( 'c_List_Olist_ONil'( X ), 'c_List_Omap'( Y, 'c_List_Olist_ONil'( Z
% 1.17/1.54 ), Z, X ) ) ],
% 1.17/1.54 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 1.17/1.54 Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Z, 'c_List_Olist_ONil'(
% 1.17/1.54 'tc_Lambda_OdB' ) ) ],
% 1.17/1.54 [ =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 1.17/1.54 'c_Lambda_OdB_OAbs'( X ), 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ),
% 1.17/1.54 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ],
% 1.17/1.54 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB',
% 1.17/1.54 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( Z ) ) ), =( Y,
% 1.17/1.54 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) ) ],
% 1.17/1.54 [ =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ),
% 1.17/1.54 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB'
% 1.17/1.54 ), 'c_Lambda_OdB_OAbs'( X ) ) ],
% 1.17/1.54 [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Olist_ONil'( Z ), T, Z ), Y ) ],
% 1.17/1.54 [ ~( 'class_OrderedGroup_Osemigroup__add'( X ) ), =( 'c_List_Ofoldl'(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.54 X ), Y ), Z ), T, X, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.17/1.54 ), 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Z, T, X, X ) ) ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ 'c_Lambda_Obeta'( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Y ), Z ),
% 1.17/1.54 hAPP( hAPP( hAPP( 'c_Lambda_Osubst', T ), Y ), Z ) ), ~( 'c_Lambda_Obeta'(
% 1.17/1.54 X, T ) ) ],
% 1.17/1.54 [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', hAPP( hAPP( 'c_Lambda_Olift',
% 1.17/1.54 X ), Y ) ), Z ), Y ), X ) ],
% 1.17/1.54 [ 'c_Type_Otypings'( 'c_Type_Oshift'( X, Y, Z, 'tc_Type_Otype' ),
% 1.17/1.54 'c_List_Omap'( 'c_COMBC'( 'c_Lambda_Olift', Y, 'tc_Lambda_OdB', 'tc_nat'
% 1.17/1.54 , 'tc_Lambda_OdB' ), T, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), U ), ~(
% 1.17/1.54 'c_Type_Otypings'( X, T, U ) ) ],
% 1.17/1.54 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), hAPP( 'c_Lambda_OdB_OVar', Y ) ) ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ ~( 'c_Lambda_Obeta'( hAPP( 'c_Lambda_OdB_OVar', X ), Y ) ) ],
% 1.17/1.54 [ ~( =( hAPP( 'c_Lambda_OdB_OVar', X ), 'c_Lambda_OdB_OAbs'( Y ) ) ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ =( hAPP( X, Y ), Z ), ~( 'c_Type_Otyping'( X, hAPP(
% 1.17/1.54 'c_Lambda_OdB_OVar', Y ), Z ) ) ],
% 1.17/1.54 [ 'c_Type_Otyping'( X, hAPP( 'c_Lambda_OdB_OVar', Y ), hAPP( X, Y ) ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ hBOOL( 'c_List_Olistsp'( X, 'c_List_Olist_ONil'( Y ), Y ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP( 'c_Lambda_Olift', X ), Y
% 1.17/1.54 ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_OdB_OAbs'( X ) ) ), ~(
% 1.17/1.54 hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ), X )
% 1.17/1.54 , 'c_Power_Opower__class_Opower'( Y, T, X ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ),
% 1.17/1.54 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.54 ), X ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, 'tc_nat'
% 1.17/1.54 ), Z ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z
% 1.17/1.54 ), X ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ),
% 1.17/1.54 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.54 ), X ), Y ) ) ) ],
% 1.17/1.54 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_Suc'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.17/1.54 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, 'c_Suc'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.17/1.54 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.54 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Suc'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 1.17/1.54 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Suc'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Suc'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.17/1.54 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_Suc'(
% 1.17/1.54 'v_sko__List__Xlexn__Xinduct__1'( X ) ) ) ) ), ~( hBOOL( hAPP( X,
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.17/1.54 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 'tc_nat' ) ) ) ],
% 1.17/1.54 [ ~( =( 'c_Power_Opower__class_Opower'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hBOOL(
% 1.17/1.54 hAPP( X, 'c_Suc'( 'c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1'( X ) ) )
% 1.17/1.54 ), ~( hBOOL( hAPP( X, Y ) ) ) ],
% 1.17/1.54 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Suc'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.17/1.54 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.17/1.54 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.17/1.54 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.17/1.54 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.54 [ =( X, 'c_Suc'( 'c_ATP__Linkup_Osko__Nat__Xnat__Xexhaust__1__1'( X ) )
% 1.17/1.54 ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.17/1.54 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.54 'tc_nat' ), 'c_Suc'( Z ) ), X ), 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'( Z ) ), Y ) ) ) ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'( X ) ), Y ), 'tc_nat' )
% 1.17/1.54 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'( X ) ), Z
% 1.17/1.54 ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ) )
% 1.17/1.54 ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ),
% 1.17/1.54 'c_ATP__Linkup_Osko__Nat__XSuc__lessE__1__1'( X, Y ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'tc_nat' ), Y ) ) ) ],
% 1.17/1.54 [ ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), X ) ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), 'c_Suc'( Y ) ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), 'c_Suc'( Y ) )
% 1.17/1.54 ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.17/1.54 [ =( X, 'c_Suc'( 'c_ATP__Linkup_Osko__Nat__XlessE__1__1'( Y, X ) ) ),
% 1.17/1.54 =( X, 'c_Suc'( Y ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y,
% 1.17/1.54 'tc_nat' ), X ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), 'c_Suc'( hAPP(
% 1.17/1.54 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), 'c_Suc'( hAPP(
% 1.17/1.54 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), 'c_Suc'( hAPP(
% 1.17/1.54 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_lessequals'( 'c_Suc'( X ), 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.17/1.54 hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.17/1.54 hAPP( 'c_lessequals'( 'c_Suc'( X ), 'tc_nat' ), Y ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_lessequals'( 'c_Suc'( X ), 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.17/1.54 hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.17/1.54 hAPP( 'c_lessequals'( 'c_Suc'( X ), 'tc_nat' ), Y ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ),
% 1.17/1.54 'c_ATP__Linkup_Osko__Nat__XlessE__1__1'( X, Y ) ) ), =( Y, 'c_Suc'( X ) )
% 1.17/1.54 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ =( X, 'c_Suc'( 'c_ATP__Linkup_Osko__Nat__XSuc__lessE__1__1'( Y, X ) )
% 1.17/1.54 ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Suc'( Y ), 'tc_nat' ),
% 1.17/1.54 X ) ) ) ],
% 1.17/1.54 [ =( X, Y ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ),
% 1.17/1.54 'c_Suc'( Y ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ), X ) )
% 1.17/1.54 ) ],
% 1.17/1.54 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Ofoldl'(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ), Z, X, X
% 1.17/1.54 ) ), 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ) ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'c_Suc'( hAPP(
% 1.17/1.54 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.17/1.54 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.17/1.54 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.54 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ) ) ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), 'c_Code__Numeral_Onat__of'( X )
% 1.17/1.54 ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.17/1.54 'c_Code__Numeral_Onat__of'( X ) ) ), =( X, 'c_Code__Numeral_Oof__nat'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.17/1.54 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.17/1.54 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.17/1.54 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.17/1.54 Y, 'tc_nat' ), X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), Y ) ) ) ],
% 1.17/1.54 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP(
% 1.17/1.54 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ),
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.17/1.54 Y ), Z ) ) ), ~( hBOOL( hAPP( X,
% 1.17/1.54 'c_ATP__Linkup_Osko__Nat__Xnat__diff__split__1__1'( X, Y, Z ) ) ) ), ~(
% 1.17/1.54 hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.17/1.54 [ ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ),
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.17/1.54 X, 'tc_nat' ), Y ) ) ],
% 1.17/1.54 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ),
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.17/1.54 X, 'tc_nat' ), Y ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.17/1.54 Y ), Z ) ) ), ~( hBOOL( hAPP( X,
% 1.17/1.54 'c_ATP__Linkup_Osko__Nat__Xnat__diff__split__asm__1__1'( X, Y, Z ) ) ) )
% 1.17/1.54 , ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.17/1.54 Y ), Z ) ) ), ~( hBOOL( hAPP( X,
% 1.17/1.54 'c_ATP__Linkup_Osko__Nat__Xnat__diff__split__1__1'( X, Y, Z ) ) ) ),
% 1.17/1.54 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP(
% 1.17/1.54 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL(
% 1.17/1.54 hAPP( 'c_lessequals'( Y, 'tc_nat' ), X ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Z ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.17/1.54 Y ), Z ) ) ), ~( hBOOL( hAPP( X,
% 1.17/1.54 'c_ATP__Linkup_Osko__Nat__Xnat__diff__split__asm__1__1'( X, Y, Z ) ) ) )
% 1.17/1.54 , hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.17/1.54 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.17/1.54 'tc_nat' ), X ), Z ), 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z
% 1.17/1.54 , 'tc_nat' ), X ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP(
% 1.17/1.54 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL(
% 1.17/1.54 hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_lessequals'( Y, 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y
% 1.17/1.54 , 'tc_nat' ), X ) ) ) ],
% 1.17/1.54 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.17/1.54 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.17/1.54 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), Z ) ), ~(
% 1.17/1.54 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.54 'tc_nat' ), X ), Z ), 'tc_nat' ), Y ) ) ) ],
% 1.17/1.54 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ) ), Y ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), X ) ) ],
% 1.17/1.54 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), 'c_Suc'(
% 1.17/1.54 Y ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.17/1.54 'tc_nat' ) ) ), Y ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.17/1.54 Y ), Z ) ) ), hBOOL( hAPP( X, 'c_Suc'(
% 1.17/1.54 'c_ATP__Linkup_Osko__Nat__Xzero__induct__lemma__1__1'( X ) ) ) ), ~(
% 1.17/1.54 hBOOL( hAPP( X, Y ) ) ) ],
% 1.17/1.54 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), 'c_Suc'( X )
% 1.17/1.54 ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ],
% 1.17/1.54 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), 'c_Suc'( X )
% 1.17/1.54 ), Y ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X
% 1.17/1.54 ), Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ), X ) ) ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ 'c_List_Olist__all2'( hAPP( hAPP( 'c_COMBB'( X, 'tc_fun'( Y, 'tc_bool'
% 1.17/1.54 ), Z ), T ), U ), W, V0, Z, Y ), ~( 'c_List_Olist__all2'( T,
% 1.17/1.54 'c_List_Omap'( U, W, Z, X ), V0, X, Y ) ) ],
% 1.17/1.54 [ 'c_List_Olist__all2'( X, 'c_List_Omap'( Y, Z, T, U ), W, U, V0 ), ~(
% 1.17/1.54 'c_List_Olist__all2'( hAPP( hAPP( 'c_COMBB'( U, 'tc_fun'( V0, 'tc_bool' )
% 1.17/1.54 , T ), X ), Y ), Z, W, T, V0 ) ) ],
% 1.17/1.54 [ =( 'c_Lambda_Osubstn'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.17/1.54 , hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Y ),
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.17/1.54 [ =( 'c_Lambda_OdB_OdB__size'( hAPP( 'c_Lambda_OdB_OVar', X ) ),
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.54 [ =( 'c_Nat_Osize__class_Osize'( hAPP( 'c_Lambda_OdB_OVar', X ),
% 1.17/1.54 'tc_Lambda_OdB' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.54 [ =( hAPP( hAPP( 'c_Lambda_Olift', hAPP( 'c_Lambda_OdB_OVar', X ) ), Y )
% 1.17/1.54 , hAPP( 'c_Lambda_OdB_OVar', X ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ) ],
% 1.17/1.54 [ =( 'c_Lambda_Oliftn'( X, hAPP( 'c_Lambda_OdB_OVar', Y ), Z ), hAPP(
% 1.17/1.54 'c_Lambda_OdB_OVar', Y ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y
% 1.17/1.54 , 'tc_nat' ), Z ) ) ) ],
% 1.17/1.54 [ =( 'c_Lambda_Osubstn'( hAPP( 'c_Lambda_OdB_OVar', X ), Y, Z ), hAPP(
% 1.17/1.54 'c_Lambda_OdB_OVar', X ) ), =( X, Z ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' ), X ) ) ],
% 1.17/1.54 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 1.17/1.54 Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( 'c_Lambda_OdB_OAbs'( X )
% 1.17/1.54 , Y ) ],
% 1.17/1.54 [ 'c_Lambda_Obeta'( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y,
% 1.17/1.54 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 1.17/1.54 , Z, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), ~( 'c_Lambda_Obeta'( X, Z )
% 1.17/1.54 ) ],
% 1.17/1.54 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ),
% 1.17/1.54 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 1.17/1.54 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T, 'tc_Lambda_OdB',
% 1.17/1.54 'tc_Lambda_OdB' ) ) ), =( Y, T ) ],
% 1.17/1.54 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ),
% 1.17/1.54 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 1.17/1.54 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T, 'tc_Lambda_OdB',
% 1.17/1.54 'tc_Lambda_OdB' ) ) ), =( X, Z ) ],
% 1.17/1.54 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB',
% 1.17/1.54 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( Z ) ) ), =( X,
% 1.17/1.54 'c_Lambda_OdB_OAbs'( Z ) ) ],
% 1.17/1.54 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_List_Ofoldl'(
% 1.17/1.54 'c_Lambda_OdB_OApp', Z, 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ),
% 1.17/1.54 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( hAPP( hAPP(
% 1.17/1.54 'c_Lambda_OdB_OApp', X ), Y ), Z ) ],
% 1.17/1.54 [ =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_List_Ofoldl'(
% 1.17/1.54 'c_Lambda_OdB_OApp', hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ),
% 1.17/1.54 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB'
% 1.17/1.54 ) ) ],
% 1.17/1.54 [ 'c_Type_Otypings'( X, 'c_List_Omap'( 'c_COMBC'( 'c_COMBC'(
% 1.17/1.54 'c_Lambda_Osubst', Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB', 'tc_fun'(
% 1.17/1.54 'tc_nat', 'tc_Lambda_OdB' ) ), Z, 'tc_Lambda_OdB', 'tc_nat',
% 1.17/1.54 'tc_Lambda_OdB' ), T, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), U ), ~(
% 1.17/1.54 'c_Type_Otypings'( 'c_Type_Oshift'( X, Z, W, 'tc_Type_Otype' ), T, U ) )
% 1.17/1.54 , ~( 'c_Type_Otyping'( X, Y, W ) ) ],
% 1.17/1.54 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( hAPP( Y, Z ), X ), hAPP( Y, T ) ) ), ~( hBOOL(
% 1.17/1.54 hAPP( 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' ), T ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( hAPP( Y,
% 1.17/1.54 'c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__less__iff__1__1'(
% 1.17/1.54 Y, X ) ), X ), hAPP( Y, 'c_Suc'(
% 1.17/1.54 'c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__less__iff__1__1'(
% 1.17/1.54 Y, X ) ) ) ) ) ) ],
% 1.17/1.54 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( hAPP( T, Y ), X ), hAPP( T, Z ) ) ) ), ~(
% 1.17/1.54 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( T,
% 1.17/1.54 'c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__less__iff__1__1'(
% 1.17/1.54 T, X ) ), X ), hAPP( T, 'c_Suc'(
% 1.17/1.54 'c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__less__iff__1__1'(
% 1.17/1.54 T, X ) ) ) ) ) ) ],
% 1.17/1.54 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( hAPP( Y, Z ), X ), hAPP( Y, T ) ) ), ~( hBOOL(
% 1.17/1.54 hAPP( 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' ), T ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( hAPP( Y,
% 1.17/1.54 'c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__less__1__1'( Y
% 1.17/1.54 , X ) ), X ), hAPP( Y, 'c_Suc'(
% 1.17/1.54 'c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__less__1__1'( Y
% 1.17/1.54 , X ) ) ) ) ) ) ],
% 1.17/1.54 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.17/1.54 'c_Finite__Set_Osetsum'( 'c_COMBS'( hAPP( hAPP( 'c_COMBB'( X, 'tc_fun'( X
% 1.17/1.54 , X ), Y ), 'c_HOL_Ominus__class_Ominus'( X ) ), Z ), T, Y, X, X ), U, Y
% 1.17/1.54 , X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ),
% 1.17/1.54 'c_Finite__Set_Osetsum'( Z, U, Y, X ) ), 'c_Finite__Set_Osetsum'( T, U, Y
% 1.17/1.54 , X ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.17/1.54 ) ), 'tc_nat' ), X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.17/1.54 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), Y ) ) ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.17/1.54 'c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1'( X, Y ),
% 1.17/1.54 'tc_nat' ), Y ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.17/1.54 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), 'c_Suc'( Y ) ) ) )
% 1.17/1.54 ],
% 1.17/1.54 [ =( X, 'c_Suc'( 'c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1'( X ) )
% 1.17/1.54 ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 'tc_nat' ), 'tc_nat' ), X ) ) ) ],
% 1.17/1.54 [ =( X, 'c_Suc'( 'c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1'( X
% 1.17/1.54 ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ) ) ],
% 1.17/1.54 [ =( X, 'c_Suc'(
% 1.17/1.54 'c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1'( X, Y ) ) ), =(
% 1.17/1.54 X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), 'c_Suc'( Y ) ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.17/1.54 ) ), 'tc_nat' ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.17/1.54 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), X ) ) ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.17/1.54 ) ), 'tc_nat' ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.17/1.54 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), X ) ) ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ =( 'c_List_Ofilter'( X, 'c_List_Ofilter'( Y, Z, T ), T ),
% 1.17/1.54 'c_List_Ofilter'( 'c_COMBS'( hAPP( hAPP( 'c_COMBB'( 'tc_bool', 'tc_fun'(
% 1.17/1.54 'tc_bool', 'tc_bool' ), T ), 'c_and' ), Y ), X, T, 'tc_bool', 'tc_bool' )
% 1.17/1.54 , Z, T ) ) ],
% 1.17/1.54 [ =( 'c_HOL_Oord__class_Oless'( 'v_n', 'tc_nat' ), 'c_lessequals'(
% 1.17/1.54 'c_Suc'( 'v_n' ), 'tc_nat' ) ) ],
% 1.17/1.54 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ) ), Y )
% 1.17/1.54 , 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( 'c_Lambda_OdB_OVar', Z ), T
% 1.17/1.54 , 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ],
% 1.17/1.54 [ ~( =( hAPP( 'c_Lambda_OdB_OVar', X ), 'c_List_Ofoldl'(
% 1.17/1.54 'c_Lambda_OdB_OApp', Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( Z,
% 1.17/1.54 'c_List_Olist_ONil'( 'tc_Lambda_OdB' ) ) ],
% 1.17/1.54 [ =( hAPP( 'c_Lambda_OdB_OVar', X ), 'c_List_Ofoldl'(
% 1.17/1.54 'c_Lambda_OdB_OApp', hAPP( 'c_Lambda_OdB_OVar', X ), 'c_List_Olist_ONil'(
% 1.17/1.54 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ],
% 1.17/1.54 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( 'c_Lambda_OdB_OVar'
% 1.17/1.54 , X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 1.17/1.54 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T, 'tc_Lambda_OdB',
% 1.17/1.54 'tc_Lambda_OdB' ) ) ) ],
% 1.17/1.54 [ =( X, Y ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'(
% 1.17/1.54 'c_Lambda_OdB_OApp', hAPP( 'c_Lambda_OdB_OVar', T ), U, 'tc_Lambda_OdB',
% 1.17/1.54 'tc_Lambda_OdB' ), Y ) ), ~( 'c_Type_Otyping'( Z, 'c_List_Ofoldl'(
% 1.17/1.54 'c_Lambda_OdB_OApp', hAPP( 'c_Lambda_OdB_OVar', T ), U, 'tc_Lambda_OdB',
% 1.17/1.54 'tc_Lambda_OdB' ), X ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.17/1.54 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.54 'tc_nat' ), Y ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.54 'tc_nat' ), Y ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.17/1.54 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ) ) ],
% 1.17/1.54 [ ~( =( hAPP( X, hAPP( Y, 'c_List_Osko__List__Xfoldl__apply__inv__1__1'(
% 1.17/1.54 X, Y, Z, T ) ) ), 'c_List_Osko__List__Xfoldl__apply__inv__1__1'( X, Y, Z
% 1.17/1.54 , T ) ) ), =( 'c_List_Ofoldl'( U, hAPP( X, W ), V0, T, V1 ), hAPP( X,
% 1.17/1.54 'c_List_Ofoldl'( hAPP( hAPP( 'c_COMBB'( 'tc_fun'( V1, T ), 'tc_fun'( V1,
% 1.17/1.54 Z ), Z ), hAPP( 'c_COMBB'( T, Z, V1 ), Y ) ), hAPP( hAPP( 'c_COMBB'( T,
% 1.17/1.54 'tc_fun'( V1, T ), Z ), U ), X ) ), W, V0, Z, V1 ) ) ) ],
% 1.17/1.54 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( 'c_List_Olistsum'(
% 1.17/1.54 'c_List_Omap'( 'c_COMBS'( hAPP( hAPP( 'c_COMBB'( X, 'tc_fun'( X, X ), Y )
% 1.17/1.54 , 'c_HOL_Ominus__class_Ominus'( X ) ), Z ), T, Y, X, X ), U, Y, X ), X )
% 1.17/1.54 , hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), 'c_List_Olistsum'(
% 1.17/1.54 'c_List_Omap'( Z, U, Y, X ), X ) ), 'c_List_Olistsum'( 'c_List_Omap'( T,
% 1.17/1.54 U, Y, X ), X ) ) ) ],
% 1.17/1.54 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.17/1.54 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.17/1.54 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.54 'tc_nat' ), Y ) ) ) ],
% 1.17/1.54 [ =( 'c_Suc'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X )
% 1.17/1.54 , 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), X ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.54 'tc_nat' ), X ) ) ) ],
% 1.17/1.54 [ =( X, 'c_Suc'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X
% 1.17/1.54 ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.54 'tc_nat' ), X ) ) ) ],
% 1.17/1.54 [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', hAPP( 'c_Lambda_OdB_OVar', X )
% 1.17/1.54 ), Y ), Z ), hAPP( 'c_Lambda_OdB_OVar', hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.17/1.54 'tc_nat' ) ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, 'tc_nat'
% 1.17/1.54 ), X ) ) ) ],
% 1.17/1.54 [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', hAPP( 'c_Lambda_OdB_OVar', X )
% 1.17/1.54 ), Y ), Z ), hAPP( 'c_Lambda_OdB_OVar', hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.17/1.54 'tc_nat' ) ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, 'tc_nat'
% 1.17/1.54 ), X ) ) ) ],
% 1.17/1.54 [ =( 'c_List_Olistsp'( 'c_COMBS'( hAPP( hAPP( 'c_COMBB'( 'tc_bool',
% 1.17/1.54 'tc_fun'( 'tc_bool', 'tc_bool' ), 't_a' ), 'c_and' ), X ), Y, 't_a',
% 1.17/1.54 'tc_bool', 'tc_bool' ), 'v_x', 't_a' ), hAPP( hAPP( 'c_and',
% 1.17/1.54 'c_List_Olistsp'( X, 'v_x', 't_a' ) ), 'c_List_Olistsp'( Y, 'v_x', 't_a'
% 1.17/1.54 ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 1.17/1.54 , hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ) ), Y ), Z,
% 1.17/1.54 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_InductTermi_OIT', Y ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT',
% 1.17/1.54 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP( hAPP( 'c_Lambda_Osubst'
% 1.17/1.54 , X ), Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z, 'tc_Lambda_OdB'
% 1.17/1.54 , 'tc_Lambda_OdB' ) ) ) ) ],
% 1.17/1.54 [ =( hAPP( hAPP( 'c_Lambda_Olift', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 1.17/1.54 , X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), Z ), 'c_List_Ofoldl'(
% 1.17/1.54 'c_Lambda_OdB_OApp', hAPP( hAPP( 'c_Lambda_Olift', X ), Z ),
% 1.17/1.54 'c_List_Omap'( 'c_COMBC'( 'c_Lambda_Olift', Z, 'tc_Lambda_OdB', 'tc_nat'
% 1.17/1.54 , 'tc_Lambda_OdB' ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 1.17/1.54 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ],
% 1.17/1.54 [ hBOOL( 'c_List_Olistsp'( 'c_InductTermi_OIT', 'c_List_Omap'( 'c_COMBC'(
% 1.17/1.54 'c_Lambda_Olift', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_Lambda_OdB'
% 1.17/1.54 , 'tc_nat', 'tc_Lambda_OdB' ), X, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 1.17/1.54 'tc_Lambda_OdB' ) ), ~( hBOOL( 'c_List_Olistsp'( 'c_InductTermi_OIT', X,
% 1.17/1.54 'tc_Lambda_OdB' ) ) ) ],
% 1.17/1.54 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ) ],
% 1.17/1.54 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ) ],
% 1.17/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ) ],
% 1.17/1.54 [ ~( 'class_Orderings_Oorder'( X ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), 'c_Suc'( Y ) ), 'tc_nat' )
% 1.17/1.54 , X ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ) ) ],
% 1.17/1.54 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.17/1.54 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( T, X ), U ) ) ) ],
% 1.17/1.54 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.17/1.54 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( T, X ), U ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), X ) ),
% 1.17/1.54 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 'tc_nat' ), 'tc_nat' ), X ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.54 'tc_nat' ), Y ) ) ) ],
% 1.17/1.54 [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Omap'( Z, T, U, W ), V0, W ),
% 1.17/1.54 'c_List_Ofoldl'( 'c_COMBC'( hAPP( hAPP( 'c_COMBB'( 'tc_fun'( W, V0 ),
% 1.17/1.54 'tc_fun'( 'tc_fun'( U, W ), 'tc_fun'( U, V0 ) ), V0 ), 'c_COMBB'( W, V0,
% 1.17/1.54 U ) ), X ), Z, V0, 'tc_fun'( U, W ), 'tc_fun'( U, V0 ) ), Y, T, V0, U ) )
% 1.17/1.54 ],
% 1.17/1.54 [ =( 'c_Suc'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X )
% 1.17/1.54 , 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ), ~( hBOOL(
% 1.17/1.54 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.54 'tc_nat' ), X ) ) ) ],
% 1.17/1.54 [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', hAPP( hAPP(
% 1.17/1.54 'c_Lambda_OdB_OApp', X ), Y ) ), Z ), T ), hAPP( hAPP(
% 1.17/1.54 'c_Lambda_OdB_OApp', hAPP( hAPP( hAPP( 'c_Lambda_Osubst', X ), Z ), T ) )
% 1.17/1.54 , hAPP( hAPP( hAPP( 'c_Lambda_Osubst', Y ), Z ), T ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), 'c_Suc'( Y ) )
% 1.17/1.54 ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.17/1.54 hAPP( 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'tc_nat' ), Y ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 'tc_nat' ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.17/1.54 'tc_nat' ), X ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y,
% 1.17/1.54 'tc_nat' ), X ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.17/1.54 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.54 'tc_nat' ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X
% 1.17/1.54 ) ) ) ) ],
% 1.17/1.54 [ ~( =( hAPP( 'c_Lambda_OdB_OVar', X ), hAPP( 'c_Lambda_OdB_OVar', Y ) )
% 1.17/1.54 ), =( X, Y ) ],
% 1.17/1.54 [ hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( hBOOL(
% 1.17/1.54 hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ) ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( 'c_Lambda_OdB_OVar'
% 1.17/1.54 , X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 1.17/1.54 'c_Lambda_OdB_OApp', hAPP( 'c_Lambda_OdB_OVar', Z ), T, 'tc_Lambda_OdB',
% 1.17/1.54 'tc_Lambda_OdB' ) ) ), =( X, Z ) ],
% 1.17/1.54 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( 'c_Lambda_OdB_OVar'
% 1.17/1.54 , X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 1.17/1.54 'c_Lambda_OdB_OApp', hAPP( 'c_Lambda_OdB_OVar', Z ), T, 'tc_Lambda_OdB',
% 1.17/1.54 'tc_Lambda_OdB' ) ) ), =( Y, T ) ],
% 1.17/1.54 [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', hAPP( 'c_Lambda_OdB_OVar', X )
% 1.17/1.54 ), Y ), X ), Y ) ],
% 1.17/1.54 [ ~( =( X, 'c_Suc'( X ) ) ) ],
% 1.17/1.54 [ ~( =( 'c_Suc'( X ), X ) ) ],
% 1.17/1.54 [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', hAPP( 'c_Lambda_OdB_OVar', X )
% 1.17/1.54 ), Y ), Z ), hAPP( 'c_Lambda_OdB_OVar', X ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Z ) ) ) ],
% 1.17/1.54 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 'tc_nat' ), 'tc_nat' ), X ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.17/1.54 ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'tc_nat' ), Y )
% 1.17/1.54 ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' ), Y ) ) ),
% 1.17/1.54 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Z ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), 'c_Suc'( X ) )
% 1.17/1.54 ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), 'c_Suc'( X ) )
% 1.17/1.54 ) ],
% 1.17/1.54 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X )
% 1.17/1.54 , Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ) ],
% 1.17/1.54 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X )
% 1.17/1.54 , Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.17/1.54 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.17/1.54 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 1.17/1.54 , hAPP( 'c_Lambda_OdB_OVar', X ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) )
% 1.17/1.54 ), ~( hBOOL( 'c_List_Olistsp'( 'c_InductTermi_OIT', Y, 'tc_Lambda_OdB' )
% 1.17/1.54 ) ) ],
% 1.17/1.54 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP( hAPP(
% 1.17/1.54 'c_Lambda_OdB_OApp', Z ), T ) ) ), =( X, Z ) ],
% 1.17/1.54 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP( hAPP(
% 1.17/1.54 'c_Lambda_OdB_OApp', Z ), T ) ) ), =( Y, T ) ],
% 1.17/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ],
% 1.17/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), =( Z, Y ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ],
% 1.17/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ), =( Z, Y ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), hBOOL(
% 1.17/1.54 hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), X ) ), =( Y, X ) ],
% 1.17/1.54 [ ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ),
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ),
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ],
% 1.17/1.54 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ), =( Z, Y ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' ), Y ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), hBOOL(
% 1.17/1.54 hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), X ) ), =( Y, X ) ],
% 1.17/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ), =( Z, Y ) ],
% 1.17/1.54 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), Y ) ) ) ],
% 1.17/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), Y ) ) ) ],
% 1.17/1.54 [ ~( 'class_Orderings_Oorder'( X ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), Y ) ) ) ],
% 1.17/1.54 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), X ) ) ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), X ) ) ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ ~( =( hAPP( 'c_Lambda_OdB_OVar', X ), 'c_List_Ofoldl'(
% 1.17/1.54 'c_Lambda_OdB_OApp', Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =(
% 1.17/1.54 hAPP( 'c_Lambda_OdB_OVar', X ), Y ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), Z ) ),
% 1.17/1.54 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Z ) ) ) ],
% 1.17/1.54 [ =( X, Y ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ),
% 1.17/1.54 'c_Suc'( Y ) ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' )
% 1.17/1.54 , Y ) ) ],
% 1.17/1.54 [ =( X, Y ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ),
% 1.17/1.54 'c_Suc'( X ) ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' )
% 1.17/1.54 , X ) ) ],
% 1.17/1.54 [ =( X, Y ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y )
% 1.17/1.54 ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), 'c_Suc'( Y
% 1.17/1.54 ) ) ) ) ],
% 1.17/1.54 [ ~( =( hAPP( 'c_Lambda_OdB_OVar', X ), hAPP( hAPP( 'c_Lambda_OdB_OApp'
% 1.17/1.54 , Y ), Z ) ) ) ],
% 1.17/1.54 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), 'c_Suc'( X )
% 1.17/1.54 ), 'c_Suc'( Y ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' )
% 1.17/1.54 , X ), Y ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 'tc_nat' ), 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.17/1.54 ) ) ],
% 1.17/1.54 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.17/1.54 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.17/1.54 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ),
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.17/1.54 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), X ),
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.17/1.54 X ) ), =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ),
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.54 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 X ) ) ],
% 1.17/1.54 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.17/1.54 , Y ) ],
% 1.17/1.54 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 X ) ) ],
% 1.17/1.54 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 X ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP(
% 1.17/1.54 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL(
% 1.17/1.54 hAPP( 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' ), X ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' ), Y ) ) ) ],
% 1.17/1.54 [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', 'c_List_Ofoldl'(
% 1.17/1.54 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), Z ), T )
% 1.17/1.54 , 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( hAPP( hAPP(
% 1.17/1.54 'c_Lambda_Osubst', X ), Z ), T ), 'c_List_Omap'( 'c_COMBC'( 'c_COMBC'(
% 1.17/1.54 'c_Lambda_Osubst', Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB', 'tc_fun'(
% 1.17/1.54 'tc_nat', 'tc_Lambda_OdB' ) ), T, 'tc_Lambda_OdB', 'tc_nat',
% 1.17/1.54 'tc_Lambda_OdB' ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'tc_Lambda_OdB'
% 1.17/1.54 , 'tc_Lambda_OdB' ) ) ],
% 1.17/1.54 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.17/1.54 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.17/1.54 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), 'c_Suc'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ) ],
% 1.17/1.54 [ =( hAPP( hAPP( hAPP( 'c_Lambda_Osubst', hAPP( 'c_Lambda_OdB_OVar', X )
% 1.17/1.54 ), Y ), Z ), hAPP( 'c_Lambda_OdB_OVar', X ) ), =( X, Z ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' ), X ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), 'c_Suc'(
% 1.17/1.54 X ) ) ) ],
% 1.17/1.54 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( T, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.17/1.54 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ), ~( hBOOL( hAPP(
% 1.17/1.54 'c_HOL_Oord__class_Oless'( T, X ), Z ) ) ) ],
% 1.17/1.54 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ),
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.17/1.54 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ),
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.17/1.54 [ =( hAPP( hAPP( hAPP( 'c_COMBB'( X, Y, Z ), T ), U ), W ), hAPP( T,
% 1.17/1.54 hAPP( U, W ) ) ) ],
% 1.17/1.54 [ =( hAPP( 'c_COMBC'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), Y ) ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ =( hAPP( 'c_COMBS'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), hAPP( Y
% 1.17/1.54 , W ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), X ) ), =( hAPP(
% 1.17/1.54 hAPP( hAPP( 'c_Lambda_Osubst', hAPP( 'c_Lambda_OdB_OVar', X ) ), Y ), X )
% 1.17/1.54 , Y ) ],
% 1.17/1.54 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( X ), T ), T ) ) ), =( Y, Z ) ],
% 1.17/1.54 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ) ), =( Z, T ) ],
% 1.17/1.54 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 'tc_nat' ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 'tc_nat' ), 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 'tc_nat' ), 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.17/1.54 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.17/1.54 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ),
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 1.17/1.54 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 X ) ) ), =( Y, Z ) ],
% 1.17/1.54 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.54 X ) ) ), =( Y, Z ) ],
% 1.17/1.54 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ), Y ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'tc_nat' ), Y )
% 1.17/1.54 ), =( 'c_Suc'( X ), Y ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X,
% 1.17/1.54 'tc_nat' ), Y ) ) ) ],
% 1.17/1.54 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB',
% 1.17/1.54 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Z, Y,
% 1.17/1.54 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( X, Z ) ],
% 1.17/1.54 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), 'c_Suc'( X ) ), Y ) ), 'c_Suc'(
% 1.17/1.54 Z ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), X ) ), hBOOL(
% 1.17/1.54 hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.17/1.54 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ), ~(
% 1.17/1.54 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), 'c_Suc'( X ) ) ) )
% 1.17/1.54 ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), 'c_Suc'( Y ) )
% 1.17/1.54 ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), X ) ) ],
% 1.17/1.54 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP(
% 1.17/1.54 'c_Lambda_OdB_OVar', Z ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'tc_nat' ),
% 1.17/1.54 'c_Suc'( Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat'
% 1.17/1.54 ), Y ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.17/1.54 hAPP( 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'tc_nat' ), 'c_Suc'( Y ) )
% 1.17/1.54 ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'tc_nat' ),
% 1.17/1.54 'c_Suc'( Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat'
% 1.17/1.54 ), Y ) ) ) ],
% 1.17/1.54 [ hBOOL( 'c_List_Olistsp'( 'c_COMBS'( hAPP( hAPP( 'c_COMBB'( 'tc_bool',
% 1.17/1.54 'tc_fun'( 'tc_bool', 'tc_bool' ), 'tc_Lambda_OdB' ), 'c_and' ),
% 1.17/1.54 'c_InductTermi_OIT' ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 'tc_nat',
% 1.17/1.54 'tc_bool' ), 'tc_bool', 'tc_Lambda_OdB' ), 'c_All'( 'tc_nat' ) ), hAPP(
% 1.17/1.54 hAPP( 'c_COMBB'( 'tc_fun'( 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_bool' ) ),
% 1.17/1.54 'tc_fun'( 'tc_nat', 'tc_bool' ), 'tc_Lambda_OdB' ), hAPP( 'c_COMBB'(
% 1.17/1.54 'tc_fun'( 'tc_nat', 'tc_bool' ), 'tc_bool', 'tc_nat' ), 'c_All'( 'tc_nat'
% 1.17/1.54 ) ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 'tc_nat', 'tc_fun'( 'tc_nat',
% 1.17/1.54 'tc_Lambda_OdB' ) ), 'tc_fun'( 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_bool' )
% 1.17/1.54 ), 'tc_Lambda_OdB' ), hAPP( 'c_COMBB'( 'tc_fun'( 'tc_nat',
% 1.17/1.54 'tc_Lambda_OdB' ), 'tc_fun'( 'tc_nat', 'tc_bool' ), 'tc_nat' ), hAPP(
% 1.17/1.54 'c_COMBB'( 'tc_Lambda_OdB', 'tc_bool', 'tc_nat' ), 'c_InductTermi_OIT' )
% 1.17/1.54 ) ), 'c_COMBC'( hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 'tc_Lambda_OdB',
% 1.17/1.54 'tc_fun'( 'tc_nat', 'tc_Lambda_OdB' ) ), 'tc_fun'( 'tc_fun'( 'tc_nat',
% 1.17/1.54 'tc_Lambda_OdB' ), 'tc_fun'( 'tc_nat', 'tc_fun'( 'tc_nat',
% 1.17/1.54 'tc_Lambda_OdB' ) ) ), 'tc_Lambda_OdB' ), 'c_COMBB'( 'tc_Lambda_OdB',
% 1.17/1.54 'tc_fun'( 'tc_nat', 'tc_Lambda_OdB' ), 'tc_nat' ) ), 'c_Lambda_Osubst' )
% 1.17/1.54 , 'c_Lambda_OdB_OVar', 'tc_Lambda_OdB', 'tc_fun'( 'tc_nat',
% 1.17/1.54 'tc_Lambda_OdB' ), 'tc_fun'( 'tc_nat', 'tc_fun'( 'tc_nat',
% 1.17/1.54 'tc_Lambda_OdB' ) ) ) ) ) ), 'tc_Lambda_OdB', 'tc_bool', 'tc_bool' ),
% 1.17/1.54 'v_rs', 'tc_Lambda_OdB' ) ) ],
% 1.17/1.54 [ ~( =( 'v_n', 'v_ja' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT',
% 1.17/1.54 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( 'c_Lambda_OdB_OVar', 'v_ia' )
% 1.17/1.54 , 'c_List_Omap'( 'c_COMBC'( 'c_COMBC'( 'c_Lambda_Osubst', hAPP(
% 1.17/1.54 'c_Lambda_OdB_OVar', 'v_ia' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB', 'tc_fun'(
% 1.17/1.54 'tc_nat', 'tc_Lambda_OdB' ) ), 'v_ja', 'tc_Lambda_OdB', 'tc_nat',
% 1.17/1.54 'tc_Lambda_OdB' ), 'v_rs', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 1.17/1.54 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'v_n', 'tc_nat' ), 'c_Suc'(
% 1.17/1.54 'v_ja' ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'v_ja', 'tc_nat' )
% 1.17/1.54 , 'v_n' ) ), =( 'v_n', 'v_ja' ) ],
% 1.17/1.54 [ ~( hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 1.17/1.54 'c_Lambda_OdB_OApp', hAPP( 'c_Lambda_OdB_OVar', 'v_n' ), 'c_List_Omap'(
% 1.17/1.54 'c_COMBC'( 'c_COMBC'( 'c_Lambda_Osubst', hAPP( 'c_Lambda_OdB_OVar',
% 1.17/1.54 'v_ia' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB', 'tc_fun'( 'tc_nat',
% 1.17/1.54 'tc_Lambda_OdB' ) ), 'v_ja', 'tc_Lambda_OdB', 'tc_nat', 'tc_Lambda_OdB' )
% 1.17/1.54 , 'v_rs', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'tc_Lambda_OdB',
% 1.17/1.54 'tc_Lambda_OdB' ) ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'v_ja',
% 1.17/1.54 'tc_nat' ), 'v_n' ) ), =( 'v_n', 'v_ja' ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'v_n', 'tc_nat' ), 'c_Suc'(
% 1.17/1.54 'v_ja' ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 1.17/1.54 'c_Lambda_OdB_OApp', hAPP( 'c_Lambda_OdB_OVar', hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), 'v_n' ), 'c_Suc'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), 'c_List_Omap'( 'c_COMBC'(
% 1.17/1.54 'c_COMBC'( 'c_Lambda_Osubst', hAPP( 'c_Lambda_OdB_OVar', 'v_ia' ),
% 1.17/1.54 'tc_Lambda_OdB', 'tc_Lambda_OdB', 'tc_fun'( 'tc_nat', 'tc_Lambda_OdB' ) )
% 1.17/1.54 , 'v_ja', 'tc_Lambda_OdB', 'tc_nat', 'tc_Lambda_OdB' ), 'v_rs',
% 1.17/1.54 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) )
% 1.17/1.54 ) ), =( 'v_n', 'v_ja' ) ],
% 1.17/1.54 [ ~( hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 1.17/1.54 'c_Lambda_OdB_OApp', hAPP( 'c_Lambda_OdB_OVar', 'v_n' ), 'c_List_Omap'(
% 1.17/1.54 'c_COMBC'( 'c_COMBC'( 'c_Lambda_Osubst', hAPP( 'c_Lambda_OdB_OVar',
% 1.17/1.54 'v_ia' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB', 'tc_fun'( 'tc_nat',
% 1.17/1.54 'tc_Lambda_OdB' ) ), 'v_ja', 'tc_Lambda_OdB', 'tc_nat', 'tc_Lambda_OdB' )
% 1.17/1.54 , 'v_rs', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'tc_Lambda_OdB',
% 1.17/1.54 'tc_Lambda_OdB' ) ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT',
% 1.17/1.54 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( 'c_Lambda_OdB_OVar', hAPP(
% 1.17/1.54 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), 'v_n' ), 'c_Suc'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), 'c_List_Omap'( 'c_COMBC'(
% 1.17/1.54 'c_COMBC'( 'c_Lambda_Osubst', hAPP( 'c_Lambda_OdB_OVar', 'v_ia' ),
% 1.17/1.54 'tc_Lambda_OdB', 'tc_Lambda_OdB', 'tc_fun'( 'tc_nat', 'tc_Lambda_OdB' ) )
% 1.17/1.54 , 'v_ja', 'tc_Lambda_OdB', 'tc_nat', 'tc_Lambda_OdB' ), 'v_rs',
% 1.17/1.54 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) )
% 1.17/1.54 ) ), =( 'v_n', 'v_ja' ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'v_n', 'tc_nat' ), 'c_Suc'(
% 1.17/1.54 'v_ja' ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'v_ja', 'tc_nat' )
% 1.17/1.54 , 'v_n' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 1.17/1.54 'c_Lambda_OdB_OApp', hAPP( 'c_Lambda_OdB_OVar', 'v_ia' ), 'c_List_Omap'(
% 1.17/1.54 'c_COMBC'( 'c_COMBC'( 'c_Lambda_Osubst', hAPP( 'c_Lambda_OdB_OVar',
% 1.17/1.54 'v_ia' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB', 'tc_fun'( 'tc_nat',
% 1.17/1.54 'tc_Lambda_OdB' ) ), 'v_ja', 'tc_Lambda_OdB', 'tc_nat', 'tc_Lambda_OdB' )
% 1.17/1.54 , 'v_rs', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'tc_Lambda_OdB',
% 1.17/1.54 'tc_Lambda_OdB' ) ) ) ) ],
% 1.17/1.54 [ ~( hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 1.17/1.54 'c_Lambda_OdB_OApp', hAPP( 'c_Lambda_OdB_OVar', 'v_n' ), 'c_List_Omap'(
% 1.17/1.54 'c_COMBC'( 'c_COMBC'( 'c_Lambda_Osubst', hAPP( 'c_Lambda_OdB_OVar',
% 1.17/1.54 'v_ia' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB', 'tc_fun'( 'tc_nat',
% 1.17/1.54 'tc_Lambda_OdB' ) ), 'v_ja', 'tc_Lambda_OdB', 'tc_nat', 'tc_Lambda_OdB' )
% 1.17/1.54 , 'v_rs', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'tc_Lambda_OdB',
% 1.17/1.54 'tc_Lambda_OdB' ) ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'v_ja',
% 1.17/1.54 'tc_nat' ), 'v_n' ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT',
% 1.17/1.54 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( 'c_Lambda_OdB_OVar', 'v_ia' )
% 1.17/1.54 , 'c_List_Omap'( 'c_COMBC'( 'c_COMBC'( 'c_Lambda_Osubst', hAPP(
% 1.17/1.54 'c_Lambda_OdB_OVar', 'v_ia' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB', 'tc_fun'(
% 1.17/1.54 'tc_nat', 'tc_Lambda_OdB' ) ), 'v_ja', 'tc_Lambda_OdB', 'tc_nat',
% 1.17/1.54 'tc_Lambda_OdB' ), 'v_rs', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 1.17/1.54 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ) ) ],
% 1.17/1.54 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'v_n', 'tc_nat' ), 'c_Suc'(
% 1.17/1.54 'v_ja' ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 1.17/1.54 'c_Lambda_OdB_OApp', hAPP( 'c_Lambda_OdB_OVar', hAPP( hAPP(
% 1.17/1.54 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), 'v_n' ), 'c_Suc'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), 'c_List_Omap'( 'c_COMBC'(
% 1.17/1.54 'c_COMBC'( 'c_Lambda_Osubst', hAPP( 'c_Lambda_OdB_OVar', 'v_ia' ),
% 1.17/1.54 'tc_Lambda_OdB', 'tc_Lambda_OdB', 'tc_fun'( 'tc_nat', 'tc_Lambda_OdB' ) )
% 1.17/1.54 , 'v_ja', 'tc_Lambda_OdB', 'tc_nat', 'tc_Lambda_OdB' ), 'v_rs',
% 1.17/1.54 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) )
% 1.17/1.54 ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 1.17/1.54 'c_Lambda_OdB_OApp', hAPP( 'c_Lambda_OdB_OVar', 'v_ia' ), 'c_List_Omap'(
% 1.17/1.54 'c_COMBC'( 'c_COMBC'( 'c_Lambda_Osubst', hAPP( 'c_Lambda_OdB_OVar',
% 1.17/1.54 'v_ia' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB', 'tc_fun'( 'tc_nat',
% 1.17/1.54 'tc_Lambda_OdB' ) ), 'v_ja', 'tc_Lambda_OdB', 'tc_nat', 'tc_Lambda_OdB' )
% 1.17/1.54 , 'v_rs', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'tc_Lambda_OdB',
% 1.17/1.54 'tc_Lambda_OdB' ) ) ) ) ],
% 1.17/1.54 [ ~( hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 1.17/1.54 'c_Lambda_OdB_OApp', hAPP( 'c_Lambda_OdB_OVar', 'v_n' ), 'c_List_Omap'(
% 1.17/1.54 'c_COMBC'( 'c_COMBC'( 'c_Lambda_Osubst', hAPP( 'c_Lambda_OdB_OVar',
% 1.17/1.54 'v_ia' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB', 'tc_fun'( 'tc_nat',
% 1.17/1.54 'tc_Lambda_OdB' ) ), 'v_ja', 'tc_Lambda_OdB', 'tc_nat', 'tc_Lambda_OdB' )
% 1.17/1.54 , 'v_rs', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'tc_Lambda_OdB',
% 1.17/1.54 'tc_Lambda_OdB' ) ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT',
% 1.17/1.54 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', hAPP( 'c_Lambda_OdB_OVar', hAPP(
% 1.17/1.54 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), 'v_n' ), 'c_Suc'(
% 1.17/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), 'c_List_Omap'( 'c_COMBC'(
% 1.17/1.54 'c_COMBC'( 'c_Lambda_Osubst', hAPP( 'c_Lambda_OdB_OVar', 'v_ia' ),
% 1.17/1.54 'tc_Lambda_OdB', 'tc_Lambda_OdB', 'tc_fun'( 'tc_nat', 'tc_Lambda_OdB' ) )
% 1.17/1.54 , 'v_ja', 'tc_Lambda_OdB', 'tc_nat', 'tc_Lambda_OdB' ), 'v_rs',
% 1.17/1.54 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) )
% 1.17/1.54 ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'(
% 1.17/1.54 'c_Lambda_OdB_OApp', hAPP( 'c_Lambda_OdB_OVar', 'v_ia' ), 'c_List_Omap'(
% 1.17/1.54 'c_COMBC'( 'c_COMBC'( 'c_Lambda_Osubst', hAPP( 'c_Lambda_OdB_OVar',
% 1.17/1.54 'v_ia' ), 'tc_Lambda_OdB', 'tc_Lambda_OdB', 'tc_fun'( 'tc_nat',
% 1.17/1.54 'tc_Lambda_OdB' ) ), 'v_ja', 'tc_Lambda_OdB', 'tc_nat', 'tc_Lambda_OdB' )
% 1.17/1.54 , 'v_rs', 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'tc_Lambda_OdB',
% 1.17/1.54 'tc_Lambda_OdB' ) ) ) ) ],
% 1.17/1.54 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 1.17/1.54 'class_Orderings_Opreorder'( Y ) ) ],
% 1.17/1.54 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 1.17/1.54 'class_Orderings_Oorder'( Y ) ) ],
% 1.17/1.54 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 1.17/1.54 ],
% 1.17/1.54 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 1.17/1.54 ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 1.17/1.54 ],
% 1.17/1.54 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 1.17/1.54 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 1.17/1.54 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 1.17/1.54 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 1.17/1.54 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 1.17/1.54 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 1.17/1.54 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 1.17/1.54 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 1.17/1.54 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 1.17/1.54 [ 'class_OrderedGroup_Osemigroup__add'( 'tc_nat' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 1.17/1.54 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 1.17/1.54 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 1.17/1.54 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 1.17/1.54 [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Odvd'( 'tc_nat' ) ],
% 1.17/1.54 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 1.17/1.54 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 1.17/1.54 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 1.17/1.54 [ 'class_Power_Opower'( 'tc_nat' ) ],
% 1.17/1.54 [ 'class_Int_Onumber'( 'tc_nat' ) ],
% 1.17/1.54 [ 'class_Orderings_Opreorder'( 'tc_bool' ) ],
% 1.17/1.54 [ 'class_Orderings_Oorder'( 'tc_bool' ) ],
% 1.17/1.54 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 1.17/1.54 'tc_Int_Oint' ) ],
% 1.17/1.54 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 1.17/1.54 'tc_Int_Oint' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 1.17/1.54 'tc_Int_Oint' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_Int_Oint' )
% 1.17/1.54 ],
% 1.17/1.54 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'( 'tc_Int_Oint' )
% 1.17/1.54 ],
% 1.17/1.54 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_Int_Oint' ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_Int_Oint' ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ 'class_Ring__and__Field_Oring__no__zero__divisors'( 'tc_Int_Oint' ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ 'class_Ring__and__Field_Oordered__ring__strict'( 'tc_Int_Oint' ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ 'class_OrderedGroup_Opordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.17/1.54 [ 'class_OrderedGroup_Olordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.17/1.54 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_Int_Oint' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_Int_Oint' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Int_Oint' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_Int_Oint' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Int_Oint' ) ],
% 1.17/1.54 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Int_Oint' ) ],
% 1.17/1.54 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Int_Oint' ) ],
% 1.17/1.54 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Opordered__ring'( 'tc_Int_Oint' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Int_Oint' ) ],
% 1.17/1.54 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Int_Oint' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Int_Oint' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Oordered__idom'( 'tc_Int_Oint' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Int_Oint' ) ],
% 1.17/1.54 [ 'class_OrderedGroup_Osemigroup__add'( 'tc_Int_Oint' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Int_Oint' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Int_Oint' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_Int_Oint' ) ],
% 1.17/1.54 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Int_Oint' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Int_Oint' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Omult__mono'( 'tc_Int_Oint' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Ocomm__ring'( 'tc_Int_Oint' ) ],
% 1.17/1.54 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Int_Oint' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Osemiring'( 'tc_Int_Oint' ) ],
% 1.17/1.54 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Int_Oint' ) ],
% 1.17/1.54 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Int_Oint' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Oring__1'( 'tc_Int_Oint' ) ],
% 1.17/1.54 [ 'class_Divides_Osemiring__div'( 'tc_Int_Oint' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Oring'( 'tc_Int_Oint' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Oidom'( 'tc_Int_Oint' ) ],
% 1.17/1.54 [ 'class_Nat_Osemiring__char__0'( 'tc_Int_Oint' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Odvd'( 'tc_Int_Oint' ) ],
% 1.17/1.54 [ 'class_Orderings_Opreorder'( 'tc_Int_Oint' ) ],
% 1.17/1.54 [ 'class_Orderings_Olinorder'( 'tc_Int_Oint' ) ],
% 1.17/1.54 [ 'class_Divides_Oring__div'( 'tc_Int_Oint' ) ],
% 1.17/1.54 [ 'class_Orderings_Oorder'( 'tc_Int_Oint' ) ],
% 1.17/1.54 [ 'class_Int_Oring__char__0'( 'tc_Int_Oint' ) ],
% 1.17/1.54 [ 'class_Int_Onumber__ring'( 'tc_Int_Oint' ) ],
% 1.17/1.54 [ 'class_Power_Opower'( 'tc_Int_Oint' ) ],
% 1.17/1.54 [ 'class_Int_Onumber'( 'tc_Int_Oint' ) ],
% 1.17/1.54 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 1.17/1.54 'tc_Code__Numeral_Ocode__numeral' ) ],
% 1.17/1.54 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 1.17/1.54 'tc_Code__Numeral_Ocode__numeral' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 1.17/1.54 'tc_Code__Numeral_Ocode__numeral' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 1.17/1.54 'tc_Code__Numeral_Ocode__numeral' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Oordered__semiring__strict'(
% 1.17/1.54 'tc_Code__Numeral_Ocode__numeral' ) ],
% 1.17/1.54 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'(
% 1.17/1.54 'tc_Code__Numeral_Ocode__numeral' ) ],
% 1.17/1.54 [ 'class_OrderedGroup_Opordered__comm__monoid__add'(
% 1.17/1.54 'tc_Code__Numeral_Ocode__numeral' ) ],
% 1.17/1.54 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 1.17/1.54 'tc_Code__Numeral_Ocode__numeral' ) ],
% 1.17/1.54 [ 'class_OrderedGroup_Ocancel__semigroup__add'(
% 1.17/1.54 'tc_Code__Numeral_Ocode__numeral' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Opordered__semiring'(
% 1.17/1.54 'tc_Code__Numeral_Ocode__numeral' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Oordered__semiring'(
% 1.17/1.54 'tc_Code__Numeral_Ocode__numeral' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Ono__zero__divisors'(
% 1.17/1.54 'tc_Code__Numeral_Ocode__numeral' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Oordered__semidom'(
% 1.17/1.54 'tc_Code__Numeral_Ocode__numeral' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Ocomm__semiring__1'(
% 1.17/1.54 'tc_Code__Numeral_Ocode__numeral' ) ],
% 1.17/1.54 [ 'class_OrderedGroup_Oab__semigroup__mult'(
% 1.17/1.54 'tc_Code__Numeral_Ocode__numeral' ) ],
% 1.17/1.54 [ 'class_OrderedGroup_Ocomm__monoid__mult'(
% 1.17/1.54 'tc_Code__Numeral_Ocode__numeral' ) ],
% 1.17/1.54 [ 'class_OrderedGroup_Oab__semigroup__add'(
% 1.17/1.54 'tc_Code__Numeral_Ocode__numeral' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Ocomm__semiring'(
% 1.17/1.54 'tc_Code__Numeral_Ocode__numeral' ) ],
% 1.17/1.54 [ 'class_OrderedGroup_Ocomm__monoid__add'(
% 1.17/1.54 'tc_Code__Numeral_Ocode__numeral' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Ozero__neq__one'(
% 1.17/1.54 'tc_Code__Numeral_Ocode__numeral' ) ],
% 1.17/1.54 [ 'class_OrderedGroup_Osemigroup__add'(
% 1.17/1.54 'tc_Code__Numeral_Ocode__numeral' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Osemiring__1'(
% 1.17/1.54 'tc_Code__Numeral_Ocode__numeral' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Osemiring__0'(
% 1.17/1.54 'tc_Code__Numeral_Ocode__numeral' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Omult__mono1'(
% 1.17/1.54 'tc_Code__Numeral_Ocode__numeral' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Omult__zero'(
% 1.17/1.54 'tc_Code__Numeral_Ocode__numeral' ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Omult__mono'(
% 1.17/1.54 'tc_Code__Numeral_Ocode__numeral' ) ],
% 1.17/1.54 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Code__Numeral_Ocode__numeral'
% 1.17/1.54 ) ],
% 1.17/1.54 [ 'class_Ring__and__Field_Osemiring'( 'tc_Code__Numeral_Ocode__numeral'
% 1.17/1.54 ) ],
% 1.17/1.54 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Code__Numeral_Ocode__numeral' )
% 1.17/1.54 ],
% 1.17/1.54 [ 'class_Divides_Osemiring__div'( 'tc_Code__Numeral_Ocode__numeral' ) ]
% 1.17/1.54 ,
% 1.17/1.54 [ 'class_Nat_Osemiring__char__0'( 'tc_Code__Numeral_Ocode__numeral' ) ]
% 1.17/1.55 ,
% 1.17/1.55 [ 'class_Ring__and__Field_Odvd'( 'tc_Code__Numeral_Ocode__numeral' ) ]
% 1.17/1.55 ,
% 1.17/1.55 [ 'class_Orderings_Opreorder'( 'tc_Code__Numeral_Ocode__numeral' ) ]
% 1.17/1.55 ,
% 1.17/1.55 [ 'class_Orderings_Olinorder'( 'tc_Code__Numeral_Ocode__numeral' ) ]
% 1.17/1.55 ,
% 1.17/1.55 [ 'class_Orderings_Oorder'( 'tc_Code__Numeral_Ocode__numeral' ) ],
% 1.17/1.55 [ 'class_Power_Opower'( 'tc_Code__Numeral_Ocode__numeral' ) ],
% 1.17/1.55 [ 'class_Int_Onumber'( 'tc_Code__Numeral_Ocode__numeral' ) ],
% 1.17/1.55 [ =( hAPP( 'c_COMBS'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), hAPP( Y
% 1.17/1.55 , W ) ) ) ],
% 1.17/1.55 [ =( hAPP( 'c_COMBC'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), Y ) ) ]
% 1.17/1.55 ,
% 1.17/1.55 [ =( hAPP( hAPP( hAPP( 'c_COMBB'( X, Y, Z ), T ), U ), W ), hAPP( T,
% 1.17/1.55 hAPP( U, W ) ) ) ],
% 1.17/1.55 [ hBOOL( hAPP( hAPP( 'c_fequal'( X ), Y ), Y ) ) ],
% 1.17/1.55 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_fequal'( Z ), X ), Y ) ) ) ]
% 1.17/1.55 ] .
% 1.17/1.55
% 1.17/1.55
% 1.17/1.55 percentage equality = 0.262309, percentage horn = 0.894325
% 1.17/1.55 This is a problem with some equality
% 1.17/1.55
% 1.17/1.55
% 1.17/1.55
% 1.17/1.55 Options Used:
% 1.17/1.55
% 1.17/1.55 useres = 1
% 1.17/1.55 useparamod = 1
% 1.17/1.55 useeqrefl = 1
% 1.17/1.55 useeqfact = 1
% 1.17/1.55 usefactor = 1
% 1.17/1.55 usesimpsplitting = 0
% 1.17/1.55 usesimpdemod = 5
% 1.17/1.55 usesimpres = 3
% 1.17/1.55
% 1.17/1.55 resimpinuse = 1000
% 1.17/1.55 resimpclauses = 20000
% 1.17/1.55 substype = eqrewr
% 1.17/1.55 backwardsubs = 1
% 1.17/1.55 selectoldest = 5
% 1.17/1.55
% 1.17/1.55 litorderings [0] = split
% 1.17/1.55 litorderings [1] = extend the termordering, first sorting on arguments
% 1.17/1.55
% 1.17/1.55 termordering = kbo
% 1.17/1.55
% 1.17/1.55 litapriori = 0
% 1.17/1.55 termapriori = 1
% 1.17/1.55 litaposteriori = 0
% 1.17/1.55 termaposteriori = 0
% 1.17/1.55 demodaposteriori = 0
% 1.17/1.55 ordereqreflfact = 0
% 1.17/1.55
% 1.17/1.55 litselect = negord
% 1.17/1.55
% 1.17/1.55 maxweight = 15
% 1.17/1.55 maxdepth = 30000
% 1.17/1.55 maxlength = 115
% 1.17/1.55 maxnrvars = 195
% 1.17/1.55 excuselevel = 1
% 1.17/1.55 increasemaxweight = 1
% 1.17/1.55
% 1.17/1.55 maxselected = 10000000
% 1.17/1.55 maxnrclauses = 10000000
% 1.17/1.55
% 1.17/1.55 showgenerated = 0
% 1.17/1.55 showkept = 0
% 1.17/1.55 showselected = 0
% 1.17/1.55 showdeleted = 0
% 1.17/1.55 showresimp = 1
% 1.17/1.55 showstatus = 2000
% 1.17/1.55
% 1.17/1.55 prologoutput = 1
% 1.17/1.55 nrgoals = 5000000
% 1.17/1.55 totalproof = 1
% 1.17/1.55
% 1.17/1.55 Symbols occurring in the translation:
% 1.17/1.55
% 1.17/1.55 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.17/1.55 . [1, 2] (w:1, o:179, a:1, s:1, b:0),
% 1.17/1.55 ! [4, 1] (w:0, o:99, a:1, s:1, b:0),
% 1.17/1.55 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.17/1.55 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.17/1.55 'tc_nat' [41, 0] (w:1, o:14, a:1, s:1, b:0),
% 1.17/1.55 'c_Divides_Odiv__class_Odiv' [42, 3] (w:1, o:219, a:1, s:1, b:0),
% 1.17/1.55 'c_lessequals' [43, 2] (w:1, o:204, a:1, s:1, b:0),
% 1.17/1.55 hAPP [44, 2] (w:1, o:205, a:1, s:1, b:0),
% 1.17/1.55 hBOOL [45, 1] (w:1, o:104, a:1, s:1, b:0),
% 1.17/1.55 'class_OrderedGroup_Olordered__ab__group__add' [47, 1] (w:1, o:106
% 1.17/1.55 , a:1, s:1, b:0),
% 1.17/1.55 'c_HOL_Ozero__class_Ozero' [48, 1] (w:1, o:107, a:1, s:1, b:0),
% 1.17/1.55 'c_HOL_Oplus__class_Oplus' [49, 1] (w:1, o:109, a:1, s:1, b:0),
% 1.17/1.55 'c_HOL_Oord__class_Oless' [51, 2] (w:1, o:206, a:1, s:1, b:0),
% 1.17/1.55 'c_HOL_Otimes__class_Otimes' [52, 1] (w:1, o:110, a:1, s:1, b:0),
% 1.17/1.55 'c_HOL_Oone__class_Oone' [53, 1] (w:1, o:108, a:1, s:1, b:0),
% 1.17/1.55 'c_Ring__and__Field_Odvd__class_Odvd' [54, 3] (w:1, o:220, a:1, s:1
% 1.17/1.55 , b:0),
% 1.17/1.55 'class_Ring__and__Field_Oidom' [55, 1] (w:1, o:111, a:1, s:1, b:0),
% 1.17/1.55 'class_Int_Onumber__ring' [56, 1] (w:1, o:112, a:1, s:1, b:0),
% 1.17/1.55 'c_Suc' [62, 1] (w:1, o:113, a:1, s:1, b:0),
% 1.17/1.55 'class_Ring__and__Field_Oordered__semidom' [63, 1] (w:1, o:119, a:1
% 1.17/1.55 , s:1, b:0),
% 1.17/1.55 'c_Nat_Osemiring__1__class_Oof__nat' [64, 2] (w:1, o:207, a:1, s:1
% 1.17/1.55 , b:0),
% 1.17/1.55 'class_Divides_Osemiring__div' [65, 1] (w:1, o:121, a:1, s:1, b:0),
% 1.17/1.55 'c_Divides_Odiv__class_Omod' [67, 3] (w:1, o:221, a:1, s:1, b:0),
% 1.17/1.55 'class_Ring__and__Field_Osemiring__1' [68, 1] (w:1, o:127, a:1, s:1
% 1.17/1.55 , b:0),
% 1.17/1.55 'c_Power_Opower__class_Opower' [69, 3] (w:1, o:222, a:1, s:1, b:0),
% 1.17/1.55 'class_Ring__and__Field_Oring' [70, 1] (w:1, o:122, a:1, s:1, b:0),
% 1.17/1.55 'class_Int_Onumber' [71, 1] (w:1, o:128, a:1, s:1, b:0),
% 1.17/1.55 'c_HOL_Ominus__class_Ominus' [72, 1] (w:1, o:129, a:1, s:1, b:0),
% 1.17/1.55 'c_Int_Onumber__class_Onumber__of' [74, 2] (w:1, o:208, a:1, s:1, b:0
% 1.17/1.55 ),
% 1.17/1.55 'class_Ring__and__Field_Ocomm__semiring__1' [75, 1] (w:1, o:132, a:1
% 1.34/1.69 , s:1, b:0),
% 1.34/1.69 'class_Ring__and__Field_Odvd' [76, 1] (w:1, o:134, a:1, s:1, b:0),
% 1.34/1.69 'class_OrderedGroup_Omonoid__mult' [78, 1] (w:1, o:135, a:1, s:1, b:0
% 1.34/1.69 ),
% 1.34/1.69 'class_OrderedGroup_Ocomm__monoid__mult' [79, 1] (w:1, o:136, a:1, s:
% 1.34/1.69 1, b:0),
% 1.34/1.69 'c_Code__Numeral_Onat__of' [81, 1] (w:1, o:137, a:1, s:1, b:0),
% 1.34/1.69 'c_Code__Numeral_Oof__nat' [82, 1] (w:1, o:138, a:1, s:1, b:0),
% 1.34/1.69 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [86, 1]
% 1.34/1.69 (w:1, o:139, a:1, s:1, b:0),
% 1.34/1.69 'class_OrderedGroup_Ocomm__monoid__add' [87, 1] (w:1, o:140, a:1, s:1
% 1.34/1.69 , b:0),
% 1.34/1.69 'class_Ring__and__Field_Opordered__ring' [89, 1] (w:1, o:145, a:1, s:
% 1.34/1.69 1, b:0),
% 1.34/1.69 'c_Lambda_OdB_OAbs' [91, 1] (w:1, o:146, a:1, s:1, b:0),
% 1.34/1.69 'c_Lambda_Osubstn' [93, 3] (w:1, o:223, a:1, s:1, b:0),
% 1.34/1.69 'class_Ring__and__Field_Oordered__ring__strict' [94, 1] (w:1, o:118
% 1.34/1.69 , a:1, s:1, b:0),
% 1.34/1.69 'class_Nat_Osemiring__char__0' [95, 1] (w:1, o:105, a:1, s:1, b:0),
% 1.34/1.69 'c_Lambda_Oliftn' [99, 3] (w:1, o:224, a:1, s:1, b:0),
% 1.34/1.69 'c_Lambda_Olift' [100, 0] (w:1, o:60, a:1, s:1, b:0),
% 1.34/1.69 'class_OrderedGroup_Opordered__comm__monoid__add' [101, 1] (w:1, o:
% 1.34/1.69 147, a:1, s:1, b:0),
% 1.34/1.69 'class_Power_Opower' [102, 1] (w:1, o:163, a:1, s:1, b:0),
% 1.34/1.69 'class_OrderedGroup_Opordered__ab__semigroup__add' [104, 1] (w:1, o:
% 1.34/1.69 148, a:1, s:1, b:0),
% 1.34/1.69 'class_OrderedGroup_Oab__group__add' [105, 1] (w:1, o:149, a:1, s:1
% 1.34/1.69 , b:0),
% 1.34/1.69 'class_OrderedGroup_Oab__semigroup__add' [106, 1] (w:1, o:150, a:1
% 1.34/1.69 , s:1, b:0),
% 1.34/1.69 'c_Lambda_OdB_OVar' [107, 0] (w:1, o:61, a:1, s:1, b:0),
% 1.34/1.69 'class_Ring__and__Field_Osemiring' [108, 1] (w:1, o:164, a:1, s:1, b:
% 1.34/1.69 0),
% 1.34/1.69 'c_fequal' [111, 1] (w:1, o:165, a:1, s:1, b:0),
% 1.34/1.69 'c_List_Olist__all2' [112, 5] (w:1, o:235, a:1, s:1, b:0),
% 1.34/1.69 'class_Int_Oring__char__0' [113, 1] (w:1, o:166, a:1, s:1, b:0),
% 1.34/1.69 'class_Ring__and__Field_Osemiring__0' [114, 1] (w:1, o:126, a:1, s:1
% 1.34/1.69 , b:0),
% 1.34/1.69 'c_Finite__Set_Osetsum' [119, 4] (w:1, o:231, a:1, s:1, b:0),
% 1.34/1.69 'c_COMBB' [120, 3] (w:1, o:218, a:1, s:1, b:0),
% 1.34/1.69 'class_OrderedGroup_Omonoid__add' [121, 1] (w:1, o:151, a:1, s:1, b:0
% 1.34/1.69 ),
% 1.34/1.69 'c_List_Olist_ONil' [122, 1] (w:1, o:167, a:1, s:1, b:0),
% 1.34/1.69 'c_List_Olistsum' [123, 2] (w:1, o:209, a:1, s:1, b:0),
% 1.34/1.69 'c_Lambda_Osubst' [124, 0] (w:1, o:67, a:1, s:1, b:0),
% 1.34/1.69 'c_List_Ofilter' [125, 3] (w:1, o:225, a:1, s:1, b:0),
% 1.34/1.69 'class_Ring__and__Field_Opordered__cancel__semiring' [126, 1] (w:1
% 1.34/1.69 , o:168, a:1, s:1, b:0),
% 1.34/1.69 'class_OrderedGroup_Ocancel__ab__semigroup__add' [127, 1] (w:1, o:152
% 1.34/1.69 , a:1, s:1, b:0),
% 1.34/1.69 'class_OrderedGroup_Ocancel__semigroup__add' [128, 1] (w:1, o:153, a:
% 1.34/1.69 1, s:1, b:0),
% 1.34/1.69 'class_Ring__and__Field_Oordered__idom' [129, 1] (w:1, o:141, a:1, s:
% 1.34/1.69 1, b:0),
% 1.34/1.69 'tc_Lambda_OdB' [131, 0] (w:1, o:68, a:1, s:1, b:0),
% 1.34/1.69 'c_Nat_Osize__class_Osize' [132, 2] (w:1, o:210, a:1, s:1, b:0),
% 1.34/1.69 'c_Lambda_Obeta' [133, 2] (w:1, o:211, a:1, s:1, b:0),
% 1.34/1.69 'c_Type_Oshift' [137, 4] (w:1, o:232, a:1, s:1, b:0),
% 1.34/1.69 'class_Orderings_Oorder' [144, 1] (w:1, o:154, a:1, s:1, b:0),
% 1.34/1.69 'class_OrderedGroup_Oab__semigroup__idem__mult' [145, 1] (w:1, o:155
% 1.34/1.69 , a:1, s:1, b:0),
% 1.34/1.69 'class_Orderings_Olinorder' [148, 1] (w:1, o:156, a:1, s:1, b:0),
% 1.34/1.69 'c_Type_Otyping' [151, 3] (w:1, o:226, a:1, s:1, b:0),
% 1.34/1.69 'tc_Type_Otype' [152, 0] (w:1, o:72, a:1, s:1, b:0),
% 1.34/1.69 'class_Ring__and__Field_Opordered__semiring' [153, 1] (w:1, o:169, a:
% 1.34/1.69 1, s:1, b:0),
% 1.34/1.69 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [154, 1]
% 1.34/1.69 (w:1, o:157, a:1, s:1, b:0),
% 1.34/1.69 'class_Ring__and__Field_Ozero__neq__one' [155, 1] (w:1, o:170, a:1
% 1.34/1.69 , s:1, b:0),
% 1.34/1.69 'class_Ring__and__Field_Ono__zero__divisors' [156, 1] (w:1, o:117, a:
% 1.34/1.69 1, s:1, b:0),
% 1.34/1.69 'class_Ring__and__Field_Omult__zero' [157, 1] (w:1, o:114, a:1, s:1
% 1.34/1.69 , b:0),
% 1.34/1.69 'class_Ring__and__Field_Oring__1__no__zero__divisors' [158, 1] (w:1
% 1.34/1.69 , o:123, a:1, s:1, b:0),
% 1.34/1.69 'class_Ring__and__Field_Oring__no__zero__divisors' [159, 1] (w:1, o:
% 1.34/1.69 124, a:1, s:1, b:0),
% 21.82/22.17 'class_Ring__and__Field_Oordered__semiring__strict' [160, 1] (w:1, o:
% 21.82/22.17 142, a:1, s:1, b:0),
% 21.82/22.17 'class_Ring__and__Field_Oordered__semiring' [161, 1] (w:1, o:143, a:1
% 21.82/22.17 , s:1, b:0),
% 21.82/22.17 'class_Ring__and__Field_Omult__mono' [162, 1] (w:1, o:115, a:1, s:1
% 21.82/22.17 , b:0),
% 21.82/22.17 'class_Ring__and__Field_Omult__mono1' [163, 1] (w:1, o:116, a:1, s:1
% 21.82/22.17 , b:0),
% 21.82/22.17 'class_Orderings_Opreorder' [164, 1] (w:1, o:158, a:1, s:1, b:0),
% 21.82/22.17 'class_OrderedGroup_Opordered__ab__group__add' [165, 1] (w:1, o:159
% 21.82/22.17 , a:1, s:1, b:0),
% 21.82/22.17 'class_Ring__and__Field_Ocomm__ring' [167, 1] (w:1, o:130, a:1, s:1
% 21.82/22.17 , b:0),
% 21.82/22.17 'c_Lambda_OdB_OdB__size' [169, 1] (w:1, o:171, a:1, s:1, b:0),
% 21.82/22.17 'class_OrderedGroup_Oab__semigroup__mult' [170, 1] (w:1, o:160, a:1
% 21.82/22.17 , s:1, b:0),
% 21.82/22.17 'class_Ring__and__Field_Ocomm__semiring' [171, 1] (w:1, o:133, a:1
% 21.82/22.17 , s:1, b:0),
% 21.82/22.17 'class_Divides_Oring__div' [174, 1] (w:1, o:120, a:1, s:1, b:0),
% 21.82/22.17 'class_Ring__and__Field_Ocomm__ring__1' [175, 1] (w:1, o:131, a:1, s:
% 21.82/22.17 1, b:0),
% 21.82/22.17 'class_OrderedGroup_Ogroup__add' [176, 1] (w:1, o:161, a:1, s:1, b:0)
% 21.82/22.17 ,
% 21.82/22.17 'tc_fun' [177, 2] (w:1, o:212, a:1, s:1, b:0),
% 21.82/22.17 'c_COMBC' [178, 5] (w:1, o:236, a:1, s:1, b:0),
% 21.82/22.17 'v_sko__List__Xlexn__Xinduct__1' [180, 1] (w:1, o:172, a:1, s:1, b:0)
% 21.82/22.17 ,
% 21.82/22.17 'c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1' [181, 1] (w:1, o:173
% 21.82/22.17 , a:1, s:1, b:0),
% 21.82/22.17 'c_COMBS' [183, 5] (w:1, o:237, a:1, s:1, b:0),
% 21.82/22.17 'c_Lambda_OdB_OApp' [184, 0] (w:1, o:76, a:1, s:1, b:0),
% 21.82/22.17 'c_List_Omap' [187, 4] (w:1, o:233, a:1, s:1, b:0),
% 21.82/22.17 'class_Ring__and__Field_Oordered__comm__semiring__strict' [188, 1]
% 21.82/22.17 (w:1, o:144, a:1, s:1, b:0),
% 21.82/22.17 'c_List_Ofoldl' [189, 5] (w:1, o:238, a:1, s:1, b:0),
% 21.82/22.17 'class_Ring__and__Field_Oring__1' [190, 1] (w:1, o:125, a:1, s:1, b:0
% 21.82/22.17 ),
% 21.82/22.17 'c_ATP__Linkup_Osko__Nat__Xnat__diff__split__1__1' [191, 3] (w:1, o:
% 21.82/22.17 227, a:1, s:1, b:0),
% 21.82/22.17 'c_ATP__Linkup_Osko__Nat__Xnat__diff__split__asm__1__1' [192, 3] (w:1
% 21.82/22.17 , o:228, a:1, s:1, b:0),
% 21.82/22.17 'c_ATP__Linkup_Osko__Nat__Xzero__induct__lemma__1__1' [193, 1] (w:1
% 21.82/22.18 , o:174, a:1, s:1, b:0),
% 21.82/22.18 'class_OrderedGroup_Osemigroup__add' [195, 1] (w:1, o:162, a:1, s:1
% 21.82/22.18 , b:0),
% 21.82/22.18 'c_Type_Otypings' [199, 3] (w:1, o:229, a:1, s:1, b:0),
% 21.82/22.18 'c_List_Olistsp' [201, 3] (w:1, o:230, a:1, s:1, b:0),
% 21.82/22.18 'c_InductTermi_OIT' [202, 0] (w:1, o:78, a:1, s:1, b:0),
% 21.82/22.18 'c_ATP__Linkup_Osko__Nat__Xnat__Xexhaust__1__1' [203, 1] (w:1, o:175
% 21.82/22.18 , a:1, s:1, b:0),
% 21.82/22.18 'c_ATP__Linkup_Osko__Nat__XSuc__lessE__1__1' [204, 2] (w:1, o:213, a:
% 21.82/22.18 1, s:1, b:0),
% 21.82/22.18 'c_ATP__Linkup_Osko__Nat__XlessE__1__1' [205, 2] (w:1, o:214, a:1, s:
% 21.82/22.18 1, b:0),
% 21.82/22.18 'tc_bool' [206, 0] (w:1, o:79, a:1, s:1, b:0),
% 21.82/22.18 'c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__less__iff__1__1'
% 21.82/22.18 [211, 2] (w:1, o:215, a:1, s:1, b:0),
% 21.82/22.18 'c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__less__1__1' [
% 21.82/22.18 213, 2] (w:1, o:216, a:1, s:1, b:0),
% 21.82/22.18 'c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1' [214, 2] (w:
% 21.82/22.18 1, o:217, a:1, s:1, b:0),
% 21.82/22.18 'c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1' [215, 1] (w:1, o:176
% 21.82/22.18 , a:1, s:1, b:0),
% 21.82/22.18 'c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1' [216, 1] (w:1, o:
% 21.82/22.18 177, a:1, s:1, b:0),
% 21.82/22.18 'c_and' [218, 0] (w:1, o:83, a:1, s:1, b:0),
% 21.82/22.18 'v_n' [219, 0] (w:1, o:84, a:1, s:1, b:0),
% 21.82/22.18 'c_List_Osko__List__Xfoldl__apply__inv__1__1' [221, 4] (w:1, o:234
% 21.82/22.18 , a:1, s:1, b:0),
% 21.82/22.18 't_a' [222, 0] (w:1, o:85, a:1, s:1, b:0),
% 21.82/22.18 'v_x' [224, 0] (w:1, o:87, a:1, s:1, b:0),
% 21.82/22.18 'c_All' [229, 1] (w:1, o:178, a:1, s:1, b:0),
% 21.82/22.18 'v_rs' [230, 0] (w:1, o:90, a:1, s:1, b:0),
% 21.82/22.18 'v_ja' [231, 0] (w:1, o:92, a:1, s:1, b:0),
% 21.82/22.18 'v_ia' [232, 0] (w:1, o:91, a:1, s:1, b:0),
% 21.82/22.18 'tc_Int_Oint' [235, 0] (w:1, o:95, a:1, s:1, b:0),
% 21.82/22.18 'tc_Code__Numeral_Ocode__numeral' [236, 0] (w:1, o:96, a:1, s:1, b:0)
% 21.82/22.18 .
% 21.82/22.18
% 21.82/22.18
% 21.82/22.18 Starting Search:
% 21.82/22.18
% 21.82/22.18 Resimplifying inuse:
% 21.82/22.18 Done
% 21.82/22.18
% 21.82/22.18
% 21.82/22.18 Intermediate Status:
% 21.82/22.18 Generated: 5382
% 21.82/22.18 Kept: 2423
% 21.82/22.18 Inuse: 203
% 21.82/22.18 Deleted: 3
% 21.82/22.18 Deletedinuse: 0
% 21.82/22.18
% 21.82/22.18 Resimplifying inuse:
% 21.82/22.18 Done
% 68.13/68.53
% 68.13/68.53 Resimplifying inuse:
% 68.13/68.53 Done
% 68.13/68.53
% 68.13/68.53
% 68.13/68.53 Intermediate Status:
% 68.13/68.53 Generated: 12431
% 68.13/68.53 Kept: 4506
% 68.13/68.53 Inuse: 338
% 68.13/68.53 Deleted: 8
% 68.13/68.53 Deletedinuse: 0
% 68.13/68.53
% 68.13/68.53 Resimplifying inuse:
% 68.13/68.53 Done
% 68.13/68.53
% 68.13/68.53 Resimplifying inuse:
% 68.13/68.53 Done
% 68.13/68.53
% 68.13/68.53
% 68.13/68.53 Intermediate Status:
% 68.13/68.53 Generated: 20013
% 68.13/68.53 Kept: 7052
% 68.13/68.53 Inuse: 376
% 68.13/68.53 Deleted: 10
% 68.13/68.53 Deletedinuse: 0
% 68.13/68.53
% 68.13/68.53 Resimplifying inuse:
% 68.13/68.53 Done
% 68.13/68.53
% 68.13/68.53 Resimplifying inuse:
% 68.13/68.53 Done
% 68.13/68.53
% 68.13/68.53
% 68.13/68.53 Intermediate Status:
% 68.13/68.53 Generated: 27192
% 68.13/68.53 Kept: 9100
% 68.13/68.53 Inuse: 404
% 68.13/68.53 Deleted: 13
% 68.13/68.53 Deletedinuse: 1
% 68.13/68.53
% 68.13/68.53 Resimplifying inuse:
% 68.13/68.53 Done
% 68.13/68.53
% 68.13/68.53 Resimplifying inuse:
% 68.13/68.53 Done
% 68.13/68.53
% 68.13/68.53
% 68.13/68.53 Intermediate Status:
% 68.13/68.53 Generated: 38878
% 68.13/68.53 Kept: 11842
% 68.13/68.53 Inuse: 511
% 68.13/68.53 Deleted: 16
% 68.13/68.53 Deletedinuse: 1
% 68.13/68.53
% 68.13/68.53 Resimplifying inuse:
% 68.13/68.53 Done
% 68.13/68.53
% 68.13/68.53 Resimplifying inuse:
% 68.13/68.53 Done
% 68.13/68.53
% 68.13/68.53
% 68.13/68.53 Intermediate Status:
% 68.13/68.53 Generated: 46751
% 68.13/68.53 Kept: 15009
% 68.13/68.53 Inuse: 565
% 68.13/68.53 Deleted: 17
% 68.13/68.53 Deletedinuse: 1
% 68.13/68.53
% 68.13/68.53 Resimplifying inuse:
% 68.13/68.53 Done
% 68.13/68.53
% 68.13/68.53 Resimplifying inuse:
% 68.13/68.53 Done
% 68.13/68.53
% 68.13/68.53
% 68.13/68.53 Intermediate Status:
% 68.13/68.53 Generated: 58549
% 68.13/68.53 Kept: 19338
% 68.13/68.53 Inuse: 590
% 68.13/68.53 Deleted: 17
% 68.13/68.53 Deletedinuse: 1
% 68.13/68.53
% 68.13/68.53 Resimplifying inuse:
% 68.13/68.53 Done
% 68.13/68.53
% 68.13/68.53 Resimplifying inuse:
% 68.13/68.53 Done
% 68.13/68.53
% 68.13/68.53 Resimplifying clauses:
% 68.13/68.53 Done
% 68.13/68.53
% 68.13/68.53
% 68.13/68.53 Intermediate Status:
% 68.13/68.53 Generated: 66325
% 68.13/68.53 Kept: 21338
% 68.13/68.53 Inuse: 603
% 68.13/68.53 Deleted: 343
% 68.13/68.53 Deletedinuse: 1
% 68.13/68.53
% 68.13/68.53 Resimplifying inuse:
% 68.13/68.53 Done
% 68.13/68.53
% 68.13/68.53
% 68.13/68.53 Intermediate Status:
% 68.13/68.53 Generated: 77252
% 68.13/68.53 Kept: 24157
% 68.13/68.53 Inuse: 630
% 68.13/68.53 Deleted: 343
% 68.13/68.53 Deletedinuse: 1
% 68.13/68.53
% 68.13/68.53 Resimplifying inuse:
% 68.13/68.53 Done
% 68.13/68.53
% 68.13/68.53 Resimplifying inuse:
% 68.13/68.53 Done
% 68.13/68.53
% 68.13/68.53
% 68.13/68.53 Intermediate Status:
% 68.13/68.53 Generated: 83726
% 68.13/68.53 Kept: 26160
% 68.13/68.53 Inuse: 660
% 68.13/68.53 Deleted: 343
% 68.13/68.53 Deletedinuse: 1
% 68.13/68.53
% 68.13/68.53 Resimplifying inuse:
% 68.13/68.53 Done
% 68.13/68.53
% 68.13/68.53
% 68.13/68.53 Intermediate Status:
% 68.13/68.53 Generated: 93680
% 68.13/68.53 Kept: 28205
% 68.13/68.53 Inuse: 680
% 68.13/68.53 Deleted: 343
% 68.13/68.53 Deletedinuse: 1
% 68.13/68.53
% 68.13/68.53 Resimplifying inuse:
% 68.13/68.53 Done
% 68.13/68.53
% 68.13/68.53 Resimplifying inuse:
% 68.13/68.53 Done
% 68.13/68.53
% 68.13/68.53
% 68.13/68.53 Intermediate Status:
% 68.13/68.53 Generated: 107090
% 68.13/68.53 Kept: 30527
% 68.13/68.53 Inuse: 690
% 68.13/68.53 Deleted: 343
% 68.13/68.53 Deletedinuse: 1
% 68.13/68.53
% 68.13/68.53 Resimplifying inuse:
% 68.13/68.53 Done
% 68.13/68.53
% 68.13/68.53 Resimplifying inuse:
% 68.13/68.53 Done
% 68.13/68.53
% 68.13/68.53
% 68.13/68.53 Intermediate Status:
% 68.13/68.53 Generated: 120882
% 68.13/68.53 Kept: 32857
% 68.13/68.53 Inuse: 700
% 68.13/68.53 Deleted: 343
% 68.13/68.53 Deletedinuse: 1
% 68.13/68.53
% 68.13/68.53 Resimplifying inuse:
% 68.13/68.53 Done
% 68.13/68.53
% 68.13/68.53 Resimplifying inuse:
% 68.13/68.53 Done
% 68.13/68.53
% 68.13/68.53
% 68.13/68.53 Intermediate Status:
% 68.13/68.53 Generated: 133313
% 68.13/68.53 Kept: 35135
% 68.13/68.53 Inuse: 725
% 68.13/68.53 Deleted: 343
% 68.13/68.53 Deletedinuse: 1
% 68.13/68.53
% 68.13/68.53 Resimplifying inuse:
% 68.13/68.53 Done
% 68.13/68.53
% 68.13/68.53 Resimplifying inuse:
% 68.13/68.53 Done
% 68.13/68.53
% 68.13/68.53
% 68.13/68.53 Intermediate Status:
% 68.13/68.53 Generated: 144655
% 68.13/68.53 Kept: 37305
% 68.13/68.53 Inuse: 770
% 68.13/68.53 Deleted: 343
% 68.13/68.53 Deletedinuse: 1
% 68.13/68.53
% 68.13/68.53 Resimplifying inuse:
% 68.13/68.53 Done
% 68.13/68.53
% 68.13/68.53 Resimplifying inuse:
% 68.13/68.53 Done
% 68.13/68.53
% 68.13/68.53
% 68.13/68.53 Intermediate Status:
% 68.13/68.53 Generated: 154802
% 68.13/68.53 Kept: 39358
% 68.13/68.53 Inuse: 815
% 68.13/68.53 Deleted: 343
% 68.13/68.53 Deletedinuse: 1
% 68.13/68.53
% 68.13/68.53 Resimplifying inuse:
% 68.13/68.53 Done
% 68.13/68.53
% 68.13/68.53 Resimplifying inuse:
% 68.13/68.53 Done
% 68.13/68.53
% 68.13/68.53
% 68.13/68.53 Intermediate Status:
% 68.13/68.53 Generated: 171103
% 68.13/68.53 Kept: 43458
% 68.13/68.53 Inuse: 845
% 68.13/68.53 Deleted: 343
% 68.13/68.53 Deletedinuse: 1
% 68.13/68.53
% 68.13/68.53 Resimplifying inuse:
% 68.13/68.53 Done
% 68.13/68.53
% 68.13/68.53 Resimplifying clauses:
% 68.13/68.53 Done
% 68.13/68.53
% 68.13/68.53 Resimplifying inuse:
% 68.13/68.53 Done
% 68.13/68.53
% 68.13/68.53
% 68.13/68.53 Intermediate Status:
% 68.13/68.53 Generated: 179766
% 68.13/68.53 Kept: 45844
% 68.13/68.53 Inuse: 860
% 68.13/68.53 Deleted: 771
% 68.13/68.53 Deletedinuse: 1
% 68.13/68.53
% 68.13/68.53 Resimplifying inuse:
% 68.13/68.53 Done
% 68.13/68.53
% 68.13/68.53
% 68.13/68.53 Intermediate Status:
% 68.13/68.53 Generated: 217525
% 68.13/68.53 Kept: 51368
% 68.13/68.53 Inuse: 880
% 68.13/68.53 Deleted: 771
% 68.13/68.53 Deletedinuse: 1
% 68.13/68.53
% 68.13/68.53 Resimplifying inuse:
% 68.13/68.53 Done
% 68.13/68.53
% 68.13/68.53
% 68.13/68.53 Intermediate Status:
% 68.13/68.53 Generated: 252238
% 68.13/68.53 Kept: 55569
% 68.13/68.54 Inuse: 885
% 68.13/68.54 Deleted: 771
% 68.13/68.54 Deletedinuse: 1
% 68.13/68.54
% 68.13/68.54 Resimplifying inuse:
% 68.13/68.54 Done
% 68.13/68.54
% 68.13/68.54 Resimplifying inuse:
% 68.13/68.54 Done
% 68.13/68.54
% 68.13/68.54
% 68.13/68.54 Intermediate Status:
% 68.13/68.54 Generated: 263781
% 68.13/68.54 Kept: 58657
% 68.13/68.54 Inuse: 895
% 68.13/68.54 Deleted: 771
% 68.13/68.54 Deletedinuse: 1
% 68.13/68.54
% 68.13/68.54 Resimplifying inuse:
% 68.13/68.54 Done
% 68.13/68.54
% 68.13/68.54
% 68.13/68.54 Intermediate Status:
% 68.13/68.54 Generated: 278873
% 68.13/68.54 Kept: 61489
% 68.13/68.54 Inuse: 900
% 68.13/68.54 Deleted: 771
% 68.13/68.54 Deletedinuse: 1
% 68.13/68.54
% 68.13/68.54 Resimplifying inuse:
% 68.13/68.54 Done
% 68.13/68.54
% 68.13/68.54 Resimplifying inuse:
% 68.13/68.54 Done
% 68.13/68.54
% 68.13/68.54
% 68.13/68.54 Intermediate Status:
% 68.13/68.54 Generated: 290803
% 68.13/68.54 Kept: 63743
% 68.13/68.54 Inuse: 925
% 68.13/68.54 Deleted: 771
% 68.13/68.54 Deletedinuse: 1
% 68.13/68.54
% 68.13/68.54 Resimplifying clauses:
% 68.13/68.54 Done
% 68.13/68.54
% 68.13/68.54 Resimplifying inuse:
% 68.13/68.54 Done
% 68.13/68.54
% 68.13/68.54 Resimplifying inuse:
% 68.13/68.54 Done
% 68.13/68.54
% 68.13/68.54
% 68.13/68.54 Intermediate Status:
% 68.13/68.54 Generated: 300809
% 68.13/68.54 Kept: 65791
% 68.13/68.54 Inuse: 945
% 68.13/68.54 Deleted: 949
% 68.13/68.54 Deletedinuse: 1
% 68.13/68.54
% 68.13/68.54 Resimplifying inuse:
% 68.13/68.54 Done
% 68.13/68.54
% 68.13/68.54 Resimplifying inuse:
% 68.13/68.54 Done
% 68.13/68.54
% 68.13/68.54
% 68.13/68.54 Intermediate Status:
% 68.13/68.54 Generated: 310255
% 68.13/68.54 Kept: 67894
% 68.13/68.54 Inuse: 980
% 68.13/68.54 Deleted: 949
% 68.13/68.54 Deletedinuse: 1
% 68.13/68.54
% 68.13/68.54
% 68.13/68.54 Intermediate Status:
% 68.13/68.54 Generated: 325209
% 68.13/68.54 Kept: 71026
% 68.13/68.54 Inuse: 995
% 68.13/68.54 Deleted: 949
% 68.13/68.54 Deletedinuse: 1
% 172.08/172.50
% 172.08/172.50 Resimplifying inuse:
% 172.08/172.50 Done
% 172.08/172.50
% 172.08/172.50 Resimplifying inuse:
% 172.08/172.50 Done
% 172.08/172.50
% 172.08/172.50
% 172.08/172.50 Intermediate Status:
% 172.08/172.50 Generated: 349317
% 172.08/172.50 Kept: 74330
% 172.08/172.50 Inuse: 1005
% 172.08/172.50 Deleted: 949
% 172.08/172.50 Deletedinuse: 1
% 172.08/172.50
% 172.08/172.50 Resimplifying inuse:
% 172.08/172.50 Done
% 172.08/172.50
% 172.08/172.50 Resimplifying inuse:
% 172.08/172.50 Done
% 172.08/172.50
% 172.08/172.50
% 172.08/172.50 Intermediate Status:
% 172.08/172.50 Generated: 358889
% 172.08/172.50 Kept: 76513
% 172.08/172.50 Inuse: 1035
% 172.08/172.50 Deleted: 949
% 172.08/172.50 Deletedinuse: 1
% 172.08/172.50
% 172.08/172.50 Resimplifying inuse:
% 172.08/172.50 Done
% 172.08/172.50
% 172.08/172.50 Resimplifying inuse:
% 172.08/172.50 Done
% 172.08/172.50
% 172.08/172.50
% 172.08/172.50 Intermediate Status:
% 172.08/172.50 Generated: 366566
% 172.08/172.50 Kept: 78547
% 172.08/172.50 Inuse: 1055
% 172.08/172.50 Deleted: 949
% 172.08/172.50 Deletedinuse: 1
% 172.08/172.50
% 172.08/172.50 Resimplifying inuse:
% 172.08/172.50 Done
% 172.08/172.50
% 172.08/172.50 Resimplifying inuse:
% 172.08/172.50 Done
% 172.08/172.50
% 172.08/172.50
% 172.08/172.50 Intermediate Status:
% 172.08/172.50 Generated: 376202
% 172.08/172.50 Kept: 80558
% 172.08/172.50 Inuse: 1079
% 172.08/172.50 Deleted: 949
% 172.08/172.50 Deletedinuse: 1
% 172.08/172.50
% 172.08/172.50 Resimplifying inuse:
% 172.08/172.50 Done
% 172.08/172.50
% 172.08/172.50
% 172.08/172.50 Intermediate Status:
% 172.08/172.50 Generated: 385762
% 172.08/172.50 Kept: 84775
% 172.08/172.50 Inuse: 1090
% 172.08/172.50 Deleted: 949
% 172.08/172.50 Deletedinuse: 1
% 172.08/172.50
% 172.08/172.50 Resimplifying inuse:
% 172.08/172.50 Done
% 172.08/172.50
% 172.08/172.50 Resimplifying clauses:
% 172.08/172.50 Done
% 172.08/172.50
% 172.08/172.50
% 172.08/172.50 Intermediate Status:
% 172.08/172.50 Generated: 392383
% 172.08/172.50 Kept: 88212
% 172.08/172.50 Inuse: 1095
% 172.08/172.50 Deleted: 1272
% 172.08/172.50 Deletedinuse: 1
% 172.08/172.50
% 172.08/172.50 Resimplifying inuse:
% 172.08/172.50 Done
% 172.08/172.50
% 172.08/172.50 Resimplifying inuse:
% 172.08/172.50 Done
% 172.08/172.50
% 172.08/172.50
% 172.08/172.50 Intermediate Status:
% 172.08/172.50 Generated: 413033
% 172.08/172.50 Kept: 91331
% 172.08/172.50 Inuse: 1115
% 172.08/172.50 Deleted: 1272
% 172.08/172.50 Deletedinuse: 1
% 172.08/172.50
% 172.08/172.50 Resimplifying inuse:
% 172.08/172.50 Done
% 172.08/172.50
% 172.08/172.50 Resimplifying inuse:
% 172.08/172.50 Done
% 172.08/172.50
% 172.08/172.50
% 172.08/172.50 Intermediate Status:
% 172.08/172.50 Generated: 427489
% 172.08/172.50 Kept: 93846
% 172.08/172.50 Inuse: 1155
% 172.08/172.50 Deleted: 1272
% 172.08/172.50 Deletedinuse: 1
% 172.08/172.50
% 172.08/172.50 Resimplifying inuse:
% 172.08/172.50 Done
% 172.08/172.50
% 172.08/172.50 Resimplifying inuse:
% 172.08/172.50 Done
% 172.08/172.50
% 172.08/172.50
% 172.08/172.50 Intermediate Status:
% 172.08/172.50 Generated: 435602
% 172.08/172.50 Kept: 95860
% 172.08/172.50 Inuse: 1161
% 172.08/172.50 Deleted: 1272
% 172.08/172.50 Deletedinuse: 1
% 172.08/172.50
% 172.08/172.50
% 172.08/172.50 Intermediate Status:
% 172.08/172.50 Generated: 443646
% 172.08/172.50 Kept: 97879
% 172.08/172.50 Inuse: 1165
% 172.08/172.50 Deleted: 1272
% 172.08/172.50 Deletedinuse: 1
% 172.08/172.50
% 172.08/172.50 Resimplifying inuse:
% 172.08/172.50 Done
% 172.08/172.50
% 172.08/172.50 Resimplifying inuse:
% 172.08/172.50 Done
% 172.08/172.50
% 172.08/172.50
% 172.08/172.50 Intermediate Status:
% 172.08/172.50 Generated: 457843
% 172.08/172.50 Kept: 100410
% 172.08/172.50 Inuse: 1185
% 172.08/172.50 Deleted: 1272
% 172.08/172.50 Deletedinuse: 1
% 172.08/172.50
% 172.08/172.50 Resimplifying inuse:
% 172.08/172.50 Done
% 172.08/172.50
% 172.08/172.50 Resimplifying inuse:
% 172.08/172.50 Done
% 172.08/172.50
% 172.08/172.50
% 172.08/172.50 Intermediate Status:
% 172.08/172.50 Generated: 471136
% 172.08/172.50 Kept: 102554
% 172.08/172.50 Inuse: 1205
% 172.08/172.50 Deleted: 1272
% 172.08/172.50 Deletedinuse: 1
% 172.08/172.50
% 172.08/172.50 Resimplifying inuse:
% 172.08/172.50 Done
% 172.08/172.50
% 172.08/172.50
% 172.08/172.50 Intermediate Status:
% 172.08/172.50 Generated: 481162
% 172.08/172.50 Kept: 105131
% 172.08/172.50 Inuse: 1215
% 172.08/172.50 Deleted: 1273
% 172.08/172.50 Deletedinuse: 2
% 172.08/172.50
% 172.08/172.50 Resimplifying inuse:
% 172.08/172.50 Done
% 172.08/172.50
% 172.08/172.50 Resimplifying clauses:
% 172.08/172.50 Done
% 172.08/172.50
% 172.08/172.50
% 172.08/172.50 Intermediate Status:
% 172.08/172.50 Generated: 488908
% 172.08/172.50 Kept: 107242
% 172.08/172.50 Inuse: 1220
% 172.08/172.50 Deleted: 1544
% 172.08/172.50 Deletedinuse: 2
% 172.08/172.50
% 172.08/172.50 Resimplifying inuse:
% 172.08/172.50 Done
% 172.08/172.50
% 172.08/172.50
% 172.08/172.50 Intermediate Status:
% 172.08/172.50 Generated: 496673
% 172.08/172.50 Kept: 109441
% 172.08/172.50 Inuse: 1225
% 172.08/172.50 Deleted: 1544
% 172.08/172.50 Deletedinuse: 2
% 172.08/172.50
% 172.08/172.50 Resimplifying inuse:
% 172.08/172.50 Done
% 172.08/172.50
% 172.08/172.50
% 172.08/172.50 Intermediate Status:
% 172.08/172.50 Generated: 508650
% 172.08/172.50 Kept: 112160
% 172.08/172.50 Inuse: 1235
% 172.08/172.50 Deleted: 1544
% 172.08/172.50 Deletedinuse: 2
% 172.08/172.50
% 172.08/172.50 Resimplifying inuse:
% 172.08/172.50 Done
% 172.08/172.50
% 172.08/172.50
% 172.08/172.50 Intermediate Status:
% 172.08/172.50 Generated: 519287
% 172.08/172.50 Kept: 114407
% 172.08/172.50 Inuse: 1240
% 172.08/172.50 Deleted: 1544
% 172.08/172.50 Deletedinuse: 2
% 172.08/172.50
% 172.08/172.50 Resimplifying inuse:
% 172.08/172.50 Done
% 172.08/172.50
% 172.08/172.50 Resimplifying inuse:
% 172.08/172.50 Done
% 172.08/172.50
% 172.08/172.50
% 172.08/172.50 Intermediate Status:
% 172.08/172.50 Generated: 528849
% 172.08/172.50 Kept: 116548
% 172.08/172.50 Inuse: 1260
% 172.08/172.50 Deleted: 1544
% 172.08/172.50 Deletedinuse: 2
% 172.08/172.50
% 172.08/172.50 Resimplifying inuse:
% 172.08/172.50 Done
% 172.08/172.50
% 172.08/172.50
% 172.08/172.50 Intermediate Status:
% 172.08/172.50 Generated: 536213
% 172.08/172.50 Kept: 118572
% 172.08/172.50 Inuse: 1275
% 172.08/172.50 Deleted: 1544
% 172.08/172.50 Deletedinuse: 2
% 172.08/172.50
% 172.08/172.50 Resimplifying inuse:
% 172.08/172.50 Done
% 172.08/172.50
% 172.08/172.50 Resimplifying inuse:
% 172.08/172.50 Done
% 172.08/172.50
% 172.08/172.50
% 172.08/172.50 Intermediate Status:
% 172.08/172.50 Generated: 545030
% 172.08/172.50 Kept: 120849
% 172.08/172.50 Inuse: 1295
% 172.08/172.50 Deleted: 1544
% 172.08/172.50 Deletedinuse: 2
% 172.08/172.50
% 172.08/172.50
% 172.08/172.50 Intermediate Status:
% 172.08/172.50 Generated: 552301
% 172.08/172.50 Kept: 122935
% 172.08/172.50 Inuse: 1300
% 172.08/172.50 Deleted: 1544
% 172.08/172.50 Deletedinuse: 2
% 172.08/172.50
% 172.08/172.50 Resimplifying inuse:
% 172.08/172.50 Done
% 172.08/172.50
% 172.08/172.50
% 172.08/172.50 Intermediate Status:
% 172.08/172.50 Generated: 559648
% 172.08/172.50 Kept: 125321
% 172.08/172.50 Inuse: 1305
% 172.08/172.50 Deleted: 1544
% 172.08/172.50 Deletedinuse: 2
% 172.08/172.50
% 172.08/172.50 Resimplifying inuse:
% 172.08/172.50 Done
% 172.08/172.50
% 172.08/172.50 Resimplifying clauses:
% 172.08/172.50 Done
% 172.08/172.50
% 172.08/172.50 Resimplifying inuse:
% 172.08/172.50 Done
% 172.08/172.50
% 172.08/172.50
% 172.08/172.50 Intermediate Status:
% 172.08/172.50 Generated: 571256
% 172.08/172.50 Kept: 127332
% 172.08/172.50 Inuse: 1339
% 172.08/172.50 Deleted: 1647
% 172.08/172.50 Deletedinuse: 2
% 172.08/172.50
% 172.08/172.50
% 172.08/172.50 Intermediate Status:
% 172.08/172.50 Generated: 594560
% 172.08/172.50 Kept: 131322
% 172.08/172.50 Inuse: 1340
% 172.08/172.50 Deleted: 1647
% 172.08/172.50 Deletedinuse: 2
% 172.08/172.50
% 172.08/172.50 Resimplifying inuse:
% 172.08/172.50 Done
% 172.08/172.50
% 172.08/172.50
% 172.08/172.50 Intermediate Status:
% 172.08/172.50 Generated: 619234
% 172.08/172.50 Kept: 135414
% 172.08/172.50 Inuse: 1345
% 172.08/172.50 Deleted: 1647
% 172.08/172.50 Deletedinuse: 2
% 172.08/172.50
% 172.08/172.50 Resimplifying inuse:
% 172.08/172.50 Done
% 172.08/172.50
% 172.08/172.50
% 172.08/172.50 Intermediate Status:
% 172.08/172.50 Generated: 630301
% 172.08/172.50 Kept: 138124
% 172.08/172.50 Inuse: 1360
% 172.08/172.50 Deleted: Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------