TSTP Solution File: SWW259+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW259+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Wed Jul 20 23:21:38 EDT 2022
% Result : Timeout 300.04s 300.46s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW259+1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n020.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 : Sun Jun 5 05:36:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.02/1.58 *** allocated 10000 integers for termspace/termends
% 1.02/1.58 *** allocated 10000 integers for clauses
% 1.02/1.58 *** allocated 10000 integers for justifications
% 1.02/1.58 *** allocated 15000 integers for termspace/termends
% 1.02/1.58 *** allocated 22500 integers for termspace/termends
% 1.02/1.58 *** allocated 33750 integers for termspace/termends
% 1.02/1.58 Bliksem 1.12
% 1.02/1.58
% 1.02/1.58
% 1.02/1.58 Automatic Strategy Selection
% 1.02/1.58
% 1.02/1.58 *** allocated 50625 integers for termspace/termends
% 1.02/1.58 *** allocated 75937 integers for termspace/termends
% 1.02/1.58 *** allocated 113905 integers for termspace/termends
% 1.02/1.58
% 1.02/1.58 Clauses:
% 1.02/1.58
% 1.02/1.58 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol2( Y ) ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, skol2( Y ),
% 1.02/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, skol2( X ), X ) }.
% 1.02/1.58 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), v_m____ ) }.
% 1.02/1.58 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.02/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_w____ ) ),
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, v_k____,
% 1.02/1.58 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), v_m____ ) ) ) }.
% 1.02/1.58 { ! v_k____ = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.58 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.02/1.58 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, X ) ), X ) =
% 1.02/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), T ),
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, X ) ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ),
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, Y ) ) ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, X ) ), T ), hAPP(
% 1.02/1.58 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, Y ) ), Z ) ) }.
% 1.02/1.58 { ! class_RealVector_Oreal__normed__div__algebra( X ), Y =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ) ) =
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal,
% 1.02/1.58 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 1.02/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.58 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.58 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.58 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ) ) }.
% 1.02/1.58 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.02/1.58 c_RealVector_Onorm__class_Onorm( X, Y ) ), ! Y =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.58 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless(
% 1.02/1.58 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.02/1.58 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 1.02/1.58 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.58 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ) ) = c_Groups_Oone__class_Oone( X
% 1.02/1.58 ) }.
% 1.02/1.58 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.02/1.58 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 1.02/1.58 c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.58 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.58 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 1.02/1.58 c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.58 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.02/1.58 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.02/1.58 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.02/1.58 ( X, Y, c_Groups_Oone__class_Oone( X ) ) }.
% 1.02/1.58 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.58 ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.02/1.58 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.58 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.58 ( X, Y, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless(
% 1.02/1.58 X, c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 1.02/1.58 ) ) }.
% 1.02/1.58 { ! v_a____ = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.02/1.58 { ! v_w____ = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.58 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.02/1.58 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.58 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.58 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.58 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 1.02/1.58 ), X ) ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.58 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 1.02/1.58 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 1.02/1.58 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.02/1.58 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 1.02/1.58 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.02/1.58 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.02/1.58 c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.58 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.58 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 1.02/1.58 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.58 X, Y, Z ) }.
% 1.02/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP
% 1.02/1.58 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) ), X ) =
% 1.02/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), hAPP
% 1.02/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.02/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) =
% 1.02/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y )
% 1.02/1.58 }.
% 1.02/1.58 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 1.02/1.58 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 1.02/1.58 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Z = Y,
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ) }.
% 1.02/1.58 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.58 , Y ) ) = Y }.
% 1.02/1.58 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.58 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.58 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.58 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.58 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.58 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.58 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.58 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.02/1.58 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.02/1.58 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.58 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.58 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.02/1.58 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.02/1.58 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.58 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.58 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.58 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 1.02/1.58 c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.58 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.58 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 1.02/1.58 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 1.02/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.58 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 1.02/1.58 ) ), T ), Y ) }.
% 1.02/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.02/1.58 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.02/1.58 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.58 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.02/1.58 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.58 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.58 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.58 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 1.02/1.58 ( X ) }.
% 1.02/1.58 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.02/1.58 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.02/1.58 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.02/1.58 .
% 1.02/1.58 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.02/1.58 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.02/1.58 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.58 tc_Nat_Onat ) }.
% 1.02/1.58 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.02/1.58 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.02/1.58 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 1.02/1.58 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 1.02/1.58 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.58 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.02/1.58 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.02/1.58 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.02/1.58 = c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.58 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.58 , Z ) = c_Rings_Oinverse__class_Oinverse( X, Y ), Z =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z
% 1.02/1.58 = Y }.
% 1.02/1.58 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.58 , Y ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 1.02/1.58 ( X ) }.
% 1.02/1.58 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.58 , c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse(
% 1.02/1.58 X, Y ) ) = Y }.
% 1.02/1.58 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.58 , ! c_Rings_Oinverse__class_Oinverse( X, Y ) =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.58 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.02/1.58 ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.58 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 1.02/1.58 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.58 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.58 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.58 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.02/1.58 Z ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.02/1.58 { ! class_Fields_Ofield__inverse__zero( X ), !
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Oone__class_Oone( X )
% 1.02/1.58 , Y = c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.58 { ! class_Fields_Ofield__inverse__zero( X ), ! Y =
% 1.02/1.58 c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y )
% 1.02/1.58 = c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.58 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.02/1.58 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.58 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP( hAPP
% 1.02/1.58 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ), Z = Y }.
% 1.02/1.58 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 1.02/1.58 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP(
% 1.02/1.58 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) }.
% 1.02/1.58 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP( hAPP
% 1.02/1.58 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), Z = Y }.
% 1.02/1.58 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 1.02/1.58 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP(
% 1.02/1.58 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) }.
% 1.02/1.58 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Z
% 1.02/1.58 ) ), Y ) }.
% 1.02/1.58 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.02/1.58 tc_Nat_Onat ) ) = Y }.
% 1.02/1.58 { ! c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) =
% 1.02/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.02/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.02/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) = X }.
% 1.02/1.58 { c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.58 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.02/1.58 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 1.02/1.58 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.58 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.02/1.58 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.02/1.58 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.58 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.02/1.58 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.02/1.58 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.58 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.02/1.58 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.02/1.58 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.58 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.02/1.58 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 1.02/1.58 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.58 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.02/1.58 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.58 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.02/1.58 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.02/1.58 ( X ) ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.58 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.58 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 1.02/1.58 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.02/1.58 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.02/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 1.02/1.58 .
% 1.02/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.02/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.02/1.58 .
% 1.02/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.58 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.02/1.58 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.02/1.58 ( X ) ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.58 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.02/1.58 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.02/1.58 ( X ) ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.58 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.02/1.58 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.58 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.58 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 1.02/1.58 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.02/1.58 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha1( X, Y, Z, T ),
% 1.02/1.58 alpha14( X, Y, Z, T ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha1( X, Y, Z, T ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha14( X, Y, Z, T ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.58 { ! alpha14( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.58 { ! alpha14( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 1.02/1.58 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha14( X, Y, Z, T ) }.
% 1.02/1.58 { ! alpha1( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 1.02/1.58 { ! alpha1( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 1.02/1.58 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha1( X, Y, Z, T ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha2( X, Y, Z, T ),
% 1.02/1.58 alpha15( X, Y, Z, T ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha2( X, Y, Z, T ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha15( X, Y, Z, T ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.58 { ! alpha15( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.58 { ! alpha15( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.02/1.58 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha15( X, Y, Z, T ) }.
% 1.02/1.58 { ! alpha2( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.02/1.58 { ! alpha2( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.02/1.58 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha2( X, Y, Z, T ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.58 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.58 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 1.02/1.58 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.02/1.58 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.58 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 1.02/1.58 .
% 1.02/1.58 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.58 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.58 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 1.02/1.58 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.58 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 1.02/1.58 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.02/1.58 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 1.02/1.58 ) }.
% 1.02/1.58 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.02/1.58 ) = c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.58 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.02/1.58 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.58 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.02/1.58 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.58 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.58 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.58 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.02/1.58 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.58 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.58 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.02/1.58 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.58 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.58 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.58 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 1.02/1.58 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.58 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 1.02/1.58 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.58 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.58 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.58 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.58 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.58 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 1.02/1.58 ( X ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 1.02/1.58 .
% 1.02/1.58 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.58 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.02/1.58 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.58 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.02/1.58 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.58 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 1.02/1.58 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 1.02/1.58 ( X ) ) }.
% 1.02/1.58 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.58 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.58 , Y ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.02/1.58 .
% 1.02/1.58 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.58 X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.58 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.58 , Y ) ) }.
% 1.02/1.58 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 1.02/1.58 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.02/1.58 , Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.58 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 1.02/1.58 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.58 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.02/1.58 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.02/1.58 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.02/1.58 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.58 , Z = c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse
% 1.02/1.58 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP(
% 1.02/1.58 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( X, Z ) ),
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.02/1.58 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.02/1.58 c_RealVector_Onorm__class_Onorm( X, Y ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.58 tc_RealDef_Oreal ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.58 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X, Y )
% 1.02/1.58 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.02/1.58 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.02/1.58 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.02/1.58 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 1.02/1.58 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.02/1.58 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.02/1.58 { ! class_Rings_Odivision__ring( X ), ! hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = c_Groups_Oone__class_Oone
% 1.02/1.58 ( X ), c_Rings_Oinverse__class_Oinverse( X, Z ) = Y }.
% 1.02/1.58 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.58 , c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 1.02/1.58 ) ), Z ) }.
% 1.02/1.58 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.58 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.58 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.58 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, U
% 1.02/1.58 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, T ) ) }.
% 1.02/1.58 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 1.02/1.58 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.02/1.58 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 1.02/1.58 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.02/1.58 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.58 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 1.02/1.58 tc_RealDef_Oreal ) ) }.
% 1.02/1.58 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 1.02/1.58 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oone__class_Oone( X ) ) =
% 1.02/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.02/1.58 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 1.02/1.58 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.02/1.58 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) }.
% 1.02/1.58 { ! class_RealVector_Oreal__normed__div__algebra( X ), !
% 1.02/1.58 class_Rings_Odivision__ring__inverse__zero( X ),
% 1.02/1.58 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Oinverse( X,
% 1.02/1.58 Y ) ) = c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal,
% 1.02/1.58 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.02/1.58 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.58 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.58 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.58 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.58 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.58 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.58 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.58 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.58 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.02/1.58 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.02/1.58 ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) ),
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.02/1.58 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.58 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.02/1.58 Y ) ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) ),
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.58 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.02/1.58 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.02/1.58 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.02/1.58 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.58 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.58 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ), X =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.02/1.58 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 1.02/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 1.02/1.58 tc_Nat_Onat, Z, Y ) ) }.
% 1.02/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 1.02/1.58 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.58 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 1.02/1.58 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 1.02/1.58 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.02/1.58 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 1.02/1.58 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 1.02/1.58 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.02/1.58 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 1.02/1.58 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.02/1.58 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.02/1.58 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.58 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.02/1.58 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.02/1.58 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 1.02/1.58 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 1.02/1.58 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.58 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.02/1.58 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 1.02/1.58 ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.58 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.02/1.58 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 1.02/1.58 ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.58 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.58 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.58 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.02/1.58 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.02/1.58 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.58 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.58 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.02/1.58 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.58 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.02/1.58 { c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 1.02/1.58 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), v_w____ ), v_k____ )
% 1.02/1.58 ), v_a____ ) ) = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.02/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ) ), X ) =
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.02/1.58 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.02/1.58 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.02/1.58 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.02/1.58 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.58 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 1.02/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 1.02/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 1.02/1.58 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 1.02/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.02/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 1.02/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.58 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 1.02/1.58 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 1.02/1.58 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 1.02/1.58 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 1.02/1.58 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.02/1.58 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 1.02/1.58 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 1.02/1.58 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 1.02/1.58 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.58 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.02/1.58 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.02/1.58 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.58 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.02/1.58 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.02/1.58 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.58 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.02/1.58 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 1.02/1.58 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.02/1.58 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.02/1.58 T, Y ), Z = Y }.
% 1.02/1.58 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 1.02/1.58 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.02/1.58 T, Y ) }.
% 1.02/1.58 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.02/1.58 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.02/1.58 Y, Z ), T = Y }.
% 1.02/1.58 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 1.02/1.58 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.02/1.58 Y, Z ) }.
% 1.02/1.58 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.58 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 1.02/1.58 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 1.02/1.58 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.02/1.58 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.02/1.58 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.02/1.58 T, Y ), Z = Y }.
% 1.02/1.58 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 1.02/1.58 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.02/1.58 T, Y ), Z = Y }.
% 1.02/1.58 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.02/1.58 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 1.02/1.58 Y, T ), Z = Y }.
% 1.02/1.58 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 1.02/1.58 c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.58 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 1.02/1.58 c_Groups_Oone__class_Oone( X ) = Y }.
% 1.02/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 1.02/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.02/1.58 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.02/1.58 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.58 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.02/1.58 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.02/1.58 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.02/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.02/1.58 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 1.02/1.58 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 1.02/1.58 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.02/1.58 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.02/1.58 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.02/1.58 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.02/1.58 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.02/1.58 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.02/1.58 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.58 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.02/1.58 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.02/1.58 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 1.02/1.58 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.02/1.58 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 1.02/1.58 ( X, T, Y ) }.
% 1.02/1.58 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.58 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.02/1.58 , Y, Z ) ) }.
% 1.02/1.58 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.02/1.58 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 1.02/1.58 ( X, Z, Y ) }.
% 1.02/1.58 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.58 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.02/1.58 , T, Y ) ) }.
% 1.02/1.58 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.58 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 1.02/1.58 , Y, T ) ) }.
% 1.02/1.58 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.58 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.02/1.58 , T, Y ) ) }.
% 1.02/1.58 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.58 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.58 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 1.02/1.58 , T ) ) }.
% 1.02/1.58 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 1.02/1.58 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 1.02/1.58 ( X, Z, Y ) }.
% 1.02/1.58 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.02/1.58 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 1.02/1.58 ( X, Z, Y ) }.
% 1.02/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.58 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.58 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.02/1.58 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.02/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.58 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.02/1.58 ) }.
% 1.02/1.58 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.02/1.58 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.02/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.58 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.02/1.58 ), ! U = T }.
% 1.02/1.58 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.02/1.58 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.02/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.58 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.02/1.58 ), ! Z = Y }.
% 1.02/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.02/1.58 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.58 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 1.02/1.58 ) ), Z ) }.
% 1.02/1.58 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.02/1.58 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.02/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.58 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.02/1.58 ), U = Z, T = Y }.
% 1.02/1.58 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.02/1.58 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.02/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.58 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.02/1.58 ) }.
% 1.02/1.58 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.02/1.58 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.02/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.58 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.02/1.58 ) }.
% 1.02/1.58 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.02/1.58 = Y }.
% 1.02/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.02/1.58 = Y }.
% 1.02/1.58 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.02/1.58 = Y }.
% 1.02/1.58 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.02/1.58 = Y }.
% 1.02/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.02/1.58 = Y }.
% 1.02/1.58 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.02/1.58 = Y }.
% 1.02/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.02/1.58 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.02/1.58 tc_Nat_Onat ) ) = Y }.
% 1.02/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.58 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 1.02/1.58 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.02/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.58 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 1.02/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.02/1.58 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 1.02/1.58 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.02/1.58 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.58 { c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 1.02/1.58 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol3 ), v_k____ ) )
% 1.02/1.58 , v_a____ ) ) = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.58 { c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex,
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 1.02/1.58 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), v_w____ ), v_k____ )
% 1.02/1.58 ), v_a____ ) ), c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) =
% 1.02/1.58 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ),
% 1.02/1.58 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) }.
% 1.02/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 1.02/1.58 hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), v_w____ ),
% 1.02/1.58 v_k____ ) ), v_a____ ) = c_Groups_Ouminus__class_Ouminus(
% 1.02/1.58 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) }
% 1.02/1.58 .
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.58 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.02/1.58 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.58 tc_Nat_Onat ), Y ) }.
% 1.02/1.58 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.58 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 1.02/1.58 ), X ) ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.58 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.58 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 1.02/1.58 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.58 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.02/1.58 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 1.02/1.58 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.58 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.02/1.58 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 1.02/1.58 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.58 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 1.02/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 1.02/1.58 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.58 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 1.02/1.58 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.02/1.58 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 1.02/1.58 X, Y ) }.
% 1.02/1.58 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.02/1.58 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 1.02/1.58 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.02/1.58 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 1.02/1.58 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 1.02/1.58 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 1.02/1.58 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 1.02/1.58 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.02/1.58 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 1.02/1.58 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 1.02/1.58 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 1.02/1.58 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 1.02/1.58 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.58 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 1.02/1.58 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.58 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.02/1.58 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.02/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Oplus__class_Oplus(
% 1.02/1.58 X, Z, Y ) }.
% 1.02/1.58 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.02/1.58 ) = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus(
% 1.02/1.58 X, Y ) ) }.
% 1.02/1.58 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, Z
% 1.02/1.58 , Y ) = c_Groups_Oplus__class_Oplus( X, Z,
% 1.02/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.58 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z, Y )
% 1.02/1.58 = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.58 , Y ) ) }.
% 1.02/1.58 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.58 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 1.02/1.58 c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 1.02/1.58 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 1.02/1.58 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.02/1.58 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.02/1.58 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 1.02/1.58 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.58 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 1.02/1.58 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.02/1.58 ) }.
% 1.02/1.58 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.02/1.58 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.02/1.58 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 1.02/1.58 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.58 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.02/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.02/1.58 = Y }.
% 1.02/1.58 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 1.02/1.58 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 1.02/1.58 ) }.
% 1.02/1.58 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.02/1.58 ) }.
% 1.02/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.02/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 1.02/1.58 ( X ) }.
% 1.02/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.58 , Y ) }.
% 1.02/1.58 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 1.02/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 1.02/1.58 = Y }.
% 1.02/1.58 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 1.02/1.58 ) }.
% 1.02/1.58 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.58 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.02/1.58 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.58 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.02/1.58 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 1.02/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 1.02/1.58 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 1.02/1.58 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.02/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 1.02/1.58 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 1.02/1.58 ( X, Y ), Z ) }.
% 1.02/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.02/1.58 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 1.02/1.58 ( X, Z ), Y ) }.
% 1.02/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.58 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 1.02/1.58 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.02/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.58 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 1.02/1.58 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 1.02/1.58 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 1.02/1.58 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 1.02/1.58 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.58 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.02/1.58 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 1.02/1.58 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.58 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 1.02/1.58 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.02/1.58 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 1.02/1.58 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.02/1.58 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 1.02/1.58 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.02/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 1.02/1.58 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.02/1.58 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 1.02/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 1.02/1.58 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.02/1.58 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.02/1.58 ( X, Y ) ) }.
% 1.02/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 1.02/1.58 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 1.02/1.58 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.02/1.58 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.58 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.02/1.58 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.58 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 1.02/1.58 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 1.02/1.58 ) ), Y ) }.
% 1.02/1.58 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 1.02/1.58 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.02/1.58 ( X, Y ) ) }.
% 1.02/1.58 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.58 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.58 Z, Y ) ) = Y }.
% 1.02/1.58 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 1.02/1.58 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.02/1.58 Y ) ) = Y }.
% 1.02/1.58 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.58 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 1.02/1.58 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.02/1.58 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.02/1.58 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.58 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 1.02/1.58 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.02/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.58 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.02/1.58 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 1.02/1.58 Y ) ) = c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 1.02/1.58 ( X, Y, Z ) ) }.
% 1.02/1.58 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.02/1.58 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ouminus__class_Ouminus( X, Y
% 1.02/1.58 ) ) = c_RealVector_Onorm__class_Onorm( X, Y ) }.
% 1.02/1.58 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.58 Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.02/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.58 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 1.02/1.58 ( X ) ) }.
% 1.02/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.02/1.58 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.02/1.58 , Z, Y ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.58 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 1.02/1.58 .
% 1.02/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.58 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.02/1.58 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.02/1.58 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.58 , Y ) }.
% 1.02/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.02/1.58 , Y ) }.
% 1.02/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.02/1.58 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.02/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.02/1.58 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.02/1.58 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.58 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 1.02/1.58 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 1.02/1.58 ( X, Z ) }.
% 1.02/1.58 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.58 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.58 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 1.02/1.58 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.58 Z ) = Y }.
% 1.02/1.58 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.58 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.58 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.58 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.58 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 1.02/1.58 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 1.02/1.58 ( X, Y ) }.
% 1.02/1.58 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.02/1.58 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.58 X ) }.
% 1.02/1.58 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.02/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.58 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.02/1.58 Z ) ), U ), T ) = Y }.
% 1.02/1.58 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.02/1.58 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.02/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.58 ( X ), Z ), U ), Y ) }.
% 1.02/1.58 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.02/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.58 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.02/1.58 W ) ), U ), Y ) }.
% 1.02/1.58 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.02/1.58 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.02/1.58 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.02/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.58 ( X ), Z ), U ), Y ) }.
% 1.02/1.58 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.02/1.58 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.02/1.58 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.02/1.58 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.02/1.58 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 1.02/1.58 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 1.02/1.58 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 1.02/1.58 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.02/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.58 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 1.02/1.58 Z ) ), Y ) ) }.
% 1.02/1.58 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 1.02/1.58 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 1.02/1.58 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 1.02/1.58 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 1.02/1.58 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.58 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.58 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 1.02/1.58 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 1.02/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 1.02/1.58 c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.58 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 1.02/1.58 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.02/1.58 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) ), Y
% 1.02/1.58 ) }.
% 1.02/1.58 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.58 , c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.58 , Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.02/1.58 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.02/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.58 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.02/1.58 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.02/1.58 X, W, Z ) ), U ), T ), Y ) }.
% 1.02/1.58 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.02/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.58 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.02/1.58 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.02/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.58 ( X ), Z ), U ), Y ) ) }.
% 1.02/1.58 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.02/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.58 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 1.02/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 1.02/1.58 ( X, Z, W ) ), U ), Y ) ) }.
% 1.02/1.58 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 1.02/1.58 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.02/1.58 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.58 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.58 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.02/1.58 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 1.02/1.58 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 1.02/1.58 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.02/1.58 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 1.02/1.58 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 1.02/1.58 .
% 1.02/1.58 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.58 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X
% 1.02/1.58 , c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.02/1.58 Y ) ), c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ),
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.02/1.58 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.02/1.58 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.58 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.02/1.58 { alpha23( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 1.02/1.58 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.02/1.58 { alpha23( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 1.02/1.58 ( X, Y ), Z ) ) }.
% 1.02/1.58 { ! alpha23( X, Y, Z ), alpha24( X, Y, Z ), Z = Y }.
% 1.02/1.58 { ! alpha23( X, Y, Z ), alpha24( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 1.02/1.58 ) ) }.
% 1.02/1.58 { ! alpha24( X, Y, Z ), alpha23( X, Y, Z ) }.
% 1.02/1.58 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha23( X, Y, Z ) }.
% 1.02/1.58 { ! alpha24( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 1.02/1.58 }.
% 1.02/1.58 { ! alpha24( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 1.02/1.58 X, Y ), Z ) ), alpha24( X, Y, Z ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 1.02/1.58 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.02/1.58 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 1.02/1.58 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 1.02/1.58 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 1.02/1.58 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 1.02/1.58 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 1.02/1.58 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.58 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.02/1.58 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 1.02/1.58 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.02/1.58 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 1.02/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 1.02/1.58 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 1.02/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.58 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.58 tc_Nat_Onat ), X ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.58 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 1.02/1.58 .
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.58 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.58 tc_Nat_Onat ), X ) }.
% 1.02/1.58 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.58 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.58 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.58 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.02/1.58 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.58 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 1.02/1.58 ( tc_Nat_Onat ) ) = X }.
% 1.02/1.58 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.58 tc_Nat_Onat ), X ) = X }.
% 1.02/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.58 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.58 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.58 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.58 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.02/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.02/1.58 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.02/1.58 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.02/1.58 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.02/1.58 .
% 1.02/1.58 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.02/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 1.02/1.58 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.58 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.02/1.58 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.02/1.58 .
% 1.02/1.58 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.02/1.58 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.02/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 1.02/1.58 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.58 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.02/1.58 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 1.02/1.58 .
% 1.02/1.58 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.02/1.58 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 1.02/1.58 , X ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.58 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 1.02/1.58 .
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.58 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 1.02/1.58 .
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.02/1.58 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 1.02/1.58 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.58 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 1.02/1.58 .
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.02/1.58 ( tc_Nat_Onat, Y, X ), X ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.02/1.58 ( tc_Nat_Onat, Y, X ), Y ) }.
% 1.02/1.58 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 1.02/1.58 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 1.02/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.02/1.58 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.58 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 1.02/1.58 tc_Nat_Onat ) }.
% 1.02/1.58 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.58 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 1.02/1.58 tc_Nat_Onat ) }.
% 1.02/1.58 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.02/1.58 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.58 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.02/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.02/1.58 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.02/1.58 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 1.02/1.58 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.02/1.58 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 1.02/1.58 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.02/1.58 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.02/1.58 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 1.02/1.58 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.02/1.58 , Y ), X ) }.
% 1.02/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.58 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.58 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.58 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.58 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.02/1.58 tc_Nat_Onat, Y, X ) ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.58 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.02/1.58 tc_Nat_Onat, Y, X ) ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.58 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.02/1.58 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.58 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.02/1.58 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.58 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.58 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.58 Y ), X ) ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.58 tc_Nat_Onat ), Z ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.58 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 1.02/1.58 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.58 tc_Nat_Onat ), Y ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.58 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 1.02/1.58 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.58 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.58 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.58 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.58 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.58 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.58 tc_Nat_Onat ), X ), Y ) }.
% 1.02/1.58 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.58 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X
% 1.02/1.58 , c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( X, Z ) ) =
% 1.02/1.58 c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.02/1.58 Y ) ), c_Groups_Ominus__class_Ominus( X, Y, Z ) ) ),
% 1.02/1.58 c_Rings_Oinverse__class_Oinverse( X, Z ) ) ) }.
% 1.02/1.58 { c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, Y, X ) =
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y,
% 1.02/1.58 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, X ) ) }.
% 1.02/1.58 { X = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), Y =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 1.02/1.58 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex
% 1.02/1.58 , c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 1.02/1.58 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), X ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol4( X, Y ) ), Y )
% 1.02/1.58 ) ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.58 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 1.02/1.58 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 1.02/1.58 ) ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.58 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.02/1.58 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 1.02/1.58 ) ) }.
% 1.02/1.58 { ! c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) =
% 1.02/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, X,
% 1.02/1.58 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) ),
% 1.02/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.02/1.58 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, X,
% 1.02/1.58 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) ),
% 1.02/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, X, c_Complex_Oii ) ),
% 1.02/1.58 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.02/1.58 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, X, c_Complex_Oii ) )
% 1.02/1.58 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.02/1.58 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 1.02/1.58 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ) ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.02/1.58 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) =
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 1.02/1.58 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) }.
% 1.02/1.58 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) =
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 1.02/1.58 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) }.
% 1.02/1.58 { ! c_Complex_Oii = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.02/1.58 { ! c_Complex_Oii = c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 1.02/1.58 { c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, c_Complex_Oii ) =
% 1.02/1.58 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, c_Complex_Oii ) }.
% 1.02/1.58 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.58 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.58 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 1.02/1.58 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.58 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.02/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.58 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.02/1.58 ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.58 ( tc_Nat_Onat, Y, Z ), X ) }.
% 1.02/1.58 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.58 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 1.02/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 1.02/1.58 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.58 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 1.02/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 1.02/1.58 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.58 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.02/1.58 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.02/1.58 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.58 tc_Nat_Onat, Y, X ), Y ) = X }.
% 1.02/1.58 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.58 tc_Nat_Onat, Y, X ), X ) = Y }.
% 1.02/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.02/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.02/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 1.02/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.58 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.58 ( tc_Nat_Onat, Y, X ), Y ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.58 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.58 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 1.02/1.58 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.02/1.58 c_Complex_Oii ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.58 tc_Complex_Ocomplex ), c_Complex_Oii ), X ) ) =
% 1.02/1.58 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, X ) }.
% 1.02/1.58 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.02/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 1.02/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.58 tc_Nat_Onat, Z, X ), Y ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.02/1.58 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 1.02/1.58 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 1.02/1.58 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 1.02/1.58 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y = X }.
% 1.02/1.58 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 1.02/1.58 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.02/1.58 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 1.02/1.58 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) }.
% 1.02/1.58 { ! X = c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ),
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.02/1.58 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.02/1.58 , alpha3( X, Y, Z ) }.
% 1.02/1.58 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.02/1.58 , alpha16( X, Y, Z ) }.
% 1.02/1.58 { ! alpha3( X, Y, Z ), ! alpha16( X, Y, Z ), hBOOL( hAPP( Z,
% 1.02/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.02/1.58 { ! alpha16( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.02/1.58 T ), hBOOL( hAPP( Z, T ) ) }.
% 1.02/1.58 { ! hBOOL( hAPP( Z, skol5( T, U, Z ) ) ), alpha16( X, Y, Z ) }.
% 1.02/1.58 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol5( X, Y, Z ) ),
% 1.02/1.58 alpha16( X, Y, Z ) }.
% 1.02/1.58 { ! alpha3( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 1.02/1.58 , hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.02/1.58 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha3( X, Y, Z ) }.
% 1.02/1.58 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha3
% 1.02/1.58 ( X, Y, Z ) }.
% 1.02/1.58 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.02/1.58 , ! alpha4( X, Y, Z ) }.
% 1.02/1.58 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.02/1.58 , ! alpha17( X, Y, Z ) }.
% 1.02/1.58 { alpha4( X, Y, Z ), alpha17( X, Y, Z ), hBOOL( hAPP( Z,
% 1.02/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.02/1.58 { ! alpha17( X, Y, Z ), ! hBOOL( hAPP( Z, skol6( T, U, Z ) ) ) }.
% 1.02/1.58 { ! alpha17( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.02/1.58 skol6( X, Y, Z ) ) }.
% 1.02/1.58 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 1.02/1.58 ) ), alpha17( X, Y, Z ) }.
% 1.02/1.58 { ! alpha4( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }
% 1.02/1.58 .
% 1.02/1.58 { ! alpha4( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 1.02/1.58 tc_Nat_Onat ) ) ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha4( X, Y, Z ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.58 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.58 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 1.02/1.58 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 1.02/1.58 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.02/1.58 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 1.02/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.02/1.58 c_Complex_Oii ), c_Complex_Oii ) = c_Groups_Ouminus__class_Ouminus(
% 1.02/1.58 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) }
% 1.02/1.58 .
% 1.02/1.58 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 1.02/1.58 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.02/1.58 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.58 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.58 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 1.02/1.58 ( tc_Nat_Onat ) ) ), X ) ) }.
% 1.02/1.58 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 1.02/1.58 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.02/1.58 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 1.02/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 1.02/1.58 ( tc_Nat_Onat ) ) ) ) }.
% 1.02/1.58 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 1.02/1.58 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 1.02/1.58 c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.58 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.02/1.58 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 1.02/1.58 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 1.02/1.58 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.58 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 1.02/1.58 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 1.02/1.58 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 1.02/1.58 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 1.02/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.58 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.58 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.58 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.02/1.58 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.58 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.02/1.58 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 1.02/1.58 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus(
% 1.02/1.58 X, U, Z ), c_Groups_Ominus__class_Ominus( X, T, Y ) ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.02/1.58 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.02/1.58 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Ouminus__class_Ouminus
% 1.02/1.58 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.58 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.58 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol7( Z, T ) ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.58 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol7( X, Y ) ), X ) =
% 1.02/1.58 Y }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.58 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol8( Z, T ) ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.58 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol8( X, Y ) ), X ) =
% 1.02/1.58 Y }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.58 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), ! hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), X ) = Y, Z = skol8
% 1.02/1.58 ( X, Y ) }.
% 1.02/1.58 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex
% 1.02/1.58 , v_pa____ ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, v_k____,
% 1.02/1.58 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.02/1.58 { c_Complex_Oexpi( c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X )
% 1.02/1.58 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.02/1.58 c_Complex_Oexpi( Y ) ), c_Complex_Oexpi( X ) ) }.
% 1.02/1.58 { c_Complex_Oexpi( c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) =
% 1.02/1.58 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 1.02/1.58 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.58 tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ),
% 1.02/1.58 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 1.02/1.58 v_pa____ ) ) }.
% 1.02/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.02/1.58 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 1.02/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 1.02/1.58 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 1.02/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 1.02/1.58 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 1.02/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.02/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.02/1.58 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 1.02/1.58 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.02/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.02/1.58 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 1.02/1.58 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.02/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 1.02/1.58 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.02/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.02/1.58 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.02/1.58 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 1.02/1.58 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.58 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.58 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 1.02/1.58 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.58 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.58 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 1.02/1.58 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.58 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 1.02/1.58 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 1.02/1.58 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.58 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 1.02/1.58 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 1.02/1.58 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.02/1.58 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.58 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.02/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 1.02/1.58 { ! class_Groups_Ozero( X ), !
% 1.02/1.58 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.58 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.58 tc_Polynomial_Opoly( X ) ),
% 1.02/1.58 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.58 { c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 1.02/1.58 v_q____ ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 1.02/1.58 tc_Complex_Ocomplex, v_pa____ ) }.
% 1.02/1.58 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, v_k____,
% 1.02/1.58 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) =
% 1.02/1.58 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 1.02/1.58 c_Polynomial_OpCons( tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(
% 1.02/1.58 tc_Complex_Ocomplex ), c_Polynomial_Omonom( tc_Complex_Ocomplex, v_a____
% 1.02/1.58 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, v_k____,
% 1.02/1.58 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) ) }.
% 1.02/1.58 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), v_c____ ) =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.58 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.58 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.02/1.58 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP
% 1.02/1.58 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.02/1.58 Y ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.02/1.58 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 1.02/1.58 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 1.02/1.58 tc_Complex_Ocomplex, v_p ) ) }.
% 1.02/1.58 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 1.02/1.58 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 1.02/1.58 tc_Complex_Ocomplex, v_pa____ ) ) }.
% 1.02/1.58 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.02/1.58 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), v_c____ ) ),
% 1.02/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.02/1.58 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), X ) ) ) }.
% 1.02/1.58 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) =
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.02/1.58 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ), X ) = hAPP(
% 1.02/1.58 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ),
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_c____, X ) ) }.
% 1.02/1.58 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.02/1.58 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.02/1.58 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 1.02/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.02/1.58 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), X ) ) ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ),
% 1.02/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_w____ ) ),
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.58 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.02/1.58 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_s____ ), X ) ), v_m____ ) }.
% 1.02/1.58 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), v_c____ ) =
% 1.02/1.58 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) }.
% 1.02/1.58 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.02/1.58 X ) ) }.
% 1.02/1.58 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.58 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 1.02/1.58 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 1.02/1.58 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 1.02/1.58 tc_Complex_Ocomplex, v_q____ ) ) }.
% 1.02/1.58 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 1.02/1.58 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 1.02/1.58 tc_Complex_Ocomplex, v_q____ ) ) }.
% 1.02/1.58 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 1.02/1.58 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 1.02/1.58 tc_Complex_Ocomplex, c_Polynomial_OpCons( tc_Complex_Ocomplex,
% 1.02/1.58 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), c_Polynomial_Omonom(
% 1.02/1.58 tc_Complex_Ocomplex, v_a____, c_Groups_Ominus__class_Ominus( tc_Nat_Onat
% 1.02/1.58 , v_k____, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) ) ) }.
% 1.02/1.58 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.58 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 1.02/1.58 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.02/1.58 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.02/1.58 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 1.02/1.58 ( tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 1.02/1.58 .
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.02/1.58 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 1.02/1.58 ( tc_Int_Oint ) ) ) }.
% 1.02/1.58 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.02/1.58 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Z ) =
% 1.02/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, c_Nat_OSuc(
% 1.02/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) =
% 1.02/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.58 tc_Nat_Onat, Z, Y ), c_Nat_OSuc( X ) ) }.
% 1.02/1.58 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 1.02/1.58 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 1.02/1.58 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) }.
% 1.02/1.58 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) =
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 1.02/1.58 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 1.02/1.58 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.02/1.58 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.02/1.58 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 1.02/1.58 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 1.02/1.58 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 1.02/1.58 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.58 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 1.02/1.58 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__semidom( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.58 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.58 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.02/1.58 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.02/1.58 X ), Y ), Z = Y }.
% 1.02/1.58 { ! class_Rings_Olinordered__semidom( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 1.02/1.58 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.02/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.02/1.58 ), X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.58 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.02/1.58 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.02/1.58 ), X ) ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.02/1.58 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) }.
% 1.02/1.58 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.02/1.58 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.58 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.02/1.58 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.58 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.02/1.58 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.02/1.58 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.02/1.58 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.02/1.58 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.02/1.58 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.02/1.58 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.02/1.58 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.58 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.02/1.58 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.02/1.58 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.02/1.58 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.02/1.58 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.02/1.58 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.02/1.58 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.58 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.02/1.58 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.58 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.58 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.02/1.58 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.02/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.58 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.02/1.58 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.58 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.58 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.02/1.58 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X = Y }
% 1.02/1.58 .
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y,
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.58 { ! X = c_Nat_OSuc( X ) }.
% 1.02/1.58 { ! c_Nat_OSuc( X ) = X }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 1.02/1.58 .
% 1.02/1.58 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 1.02/1.58 ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.02/1.58 { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 1.02/1.58 , c_Nat_OSuc( X ) ) }.
% 1.02/1.58 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 1.02/1.58 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 1.02/1.58 c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 1.02/1.58 }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 1.02/1.58 c_Nat_OSuc( X ) ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 1.02/1.58 ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.58 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.02/1.58 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 1.02/1.58 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 1.02/1.58 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 1.02/1.58 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 1.02/1.58 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.02/1.58 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.02/1.58 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 1.02/1.58 .
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.02/1.58 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 1.02/1.58 .
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.02/1.58 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.02/1.58 tc_Int_Oint ) ), X ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.58 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.02/1.58 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.02/1.58 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.02/1.58 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.02/1.58 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.02/1.58 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.02/1.58 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 1.02/1.58 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.58 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.02/1.58 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 1.02/1.58 }.
% 1.02/1.58 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.02/1.59 tc_Int_Oint ) ), X ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.02/1.59 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 1.02/1.59 = X }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.02/1.59 tc_Int_Oint ) ) ) }.
% 1.02/1.59 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.02/1.59 tc_Int_Oint ) ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.02/1.59 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 1.02/1.59 }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.02/1.59 tc_Int_Oint ) ) ) }.
% 1.02/1.59 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 1.02/1.59 ( tc_Int_Oint ) ) = X }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.59 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Int_Oint ), X ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.59 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.59 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 1.02/1.59 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Int_Oint ), X ) = X }.
% 1.02/1.59 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.02/1.59 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.02/1.59 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.02/1.59 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 1.02/1.59 ( tc_Int_Oint ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 1.02/1.59 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 1.02/1.59 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.02/1.59 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 1.02/1.59 .
% 1.02/1.59 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 1.02/1.59 .
% 1.02/1.59 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 1.02/1.59 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.02/1.59 X ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.02/1.59 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 1.02/1.59 }.
% 1.02/1.59 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ouminus__class_Ouminus
% 1.02/1.59 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.02/1.59 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.02/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 1.02/1.59 ( X, Z ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.02/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.59 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 1.02/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.59 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.59 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 1.02/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.59 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.02/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.59 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.59 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.02/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.02/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.02/1.59 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.02/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 1.02/1.59 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.02/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.59 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.59 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 1.02/1.59 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.59 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 1.02/1.59 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.59 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.59 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 1.02/1.59 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.59 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.59 ( tc_Nat_Onat, Z, Y ), X ) }.
% 1.02/1.59 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.02/1.59 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.59 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.59 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), ! Y = X }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), Y = X,
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), Y = X }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 1.02/1.59 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol9( X, Y ) ) }.
% 1.02/1.59 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.02/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 1.02/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 1.02/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ),
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.59 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.02/1.59 ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! X = Z,
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 1.02/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ),
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__semidom( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone
% 1.02/1.59 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ), Y ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__semidom( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.02/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 1.02/1.59 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.59 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.59 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.59 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 1.02/1.59 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless__eq(
% 1.02/1.59 tc_Nat_Onat, Z, Y ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ),
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) ) = hAPP
% 1.02/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( X ), T ), c_Groups_Ominus__class_Ominus(
% 1.02/1.59 tc_Nat_Onat, Y, Z ) ) ), T ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__ring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP(
% 1.02/1.59 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.02/1.59 c_Polynomial_Omonom( X, c_Groups_Oone__class_Oone( X ), T ) ), Z ) ), Y )
% 1.02/1.59 = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( c_Polynomial_Opoly(
% 1.02/1.59 X, Z ), Y ) ) }.
% 1.02/1.59 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 1.02/1.59 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 1.02/1.59 ) ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 1.02/1.59 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha5( X, Y
% 1.02/1.59 , Z ), alpha18( X, Y, Z ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha5( X, Y, Z ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha18( X, Y, Z ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.59 { ! alpha18( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.59 { ! alpha18( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.02/1.59 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ) ), alpha18( X, Y, Z ) }.
% 1.02/1.59 { ! alpha5( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.02/1.59 { ! alpha5( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.59 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ), Y ), alpha5( X, Y, Z ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.02/1.59 ( X ) ), alpha6( X, Y, Z ), alpha19( X, Y, Z ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha6( X, Y, Z ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.02/1.59 ( X ) ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha19( X, Y, Z ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.02/1.59 ( X ) ) }.
% 1.02/1.59 { ! alpha19( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.59 { ! alpha19( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.02/1.59 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.02/1.59 ( X ), Y ), alpha19( X, Y, Z ) }.
% 1.02/1.59 { ! alpha6( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.02/1.59 { ! alpha6( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.59 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ) ), alpha6( X, Y, Z ) }.
% 1.02/1.59 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.02/1.59 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.59 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.59 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.59 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.59 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.59 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.02/1.59 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.02/1.59 ( X ) ) }.
% 1.02/1.59 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.59 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.59 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.02/1.59 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.59 { ! class_Rings_Oordered__semiring( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.02/1.59 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.02/1.59 { ! class_Rings_Oordered__semiring( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.02/1.59 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.59 { ! class_Rings_Oordered__comm__semiring( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.02/1.59 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.59 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.59 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.59 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.02/1.59 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.59 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.59 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.02/1.59 { ! class_Rings_Oordered__semiring( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.02/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.02/1.59 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.02/1.59 { ! class_Rings_Oordered__semiring( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.02/1.59 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.02/1.59 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.59 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.59 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.02/1.59 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.59 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.59 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.59 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.02/1.59 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.59 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.02/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.59 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.59 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.02/1.59 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.02/1.59 ( X ) ) }.
% 1.02/1.59 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.59 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.59 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.59 ) }.
% 1.02/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.59 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.02/1.59 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 1.02/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 1.02/1.59 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.59 ) }.
% 1.02/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.59 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 1.02/1.59 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.59 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.02/1.59 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 1.02/1.59 ) }.
% 1.02/1.59 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.02/1.59 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 1.02/1.59 .
% 1.02/1.59 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.02/1.59 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.02/1.59 .
% 1.02/1.59 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.02/1.59 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 1.02/1.59 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.59 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 1.02/1.59 Y, Z ) ) }.
% 1.02/1.59 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 1.02/1.59 Z, Y ) ) }.
% 1.02/1.59 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.59 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 1.02/1.59 ) ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__semidom( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__semidom( X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.59 c_Groups_Oone__class_Oone( X ) ) }.
% 1.02/1.59 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.02/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 1.02/1.59 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.02/1.59 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 1.02/1.59 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 1.02/1.59 , Y, T ) ) }.
% 1.02/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 1.02/1.59 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 1.02/1.59 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 1.02/1.59 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.02/1.59 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.02/1.59 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.02/1.59 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 1.02/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.59 , Y ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.02/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.59 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 1.02/1.59 ( X, Y ), Y ) }.
% 1.02/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.59 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.59 ) }.
% 1.02/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.59 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 1.02/1.59 ( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 1.02/1.59 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.59 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.59 ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.02/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.59 ) }.
% 1.02/1.59 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.59 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.02/1.59 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__semidom( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.59 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.02/1.59 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__semidom( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.02/1.59 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha7( X, Y ) }.
% 1.02/1.59 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.02/1.59 { ! alpha7( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.02/1.59 c_Nat_OSuc( X ) ) }.
% 1.02/1.59 { ! alpha7( X, Y ), Y = c_Nat_OSuc( skol10( Z, Y ) ) }.
% 1.02/1.59 { ! alpha7( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol10( X,
% 1.02/1.59 Y ), X ) }.
% 1.02/1.59 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 1.02/1.59 ), alpha7( X, Y ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.59 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.59 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol11( X ) ) }.
% 1.02/1.59 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.02/1.59 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha8( X, Y ), alpha20( X
% 1.02/1.59 , Y ) }.
% 1.02/1.59 { ! alpha8( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.02/1.59 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.59 { ! alpha20( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.02/1.59 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.59 { ! alpha20( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.59 { ! alpha20( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Nat_Onat ) ) }.
% 1.02/1.59 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha20( X, Y ) }.
% 1.02/1.59 { ! alpha8( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Nat_Onat ) ) }.
% 1.02/1.59 { ! alpha8( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.59 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha8( X, Y ) }.
% 1.02/1.59 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha9( X, Y ), alpha21
% 1.02/1.59 ( X, Y ) }.
% 1.02/1.59 { ! alpha9( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.02/1.59 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 1.02/1.59 { ! alpha21( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.02/1.59 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 1.02/1.59 { ! alpha21( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.59 { ! alpha21( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Nat_Onat ) ) }.
% 1.02/1.59 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha21( X, Y ) }.
% 1.02/1.59 { ! alpha9( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Nat_Onat ) ) }.
% 1.02/1.59 { ! alpha9( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.59 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha9( X, Y ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__semidom( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 1.02/1.59 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.59 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.02/1.59 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.59 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 1.02/1.59 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.59 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.59 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 1.02/1.59 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.59 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.02/1.59 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.59 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.59 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.59 ) }.
% 1.02/1.59 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.59 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.02/1.59 ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.02/1.59 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.59 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.59 ) }.
% 1.02/1.59 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.59 ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.59 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.02/1.59 ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol12( X, Y ) ) ) }.
% 1.02/1.59 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.59 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 1.02/1.59 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.02/1.59 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.02/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.02/1.59 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.02/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.02/1.59 ), X ) ) }.
% 1.02/1.59 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.59 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 1.02/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 1.02/1.59 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.59 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 1.02/1.59 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.59 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.02/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 1.02/1.59 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.02/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.02/1.59 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.59 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 1.02/1.59 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 1.02/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.02/1.59 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.59 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.02/1.59 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.59 ( tc_Nat_Onat, Y, Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z )
% 1.02/1.59 ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.59 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.02/1.59 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.59 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.02/1.59 ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.59 tc_Nat_Onat, X, Z ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Z ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.02/1.59 tc_Nat_Onat, X, Y ), Z ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ), Y ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.59 tc_Nat_Onat, Z, X ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X =
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X =
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.02/1.59 tc_Nat_Onat, X, Y ), Y ) = X }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.59 tc_Nat_Onat, Z, X ), Y ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.59 tc_Nat_Onat, X, Z ), Y ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.59 tc_Nat_Onat, Z, Y ), X ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 1.02/1.59 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.59 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.59 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.59 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 1.02/1.59 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 1.02/1.59 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.59 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.59 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ), hAPP( hAPP
% 1.02/1.59 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 1.02/1.59 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 1.02/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ),
% 1.02/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.59 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.59 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.59 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.59 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.59 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.02/1.59 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.59 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.02/1.59 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.02/1.59 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.59 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 1.02/1.59 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.02/1.59 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.59 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.02/1.59 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.02/1.59 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.02/1.59 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.59 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.02/1.59 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.02/1.59 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.02/1.59 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.59 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.59 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.59 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.59 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.02/1.59 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.59 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.59 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.59 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.02/1.59 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.59 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.02/1.59 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.02/1.59 ) ) }.
% 1.02/1.59 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.59 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.02/1.59 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.02/1.59 ) ) }.
% 1.02/1.59 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.59 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.02/1.59 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 1.02/1.59 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.59 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.59 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.02/1.59 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 1.02/1.59 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 1.02/1.59 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 1.02/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.02/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.59 }.
% 1.02/1.59 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.02/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.59 }.
% 1.02/1.59 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.59 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.02/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.02/1.59 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.02/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 1.02/1.59 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.02/1.59 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.02/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 1.02/1.59 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.59 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.59 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.59 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 1.02/1.59 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.59 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.59 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.59 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.02/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.59 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.59 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 1.02/1.59 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.59 , T, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.02/1.59 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.59 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.02/1.59 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.59 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.02/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.59 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.59 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 1.02/1.59 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.59 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.02/1.59 Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.59 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.02/1.59 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.02/1.59 , Z ), c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.02/1.59 ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc(
% 1.02/1.59 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), Z = Y, Z =
% 1.02/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.02/1.59 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.02/1.59 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.02/1.59 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc(
% 1.02/1.59 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 1.02/1.59 ( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.02/1.59 { ! class_Fields_Olinordered__field( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.59 , Y ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.02/1.59 { ! class_Fields_Olinordered__field( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.59 , Y ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.02/1.59 { ! class_Fields_Olinordered__field( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.59 , Z ), c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.02/1.59 { ! class_Fields_Olinordered__field( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.59 , Z ), c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.02/1.59 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.59 , Y ), c_Groups_Oone__class_Oone( X ) ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.59 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X )
% 1.02/1.59 , Y ) }.
% 1.02/1.59 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.59 ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.59 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Oone__class_Oone( X )
% 1.02/1.59 ) }.
% 1.02/1.59 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 1.02/1.59 , c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse
% 1.02/1.59 ( X, Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.59 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 1.02/1.59 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 1.02/1.59 ) ) = X }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.59 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X ) }.
% 1.02/1.59 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.59 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_RealDef_Oreal ) ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.59 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 1.02/1.59 tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ),
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.59 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 1.02/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.59 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 1.02/1.59 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 1.02/1.59 ) }.
% 1.02/1.59 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 1.02/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 1.02/1.59 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 1.02/1.59 ) }.
% 1.02/1.59 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 1.02/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 1.02/1.59 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.02/1.59 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.02/1.59 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 1.02/1.59 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 1.02/1.59 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.59 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 1.02/1.59 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.02/1.59 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.02/1.59 ( X, Y ) ) ) }.
% 1.02/1.59 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.59 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 1.02/1.59 Y ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.02/1.59 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.02/1.59 ( X, Y ) ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ), T =
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! T =
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ),
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.59 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 1.02/1.59 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) =
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, T,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ),
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.59 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 1.02/1.59 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) =
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.59 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 1.02/1.59 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( X ), Z ), Y ) ), hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.02/1.59 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) ) }.
% 1.02/1.59 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.02/1.59 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.02/1.59 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ) }.
% 1.02/1.59 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.02/1.59 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.02/1.59 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 1.02/1.59 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.02/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.02/1.59 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.02/1.59 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ),
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.02/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 1.02/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) }.
% 1.02/1.59 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.02/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 1.02/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ) ),
% 1.02/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.59 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.02/1.59 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 1.02/1.59 c_Groups_Oone__class_Oone( X ) ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__semiring__1( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.02/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.02/1.59 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 1.02/1.59 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.59 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 1.02/1.59 ), Y ) }.
% 1.02/1.59 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.59 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.02/1.59 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.02/1.59 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.59 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X ) )
% 1.02/1.59 }.
% 1.02/1.59 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.59 ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X )
% 1.02/1.59 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X )
% 1.02/1.59 , c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.02/1.59 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 1.02/1.59 ), c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq(
% 1.02/1.59 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 1.02/1.59 X, c_Groups_Oone__class_Oone( X ), Y ) }.
% 1.02/1.59 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.59 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.59 , Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.02/1.59 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ),
% 1.02/1.59 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 1.02/1.59 ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.02/1.59 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.59 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X ) )
% 1.02/1.59 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.59 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.02/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.02/1.59 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.59 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 1.02/1.59 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.59 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 1.02/1.59 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = X }.
% 1.02/1.59 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = X }.
% 1.02/1.59 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.02/1.59 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 1.02/1.59 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.59 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 1.02/1.59 , Y ) ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.02/1.59 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, U,
% 1.02/1.59 Z ) ), c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 1.02/1.59 ( X, T, Y ) ) ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.59 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 1.02/1.59 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.59 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 1.02/1.59 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.59 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 1.02/1.59 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.59 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.59 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.59 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 1.02/1.59 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.59 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ), U ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 1.02/1.59 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 1.02/1.59 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 1.02/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 1.02/1.59 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 1.02/1.59 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ),
% 1.02/1.59 c_Polynomial_Omonom( tc_Complex_Ocomplex, v_a____,
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, v_k____,
% 1.02/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) ), skol13 ) =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.02/1.59 { c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 1.02/1.59 skol14 ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 1.02/1.59 tc_Complex_Ocomplex, v_pa____ ) }.
% 1.02/1.59 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, skol14 ), X ) = hAPP(
% 1.02/1.59 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ),
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_c____, X ) ) }.
% 1.02/1.59 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), v_c____ ) =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), hAPP(
% 1.02/1.59 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), skol15 ) =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.02/1.59 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 1.02/1.59 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 1.02/1.59 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.02/1.59 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 1.02/1.59 v_q____ ) ), X ) = c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, hAPP
% 1.02/1.59 ( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 1.02/1.59 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 1.02/1.59 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.02/1.59 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 1.02/1.59 v_q____ ) ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ), hAPP(
% 1.02/1.59 hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), X ), v_k____ ) ),
% 1.02/1.59 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 1.02/1.59 tc_Complex_Ocomplex, v_a____, v_s____ ) ), X ) ) ) }.
% 1.02/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.59 tc_Nat_Onat, c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 1.02/1.59 tc_Complex_Ocomplex, v_s____ ), v_k____ ), c_Groups_Oone__class_Oone(
% 1.02/1.59 tc_Nat_Onat ) ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 1.02/1.59 tc_Complex_Ocomplex, c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 1.02/1.59 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 1.02/1.59 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ) }.
% 1.02/1.59 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) = hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 1.02/1.59 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 1.02/1.59 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 1.02/1.59 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.02/1.59 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 1.02/1.59 v_q____ ) ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), hAPP
% 1.02/1.59 ( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) }.
% 1.02/1.59 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ), X ) = hAPP(
% 1.02/1.59 hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 1.02/1.59 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 1.02/1.59 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 1.02/1.59 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.02/1.59 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 1.02/1.59 v_q____ ) ), X ) ), hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.02/1.59 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) }.
% 1.02/1.59 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 1.02/1.59 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 1.02/1.59 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.02/1.59 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 1.02/1.59 v_q____ ) ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) =
% 1.02/1.59 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 1.02/1.59 { c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 1.02/1.59 v_q____ ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 1.02/1.59 tc_Complex_Ocomplex, c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 1.02/1.59 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 1.02/1.59 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ) }.
% 1.02/1.59 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 1.02/1.59 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 1.02/1.59 tc_Complex_Ocomplex, c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 1.02/1.59 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 1.02/1.59 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.02/1.59 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 1.02/1.59 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 1.02/1.59 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.02/1.59 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 1.02/1.59 v_q____ ) ), X ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.02/1.59 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ), X ) ),
% 1.02/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.02/1.59 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.02/1.59 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ), X ) ),
% 1.02/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.02/1.59 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) ),
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.02/1.59 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 1.02/1.59 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 1.02/1.59 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.02/1.59 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 1.02/1.59 v_q____ ) ), X ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.02/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 1.02/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 1.02/1.59 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 1.02/1.59 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, X ) }.
% 1.02/1.59 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Z ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, Z ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ), Y = X }.
% 1.02/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 1.02/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 1.02/1.59 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( Z, Y, X ), hAPP(
% 1.02/1.59 X, T ) = hAPP( X, U ) }.
% 1.02/1.59 { ! hAPP( X, skol16( X ) ) = hAPP( X, skol31( X ) ),
% 1.02/1.59 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( Z, Y, X ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 1.02/1.59 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 1.02/1.59 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.59 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex
% 1.02/1.59 , v_pa____ ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, v_k____,
% 1.02/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), c_Orderings_Oord__class_Oless
% 1.02/1.59 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex
% 1.02/1.59 , hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 1.02/1.59 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 1.02/1.59 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.02/1.59 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 1.02/1.59 v_q____ ) ), skol17 ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 1.02/1.59 }.
% 1.02/1.59 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol18 ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ),
% 1.02/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_w____ ) ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.02/1.59 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_s____ ), X ) ), skol18 ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.59 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex, X
% 1.02/1.59 ), c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 1.02/1.59 tc_Complex_Ocomplex, v_pa____ ) ),
% 1.02/1.59 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( tc_Complex_Ocomplex
% 1.02/1.59 , tc_Complex_Ocomplex, c_Polynomial_Opoly( tc_Complex_Ocomplex, X ) ),
% 1.02/1.59 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, X ), skol19( X ) ) =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.02/1.59 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 1.02/1.59 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 1.02/1.59 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.02/1.59 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 1.02/1.59 v_q____ ) ), skol20 ) = hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.02/1.59 c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 1.02/1.59 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 1.02/1.59 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ),
% 1.02/1.59 skol32 ) }.
% 1.02/1.59 { ! class_RealVector_Oreal__normed__div__algebra( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z,
% 1.02/1.59 c_RealVector_Onorm__class_Onorm( X, Y ) ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.59 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Oinverse( X,
% 1.02/1.59 Y ) ), c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, Z ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.59 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.02/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.02/1.59 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.59 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.02/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 1.02/1.59 ( tc_Int_Oint ), Y ) }.
% 1.02/1.59 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.02/1.59 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.02/1.59 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 1.02/1.59 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 1.02/1.59 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.02/1.59 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.02/1.59 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 1.02/1.59 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.02/1.59 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.02/1.59 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.02/1.59 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.02/1.59 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.02/1.59 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus(
% 1.02/1.59 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 1.02/1.59 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) ) }
% 1.02/1.59 .
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 1.02/1.59 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus(
% 1.02/1.59 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Z, T ),
% 1.02/1.59 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) ) }
% 1.02/1.59 .
% 1.02/1.59 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.02/1.59 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.02/1.59 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.02/1.59 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Polynomial_Opoly( X ) ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 1.02/1.59 tc_Polynomial_Opoly( X ), Y ) }.
% 1.02/1.59 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.02/1.59 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.59 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 1.02/1.59 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 1.02/1.59 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 1.02/1.59 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 1.02/1.59 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 1.02/1.59 c_Polynomial_OpCons( X, Z, Y ), U = Z }.
% 1.02/1.59 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 1.02/1.59 c_Polynomial_OpCons( X, Z, Y ), T = Y }.
% 1.02/1.59 { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y, c_Polynomial_OpCons( X, U, T
% 1.02/1.59 ) = c_Polynomial_OpCons( X, Z, Y ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, Z,
% 1.02/1.59 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 1.02/1.59 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 1.02/1.59 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, T,
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 1.02/1.59 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 1.02/1.59 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, T, Z ) =
% 1.02/1.59 c_Polynomial_Omonom( X, Y, Z ), T = Y }.
% 1.02/1.59 { ! class_Groups_Ozero( X ), ! T = Y, c_Polynomial_Omonom( X, T, Z ) =
% 1.02/1.59 c_Polynomial_Omonom( X, Y, Z ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.59 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.02/1.59 c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.02/1.59 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 1.02/1.59 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.02/1.59 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.02/1.59 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 1.02/1.59 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 1.02/1.59 c_Groups_Ominus__class_Ominus( X, U, Z ), c_Groups_Ominus__class_Ominus(
% 1.02/1.59 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.02/1.59 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.59 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 1.02/1.59 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 1.02/1.59 ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 1.02/1.59 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 1.02/1.59 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 1.02/1.59 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 1.02/1.59 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.02/1.59 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 1.02/1.59 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.02/1.59 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 1.02/1.59 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.02/1.59 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 1.02/1.59 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.02/1.59 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Osmult( X,
% 1.02/1.59 c_Groups_Oone__class_Oone( X ), Y ) = Y }.
% 1.02/1.59 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 1.02/1.59 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 1.02/1.59 c_Polynomial_Osmult( X, T, Y ), c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 1.02/1.59 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) =
% 1.02/1.59 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 1.02/1.59 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.02/1.59 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 1.02/1.59 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.59 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.02/1.59 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, Y,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.59 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.02/1.59 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 1.02/1.59 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 1.02/1.59 c_Groups_Ominus__class_Ominus( X, T, Y ), Z ) }.
% 1.02/1.59 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.02/1.59 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 1.02/1.59 c_Polynomial_Omonom( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 1.02/1.59 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.02/1.59 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.02/1.59 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.02/1.59 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 1.02/1.59 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 1.02/1.59 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, Z, hAPP( hAPP
% 1.02/1.59 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }
% 1.02/1.59 .
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.02/1.59 c_Polynomial_Osmult( X, T, Z ) ), Y ) = c_Polynomial_Osmult( X, T, hAPP(
% 1.02/1.59 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y )
% 1.02/1.59 ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 1.02/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 1.02/1.59 ) ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.59 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.59 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.59 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.59 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.02/1.59 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.59 { ! class_Rings_Oidom( X ), ! c_Polynomial_Osmult( X, Z, Y ) =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.59 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.59 c_Polynomial_Osmult( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.59 { ! class_Rings_Oidom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult( X, Z, Y ) =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oone__class_Oone(
% 1.02/1.59 tc_Polynomial_Opoly( X ) ) = c_Polynomial_OpCons( X,
% 1.02/1.59 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Polynomial_Opoly( X ) ) ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.59 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Opoly( X, Z )
% 1.02/1.59 , Y ) ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.02/1.59 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), c_Polynomial_Osmult( X, T,
% 1.02/1.59 Y ) ) }.
% 1.02/1.59 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.59 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, Z, Y ) =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.59 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.59 c_Polynomial_Omonom( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.02/1.59 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 1.02/1.59 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 1.02/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 1.02/1.59 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 1.02/1.59 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 1.02/1.59 ) }.
% 1.02/1.59 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.02/1.59 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 1.02/1.59 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( X, U, Z ), c_Groups_Oplus__class_Oplus(
% 1.02/1.59 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osmult( X, T, Y ) =
% 1.02/1.59 c_Polynomial_OpCons( X, Z, Y ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.02/1.59 ( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 1.02/1.59 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.02/1.59 c_Polynomial_Omonom( X, Z, Y ) ) = c_Polynomial_Omonom( X, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 1.02/1.59 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.02/1.59 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 1.02/1.59 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.59 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, T
% 1.02/1.59 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), hAPP(
% 1.02/1.59 c_Polynomial_Opoly( X, Z ), Y ) ) ) }.
% 1.02/1.59 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Z, c_Nat_OSuc( Y ) ) =
% 1.02/1.59 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.59 c_Polynomial_Omonom( X, Z, Y ) ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.59 c_Polynomial_Omonom( X, T, Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.02/1.59 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Y,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = c_Polynomial_OpCons( X, Y
% 1.02/1.59 , c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.02/1.59 c_Polynomial_Omonom( X, U, T ) ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 1.02/1.59 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U
% 1.02/1.59 ), Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, Y ) ) }.
% 1.02/1.59 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.59 c_RealVector_Onorm__class_Onorm( X, Z ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ),
% 1.02/1.59 c_RealVector_Onorm__class_Onorm( X, T ) ) ), Z =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Oplus__class_Oplus(
% 1.02/1.59 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.59 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 1.02/1.59 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 1.02/1.59 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Osynthetic__div( X, Y, Z )
% 1.02/1.59 ), c_Polynomial_OpCons( X, hAPP( c_Polynomial_Opoly( X, Y ), Z ),
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) = Y }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 1.02/1.59 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Polynomial_OpCons( X, hAPP(
% 1.02/1.59 c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z, Y )
% 1.02/1.59 ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol21( X, Y ) ) }.
% 1.02/1.59 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__0( X ), c_Groups_Oplus__class_Oplus(
% 1.02/1.59 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, Y,
% 1.02/1.59 c_Polynomial_Osynthetic__div( X, Z, Y ) ) ) = c_Polynomial_OpCons( X,
% 1.02/1.59 hAPP( c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z
% 1.02/1.59 , Y ) ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 1.02/1.59 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 1.02/1.59 c_Polynomial_OpCons( X, Y, Z ), Y = hAPP( c_Polynomial_Opoly( X, U ), T )
% 1.02/1.59 }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 1.02/1.59 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 1.02/1.59 c_Polynomial_OpCons( X, Y, Z ), Z = c_Polynomial_Osynthetic__div( X, U, T
% 1.02/1.59 ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 1.02/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Int_Oint ) ) }.
% 1.02/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 1.02/1.59 tc_Int_Oint ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.02/1.59 tc_Int_Oint, X, Y ) ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 1.02/1.59 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 1.02/1.59 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 1.02/1.59 c_Polynomial_Opcompose( X, Z, Y ) ) ) }.
% 1.02/1.59 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol22 ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ),
% 1.02/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_w____ ) ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.59 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.02/1.59 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_s____ ), X ) ), skol22 ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.59 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 1.02/1.59 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.02/1.59 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.59 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.59 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.59 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.59 { ! skol23 = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.02/1.59 { ! skol33 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.59 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.59 tc_Nat_Onat, c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 1.02/1.59 tc_Complex_Ocomplex, skol35 ), skol33 ), c_Groups_Oone__class_Oone(
% 1.02/1.59 tc_Nat_Onat ) ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 1.02/1.59 tc_Complex_Ocomplex, c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 1.02/1.59 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 1.02/1.59 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ) }.
% 1.02/1.59 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 1.02/1.59 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 1.02/1.59 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.02/1.59 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 1.02/1.59 v_q____ ) ), X ) = c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, hAPP
% 1.02/1.59 ( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 1.02/1.59 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 1.02/1.59 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.02/1.59 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 1.02/1.59 v_q____ ) ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ), hAPP(
% 1.02/1.59 hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), X ), skol33 ) ),
% 1.02/1.59 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 1.02/1.59 tc_Complex_Ocomplex, skol23, skol35 ) ), X ) ) ) }.
% 1.02/1.59 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 1.02/1.59 , Y ) }.
% 1.02/1.59 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Polynomial_Opoly( X ) ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.02/1.59 ( X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X )
% 1.02/1.59 ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.02/1.59 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 1.02/1.59 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 1.02/1.59 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 1.02/1.59 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.02/1.59 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 1.02/1.59 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 1.02/1.59 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 1.02/1.59 Y ) ) ), Y ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.59 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.02/1.59 tc_Polynomial_Opoly( X ), T, c_Polynomial_Osmult( X, Z, Y ) ), Z =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 1.02/1.59 tc_Polynomial_Opoly( X ), T, Y ) }.
% 1.02/1.59 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.02/1.59 tc_Polynomial_Opoly( X ), Z, Y ), T = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult(
% 1.02/1.59 X, T, Z ), Y ) }.
% 1.02/1.59 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T,
% 1.02/1.59 c_Polynomial_Osmult( X, Y, Z ) ), c_Rings_Odvd__class_Odvd(
% 1.02/1.59 tc_Polynomial_Opoly( X ), T, Z ) }.
% 1.02/1.59 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Z ),
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T,
% 1.02/1.59 c_Polynomial_Osmult( X, Y, Z ) ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 1.02/1.59 tc_Polynomial_Opoly( X ), Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.02/1.59 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, T, Y ) ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 1.02/1.59 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ),
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.02/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ),
% 1.02/1.59 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.02/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), Y ),
% 1.02/1.59 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 1.02/1.59 { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.59 ( X ), Y ), T ), c_Rings_Odvd__class_Odvd( X, Y, Z ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.59 Y ), ! c_Rings_Odvd__class_Odvd( X, U, T ), c_Rings_Odvd__class_Odvd( X,
% 1.02/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.59 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.59 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.59 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), T =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 1.02/1.59 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.59 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.02/1.59 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 1.02/1.59 }.
% 1.02/1.59 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 1.02/1.59 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.02/1.59 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 1.02/1.59 }.
% 1.02/1.59 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Z =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, T, Y ) }.
% 1.02/1.59 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.59 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.02/1.59 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 1.02/1.59 }.
% 1.02/1.59 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, T, Y ),
% 1.02/1.59 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.02/1.59 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 1.02/1.59 }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y, Y
% 1.02/1.59 ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.59 Y ), ! c_Rings_Odvd__class_Odvd( X, Y, T ), c_Rings_Odvd__class_Odvd( X,
% 1.02/1.59 Z, T ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ), Y ), Y = c_Groups_Ozero__class_Ozero( X
% 1.02/1.59 ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.59 Y ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X,
% 1.02/1.59 Z, c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 1.02/1.59 , ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.59 c_Groups_Ominus__class_Ominus( X, Y, T ) ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Rings_Odvd__class_Odvd( X, Z
% 1.02/1.59 , Y ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 1.02/1.59 , c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.02/1.59 ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.02/1.59 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ), c_Rings_Odvd__class_Odvd( X
% 1.02/1.59 , Z, Y ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 1.02/1.59 , c_Rings_Odvd__class_Odvd( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y
% 1.02/1.59 ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X,
% 1.02/1.59 c_Groups_Oone__class_Oone( X ), Y ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.59 Y ), c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.02/1.59 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), Y ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, Z ),
% 1.02/1.59 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.02/1.59 ), T ), U ), Y ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.59 Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, T ),
% 1.02/1.59 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.02/1.59 ), Z ), U ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ) ) }
% 1.02/1.59 .
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__1( X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 1.02/1.59 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.02/1.59 ), T ), Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ) ) }
% 1.02/1.59 .
% 1.02/1.59 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.02/1.59 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ), alpha10( X
% 1.02/1.59 , Y, T ) }.
% 1.02/1.59 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.02/1.59 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ), alpha22( X
% 1.02/1.59 , Y, Z, T ) }.
% 1.02/1.59 { ! class_Fields_Ofield( X ), ! alpha10( X, Y, T ), ! alpha22( X, Y, Z, T )
% 1.02/1.59 , c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult
% 1.02/1.59 ( X, T, Z ), Y ) }.
% 1.02/1.59 { ! alpha22( X, Y, Z, T ), T = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.02/1.59 { ! T = c_Groups_Ozero__class_Ozero( X ), alpha22( X, Y, Z, T ) }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ), alpha22( X
% 1.02/1.59 , Y, Z, T ) }.
% 1.02/1.59 { ! alpha10( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.59 { Z = c_Groups_Ozero__class_Ozero( X ), alpha10( X, Y, Z ) }.
% 1.02/1.59 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha10( X
% 1.02/1.59 , Y, Z ) }.
% 1.02/1.59 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.59 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.02/1.59 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.02/1.59 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.02/1.59 hAPP( Y, U ) ) }.
% 1.02/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.59 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.02/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.59 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 1.02/1.59 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.59 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.02/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.59 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 1.02/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.59 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.02/1.59 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 1.02/1.59 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.02/1.59 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 1.02/1.59 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.02/1.59 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.02/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.59 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 1.02/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.59 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.02/1.59 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.02/1.59 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.02/1.59 hAPP( Y, U ) ) }.
% 1.02/1.59 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.59 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.02/1.59 ( X, Z, Y ) }.
% 1.02/1.59 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.02/1.59 ( X, Y, Z ) }.
% 1.02/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.59 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 1.02/1.59 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.59 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.02/1.59 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.02/1.59 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.02/1.59 hAPP( Y, U ) ) }.
% 1.02/1.59 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 1.02/1.59 ( Z, skol24( X, Y, Z ) ), hAPP( Y, skol24( X, Y, Z ) ) ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 1.02/1.59 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.02/1.59 Y ) }.
% 1.02/1.59 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 1.02/1.59 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.59 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.59 Y ), ! Z = Y }.
% 1.02/1.59 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.02/1.59 Z ), ! Z = Y }.
% 1.02/1.59 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.02/1.59 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 1.02/1.59 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.02/1.59 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.59 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 1.02/1.59 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.59 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.02/1.59 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.59 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.02/1.59 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 1.02/1.59 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.02/1.59 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.59 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 1.02/1.59 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.02/1.59 , ! Z = Y }.
% 1.02/1.59 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.59 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.59 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.59 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.02/1.59 , ! Z = Y }.
% 1.02/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.02/1.59 , ! Y = Z }.
% 1.02/1.59 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.59 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.02/1.59 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.59 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 1.02/1.59 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.02/1.59 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 1.02/1.59 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 1.02/1.59 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 1.02/1.59 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.02/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.02/1.59 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.02/1.59 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.59 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 1.02/1.59 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.02/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.02/1.59 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.02/1.59 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.02/1.59 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.59 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.59 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.02/1.59 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.59 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 1.02/1.59 c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP( c_Power_Opower__class_Opower
% 1.02/1.59 ( X ), Y ), Z ) ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Oone__class_Oone( X
% 1.02/1.59 ), c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.02/1.59 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 1.02/1.59 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X,
% 1.02/1.59 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Polynomial_OpCons( X,
% 1.02/1.59 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Polynomial_Opoly( X ) ) ) ), Z ) }.
% 1.02/1.59 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.02/1.59 ( X ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.02/1.59 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ), Z ), hAPP(
% 1.02/1.59 c_Polynomial_Opoly( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.59 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.02/1.59 ( X ), c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 1.02/1.59 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Polynomial_Opoly( X ) ) ) ), Y ), hAPP( c_Polynomial_Opoly( X, Y ),
% 1.02/1.59 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.59 X ) }.
% 1.02/1.59 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Y ),
% 1.02/1.59 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.59 X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ),
% 1.02/1.59 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 1.02/1.59 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Polynomial_Opoly( X ) ) ) ), Y ) }.
% 1.02/1.59 { ! class_Rings_Oidom( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 1.02/1.59 X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) )
% 1.02/1.59 , c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.02/1.59 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 1.02/1.59 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 1.02/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.59 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.02/1.59 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.02/1.59 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.59 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 1.02/1.59 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.02/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.02/1.59 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.02/1.59 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.02/1.59 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.59 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 1.02/1.59 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.02/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.59 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.59 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.59 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.02/1.59 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.59 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.02/1.59 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.59 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.59 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.59 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.59 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.59 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.59 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.02/1.59 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.59 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.02/1.59 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.59 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.02/1.59 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 1.02/1.59 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.02/1.59 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.59 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.59 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.59 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.02/1.59 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.02/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.59 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.02/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.02/1.59 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.59 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.02/1.59 ( X, Z, Y ) }.
% 1.02/1.59 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.59 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.59 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.59 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.02/1.59 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.59 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 1.02/1.59 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.02/1.59 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.02/1.59 , ! Z = Y }.
% 1.02/1.59 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.59 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.59 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.59 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.59 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.59 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.59 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.02/1.59 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.59 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.02/1.59 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.02/1.59 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.59 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.59 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 1.02/1.59 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.02/1.59 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 1.02/1.59 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 1.02/1.59 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 1.02/1.59 Y ) ) ), Y ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.02/1.59 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 1.02/1.59 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 1.02/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.02/1.59 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 1.02/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 1.02/1.59 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 1.02/1.59 }.
% 1.02/1.59 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.02/1.59 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 1.02/1.59 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 1.02/1.59 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 1.02/1.59 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.02/1.59 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 1.02/1.59 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 1.02/1.59 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 1.02/1.59 }.
% 1.02/1.59 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 1.02/1.59 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 1.02/1.59 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 1.02/1.59 .
% 1.02/1.59 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 1.02/1.59 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 1.02/1.59 }.
% 1.02/1.59 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.02/1.59 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 1.02/1.59 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Int_Oint, X, Y ), ! c_Rings_Odvd__class_Odvd
% 1.02/1.59 ( tc_Int_Oint, Y, X ), X = Y }.
% 1.02/1.59 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.02/1.59 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X
% 1.02/1.59 ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y
% 1.02/1.59 ) ) }.
% 1.02/1.59 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ),
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.59 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y
% 1.02/1.59 ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), Z =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Rings_Odvd__class_Odvd(
% 1.02/1.59 tc_Int_Oint, Y, X ) }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X = c_Nat_OSuc(
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.59 { ! X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.59 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 1.02/1.59 ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), Z =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 1.02/1.59 tc_Nat_Onat, Y, X ) }.
% 1.02/1.59 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.59 ( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.59 Z ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.02/1.59 X ) ) }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus(
% 1.02/1.59 tc_Nat_Onat, X, Y ) ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.59 ( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus(
% 1.02/1.59 tc_Int_Oint, Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 1.02/1.59 , Z ), X ) ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd
% 1.02/1.59 ( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP
% 1.02/1.59 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 1.02/1.59 tc_Int_Oint, U, T ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.02/1.59 tc_Int_Oint, U, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 1.02/1.59 , Z ), X ) ), T ) ) }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 1.02/1.59 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), T ) ),
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 1.02/1.59 tc_Int_Oint, U, T ) ) }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Ominus__class_Ominus
% 1.02/1.59 ( tc_Int_Oint, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, X )
% 1.02/1.59 , c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.59 ( tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 1.02/1.59 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ),
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.59 ( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.02/1.59 ( tc_Int_Oint, Y ), X ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }
% 1.02/1.59 .
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ), c_Rings_Odvd__class_Odvd(
% 1.02/1.59 tc_Nat_Onat, Y, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Oone__class_Oone(
% 1.02/1.59 tc_Nat_Onat ) ), X = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.02/1.59 { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd
% 1.02/1.59 ( tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, c_Groups_Ominus__class_Ominus
% 1.02/1.59 ( tc_Nat_Onat, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X )
% 1.02/1.59 , ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ),
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, c_Groups_Ominus__class_Ominus
% 1.02/1.59 ( tc_Nat_Onat, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y )
% 1.02/1.59 , ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ),
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ) }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 1.02/1.59 ) }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 1.02/1.59 ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.59 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 1.02/1.59 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.59 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ),
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Nat_Onat ), Z ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.59 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 1.02/1.59 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ), Y =
% 1.02/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.59 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.59 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 1.02/1.59 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ), Y =
% 1.02/1.59 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.59 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 1.02/1.59 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 1.02/1.59 ) }.
% 1.02/1.59 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 1.02/1.59 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 1.02/1.59 hAPP( Z, skol25( U, W, Z ) ) ) }.
% 1.02/1.59 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 1.02/1.59 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ),
% 1.02/1.59 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, skol25( X
% 1.02/1.59 , Y, Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.02/1.59 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), !
% 1.02/1.59 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, T,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP( Z, T ) ), hBOOL(
% 1.02/1.59 hAPP( Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), skol34( X,
% 1.02/1.59 Y, Z ) ) ) ) }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ), Y =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 1.02/1.59 tc_Nat_Onat, Z, X ) }.
% 1.02/1.59 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ),
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.02/1.59 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.02/1.59 tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z )
% 1.02/1.59 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X )
% 1.02/1.59 ) }.
% 1.02/1.59 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, X ) }.
% 1.02/1.59 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.59 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), alpha11( X, Y ), Y = X }
% 1.02/1.59 .
% 1.02/1.59 { ! alpha11( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.59 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.59 { ! alpha11( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.59 { ! alpha11( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.59 ( tc_Nat_Onat, X, Y ), alpha11( X, Y ) }.
% 1.02/1.59 { ! alpha12( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.59 { ! alpha12( X, Y ), ! Y = X }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, alpha12( X, Y ) }
% 1.02/1.59 .
% 1.02/1.59 { ! alpha12( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.59 { ! alpha12( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.59 ( tc_Nat_Onat, X, Y ), alpha12( X, Y ) }.
% 1.02/1.59 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.59 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.02/1.59 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), X = Y }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Y,
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.59 ( tc_Nat_Onat, Y, X ), Y = X }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X,
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, !
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.02/1.59 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Z,
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 1.02/1.59 tc_Nat_Onat, Y, Z ) }.
% 1.02/1.59 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 1.02/1.59 tc_Nat_Onat, Y, Z ) }.
% 1.02/1.59 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 1.02/1.59 ( tc_Nat_Onat, Z, Y ) }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 1.02/1.59 tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 1.02/1.59 tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.59 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.59 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.59 ( tc_Nat_Onat, X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.59 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.59 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.59 ( tc_Nat_Onat, X, Y ), ! X = Y }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.59 ( tc_Nat_Onat, X, Y ), ! X = Z, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 1.02/1.59 , Z ) }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.59 ( tc_Nat_Onat, X, Y ), ! X = Z, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat,
% 1.02/1.59 Z, Y ) }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.59 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.59 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), !
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.59 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.59 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 1.02/1.59 tc_Nat_Onat, Y, Z ) }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.59 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 1.02/1.59 ( tc_Nat_Onat, Z, Y ) }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.59 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.59 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Nat_Onat ) ) }.
% 1.02/1.59 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 1.02/1.59 tc_Nat_Onat ), X ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.59 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Nat_Onat ), Y ) }.
% 1.02/1.59 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ),
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.02/1.59 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.02/1.59 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.02/1.59 tc_Int_Oint, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z )
% 1.02/1.59 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X )
% 1.02/1.59 ) }.
% 1.02/1.59 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ), Y =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 1.02/1.59 tc_Int_Oint, Z, X ) }.
% 1.02/1.59 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 1.02/1.59 ), c_Orderings_Oord__class_Oless__eq( X, T, skol26( X, U, W, T ) ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, T, V0 ),
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.59 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, V0 ) ),
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 1.02/1.59 ( tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) )
% 1.02/1.59 ) ) }.
% 1.02/1.59 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 1.02/1.59 ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.59 c_RealVector_Onorm__class_Onorm( Y, c_Groups_Ominus__class_Ominus( Y,
% 1.02/1.59 hAPP( Z, T ), hAPP( Z, skol26( X, Y, Z, T ) ) ) ),
% 1.02/1.59 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.59 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, U ) ),
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 1.02/1.59 ( tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) )
% 1.02/1.59 ) ) }.
% 1.02/1.59 { c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 1.02/1.59 skol27 ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 1.02/1.59 tc_Complex_Ocomplex, v_pa____ ) }.
% 1.02/1.59 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, skol27 ), X ) = hAPP(
% 1.02/1.59 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ),
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_c____, X ) ) }.
% 1.02/1.59 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol28( Z, T ) ) }.
% 1.02/1.59 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.02/1.59 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol28( X, Y ) ) ) }.
% 1.02/1.59 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol29( Z, T ) ) }.
% 1.02/1.59 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.02/1.59 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol29( X, Y ) ) ) }.
% 1.02/1.59 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol30( Y ) ) }.
% 1.02/1.59 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.02/1.59 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.02/1.59 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 1.02/1.59 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol30( X ) ) ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.02/1.59 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 1.02/1.59 tc_Int_Oint, X, Y ) }.
% 1.02/1.59 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.02/1.59 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint
% 1.02/1.59 ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Nat__Transfer_Otsub( X, Y )
% 1.02/1.59 ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.02/1.59 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 1.02/1.59 tc_Int_Oint, X, Y ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.02/1.59 c_Polynomial_OpCons( X, Z, Y ) ), c_Polynomial_Opos__poly( X, Y ),
% 1.02/1.59 alpha13( X, Y, Z ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.02/1.59 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__idom( X ), ! alpha13( X, Y, Z ),
% 1.02/1.59 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 1.02/1.59 { ! alpha13( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.59 { ! alpha13( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.02/1.59 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.02/1.59 alpha13( X, Y, Z ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.59 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.02/1.59 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ), Y ) = hAPP( hAPP(
% 1.02/1.59 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ),
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.02/1.59 ( tc_Polynomial_Opoly( X ), Z, Y ), Z = Y, c_Polynomial_Opos__poly( X,
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__idom( X ), ! Z = Y,
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.02/1.59 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.02/1.59 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.02/1.59 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.02/1.59 tc_Int_Oint, X, Y ) ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.02/1.59 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X,
% 1.02/1.59 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.02/1.59 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.02/1.59 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 1.02/1.59 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 1.02/1.59 .
% 1.02/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.59 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.59 }.
% 1.02/1.59 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.59 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.02/1.59 { ! class_Divides_Osemiring__div( X ), ! T = c_Groups_Ozero__class_Ozero( X
% 1.02/1.59 ), c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.02/1.59 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.59 { ! class_Divides_Osemiring__div( X ), T = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.59 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.02/1.59 c_Divides_Odiv__class_Odiv( X, Z, Y ) }.
% 1.02/1.59 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.59 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = Z }.
% 1.02/1.59 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.59 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) = Z }.
% 1.02/1.59 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.59 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.02/1.59 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.02/1.59 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 1.02/1.59 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.02/1.59 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.59 { class_Groups_Ocancel__comm__monoid__add( tc_Complex_Ocomplex ) }.
% 1.02/1.59 { class_Groups_Ocancel__comm__monoid__add( tc_RealDef_Oreal ) }.
% 1.02/1.59 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 1.02/1.59 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 1.02/1.59 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 1.02/1.59 ) ) }.
% 1.02/1.59 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 1.02/1.59 .
% 1.02/1.59 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 1.02/1.59 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.02/1.59 tc_Int_Oint ) }.
% 1.02/1.59 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.02/1.59 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 1.02/1.59 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 1.02/1.59 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 1.02/1.59 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 1.02/1.59 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 1.02/1.59 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 1.02/1.59 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 1.02/1.59 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.02/1.59 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 1.02/1.59 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 1.02/1.59 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 1.02/1.59 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 1.02/1.59 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 1.02/1.59 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 1.02/1.59 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 1.02/1.59 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 1.02/1.59 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 1.02/1.59 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 1.02/1.59 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 1.02/1.59 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 1.02/1.59 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 1.02/1.59 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 1.02/1.59 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 1.02/1.59 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 1.02/1.59 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 1.02/1.59 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 1.02/1.59 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 1.02/1.59 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 1.02/1.59 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 1.02/1.59 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 1.02/1.59 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 1.02/1.59 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 1.02/1.59 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 1.02/1.59 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 1.02/1.59 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 1.02/1.59 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 1.02/1.59 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 1.02/1.59 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 1.02/1.59 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 1.02/1.59 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 1.02/1.59 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 1.02/1.59 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 1.02/1.59 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 1.02/1.59 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 1.02/1.59 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 1.02/1.59 { class_Orderings_Oord( tc_Int_Oint ) }.
% 1.02/1.59 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 1.02/1.59 { class_Power_Opower( tc_Int_Oint ) }.
% 1.02/1.59 { class_Groups_Ozero( tc_Int_Oint ) }.
% 1.02/1.59 { class_Rings_Oring( tc_Int_Oint ) }.
% 1.02/1.59 { class_Rings_Oidom( tc_Int_Oint ) }.
% 1.02/1.59 { class_Groups_Oone( tc_Int_Oint ) }.
% 1.02/1.59 { class_Rings_Odvd( tc_Int_Oint ) }.
% 1.02/1.59 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.02/1.59 tc_Nat_Onat ) }.
% 1.02/1.59 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.02/1.59 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 1.02/1.59 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 1.02/1.59 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 1.02/1.59 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.02/1.59 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 1.02/1.59 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.02/1.59 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 1.02/1.59 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 1.02/1.59 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 1.02/1.59 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 1.02/1.59 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 1.02/1.59 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 1.02/1.59 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 1.02/1.59 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 1.02/1.59 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 1.02/1.59 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 1.02/1.59 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 1.02/1.59 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 1.02/1.59 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 1.02/1.59 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 1.02/1.59 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 1.02/1.59 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 1.02/1.59 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 1.02/1.59 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 1.02/1.59 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 1.02/1.59 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 1.02/1.59 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 1.02/1.59 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 1.02/1.59 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 1.02/1.59 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 1.02/1.59 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 1.02/1.59 { class_Power_Opower( tc_Nat_Onat ) }.
% 1.02/1.59 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 1.02/1.59 { class_Groups_Oone( tc_Nat_Onat ) }.
% 1.02/1.59 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 1.02/1.59 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 1.02/1.59 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 1.02/1.59 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 1.02/1.59 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.02/1.59 tc_RealDef_Oreal ) }.
% 1.02/1.59 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.02/1.59 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_RealDef_Oreal ) }
% 1.02/1.59 .
% 1.02/1.59 { class_Rings_Olinordered__comm__semiring__strict( tc_RealDef_Oreal ) }.
% 1.02/1.59 { class_Fields_Olinordered__field__inverse__zero( tc_RealDef_Oreal ) }.
% 1.02/1.59 { class_Rings_Olinordered__semiring__1__strict( tc_RealDef_Oreal ) }.
% 1.02/1.59 { class_RealVector_Oreal__normed__div__algebra( tc_RealDef_Oreal ) }.
% 1.02/1.59 { class_Rings_Olinordered__semiring__strict( tc_RealDef_Oreal ) }.
% 1.02/1.59 { class_Rings_Odivision__ring__inverse__zero( tc_RealDef_Oreal ) }.
% 1.02/1.59 { class_RealVector_Oreal__normed__algebra__1( tc_RealDef_Oreal ) }.
% 1.02/1.59 { class_Groups_Oordered__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.02/1.59 { class_RealVector_Oreal__normed__algebra( tc_RealDef_Oreal ) }.
% 1.02/1.59 { class_Groups_Oordered__comm__monoid__add( tc_RealDef_Oreal ) }.
% 1.02/1.59 { class_Groups_Olinordered__ab__group__add( tc_RealDef_Oreal ) }.
% 1.02/1.59 { class_Groups_Ocancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.02/1.59 { class_Rings_Oring__1__no__zero__divisors( tc_RealDef_Oreal ) }.
% 1.02/1.59 { class_Rings_Oordered__cancel__semiring( tc_RealDef_Oreal ) }.
% 1.02/1.59 { class_RealVector_Oreal__normed__vector( tc_RealDef_Oreal ) }.
% 1.02/1.59 { class_Rings_Olinordered__ring__strict( tc_RealDef_Oreal ) }.
% 1.02/1.59 { class_Rings_Oring__no__zero__divisors( tc_RealDef_Oreal ) }.
% 1.02/1.59 { class_Rings_Oordered__comm__semiring( tc_RealDef_Oreal ) }.
% 1.02/1.59 { class_Rings_Olinordered__semiring__1( tc_RealDef_Oreal ) }.
% 1.02/1.59 { class_Groups_Oordered__ab__group__add( tc_RealDef_Oreal ) }.
% 1.02/1.59 { class_Groups_Ocancel__semigroup__add( tc_RealDef_Oreal ) }.
% 1.02/1.59 { class_Rings_Olinordered__semiring( tc_RealDef_Oreal ) }.
% 1.02/1.59 { class_Fields_Ofield__inverse__zero( tc_RealDef_Oreal ) }.
% 1.02/1.59 { class_Rings_Olinordered__semidom( tc_RealDef_Oreal ) }.
% 1.02/1.59 { class_Groups_Oab__semigroup__mult( tc_RealDef_Oreal ) }.
% 1.02/1.59 { class_Groups_Ocomm__monoid__mult( tc_RealDef_Oreal ) }.
% 1.02/1.59 { class_Groups_Oab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.02/1.59 { class_Fields_Olinordered__field( tc_RealDef_Oreal ) }.
% 1.02/1.59 { class_Rings_Oordered__semiring( tc_RealDef_Oreal ) }.
% 1.02/1.59 { class_Rings_Ono__zero__divisors( tc_RealDef_Oreal ) }.
% 1.02/1.59 { class_Groups_Ocomm__monoid__add( tc_RealDef_Oreal ) }.
% 1.02/1.59 { class_Rings_Olinordered__ring( tc_RealDef_Oreal ) }.
% 1.02/1.59 { class_Rings_Olinordered__idom( tc_RealDef_Oreal ) }.
% 1.02/1.59 { class_Rings_Ocomm__semiring__1( tc_RealDef_Oreal ) }.
% 1.02/1.59 { class_Rings_Ocomm__semiring__0( tc_RealDef_Oreal ) }.
% 1.02/1.59 { class_Rings_Odivision__ring( tc_RealDef_Oreal ) }.
% 1.02/1.59 { class_Rings_Ocomm__semiring( tc_RealDef_Oreal ) }.
% 1.02/1.59 { class_Groups_Oab__group__add( tc_RealDef_Oreal ) }.
% 1.02/1.59 { class_Rings_Ozero__neq__one( tc_RealDef_Oreal ) }.
% 1.02/1.59 { class_Rings_Oordered__ring( tc_RealDef_Oreal ) }.
% 1.02/1.60 { class_Orderings_Opreorder( tc_RealDef_Oreal ) }.
% 1.02/1.60 { class_Orderings_Olinorder( tc_RealDef_Oreal ) }.
% 1.02/1.60 { class_Groups_Omonoid__mult( tc_RealDef_Oreal ) }.
% 1.02/1.60 { class_Rings_Ocomm__ring__1( tc_RealDef_Oreal ) }.
% 1.02/1.60 { class_Groups_Omonoid__add( tc_RealDef_Oreal ) }.
% 1.02/1.60 { class_Rings_Osemiring__0( tc_RealDef_Oreal ) }.
% 1.02/1.60 { class_Groups_Ogroup__add( tc_RealDef_Oreal ) }.
% 1.02/1.60 { class_Rings_Omult__zero( tc_RealDef_Oreal ) }.
% 1.02/1.60 { class_Rings_Ocomm__ring( tc_RealDef_Oreal ) }.
% 1.02/1.60 { class_Orderings_Oorder( tc_RealDef_Oreal ) }.
% 1.02/1.60 { class_Int_Oring__char__0( tc_RealDef_Oreal ) }.
% 1.02/1.60 { class_Rings_Osemiring( tc_RealDef_Oreal ) }.
% 1.02/1.60 { class_Orderings_Oord( tc_RealDef_Oreal ) }.
% 1.02/1.60 { class_Rings_Oring__1( tc_RealDef_Oreal ) }.
% 1.02/1.60 { class_Fields_Ofield( tc_RealDef_Oreal ) }.
% 1.02/1.60 { class_Power_Opower( tc_RealDef_Oreal ) }.
% 1.02/1.60 { class_Groups_Ozero( tc_RealDef_Oreal ) }.
% 1.02/1.60 { class_Rings_Oring( tc_RealDef_Oreal ) }.
% 1.02/1.60 { class_Rings_Oidom( tc_RealDef_Oreal ) }.
% 1.02/1.60 { class_Groups_Oone( tc_RealDef_Oreal ) }.
% 1.02/1.60 { class_Rings_Odvd( tc_RealDef_Oreal ) }.
% 1.02/1.60 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.02/1.60 tc_Complex_Ocomplex ) }.
% 1.02/1.60 { class_RealVector_Oreal__normed__div__algebra( tc_Complex_Ocomplex ) }.
% 1.02/1.60 { class_Rings_Odivision__ring__inverse__zero( tc_Complex_Ocomplex ) }.
% 1.02/1.60 { class_RealVector_Oreal__normed__algebra__1( tc_Complex_Ocomplex ) }.
% 1.02/1.60 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 1.02/1.60 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.02/1.60 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.02/1.60 { class_RealVector_Oreal__normed__vector( tc_Complex_Ocomplex ) }.
% 1.02/1.60 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.02/1.60 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.02/1.60 { class_Fields_Ofield__inverse__zero( tc_Complex_Ocomplex ) }.
% 1.02/1.60 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 1.02/1.60 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 1.02/1.60 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.02/1.60 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.02/1.60 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 1.02/1.60 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 1.02/1.60 { class_Rings_Ocomm__semiring__0( tc_Complex_Ocomplex ) }.
% 1.02/1.60 { class_Rings_Odivision__ring( tc_Complex_Ocomplex ) }.
% 1.02/1.60 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 1.02/1.60 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 1.02/1.60 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 1.02/1.60 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 1.02/1.60 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 1.02/1.60 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 1.02/1.60 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 1.02/1.60 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 1.02/1.60 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 1.02/1.60 { class_Rings_Ocomm__ring( tc_Complex_Ocomplex ) }.
% 1.02/1.60 { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 1.02/1.60 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 1.02/1.60 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 1.02/1.60 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 1.02/1.60 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 1.02/1.60 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 1.02/1.60 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 1.02/1.60 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 1.02/1.60 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 1.02/1.60 { class_Rings_Odvd( tc_Complex_Ocomplex ) }.
% 1.02/1.60 { ! class_Rings_Oidom( X ),
% 1.02/1.60 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.02/1.60 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.60 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.60 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 1.02/1.60 ) ) }.
% 1.02/1.60 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.60 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 1.02/1.60 X ) ) }.
% 1.02/1.60 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.60 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 1.02/1.60 ) }.
% 1.02/1.60 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.60 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 1.02/1.60 }.
% 1.02/1.60 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.60 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.60 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.60 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.60 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.60 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.60 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.60 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.60 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.02/1.60 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.60 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 1.02/1.60 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.60 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.60 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.60 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.60 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.60 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 1.02/1.60 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.60 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.60 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.60 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.60 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.60 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.60 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.60 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.02/1.60 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.60 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 1.02/1.60 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.60 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 1.02/1.60 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.60 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 1.02/1.60 ( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.60 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 1.02/1.60 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.60 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 1.02/1.60 ( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.60 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 1.02/1.60 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.60 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 1.02/1.60 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.60 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 1.02/1.60 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.60 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 1.02/1.60 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.60 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 1.02/1.60 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.60 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 1.02/1.60 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.60 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 1.02/1.60 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.60 { ! class_Fields_Ofield( X ), class_Divides_Osemiring__div(
% 1.02/1.60 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.60 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 1.02/1.60 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.60 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 1.02/1.60 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.60 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 1.02/1.60 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.60 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 1.02/1.60 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.60 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 1.02/1.60 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.60 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 1.02/1.60 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.60 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 1.02/1.60 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.60 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 1.02/1.60 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.60 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 1.02/1.60 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.60 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 1.02/1.60 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.60 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 1.02/1.60 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.60 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 1.02/1.60 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.60 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 1.02/1.60 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.60 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 1.02/1.60 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.60 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 1.02/1.60 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.60 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 1.02/1.60 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.60 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 1.02/1.60 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.60 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 1.02/1.60 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.60 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 1.02/1.60 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.60 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 1.02/1.60 }.
% 1.02/1.60 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 1.02/1.60 ) ) }.
% 1.02/1.60 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 1.02/1.60 .
% 1.02/1.60 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 1.02/1.60 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.60 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 1.02/1.60 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.60 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.02/1.60 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.02/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 1.02/1.60 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), !
% 1.02/1.60 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 1.02/1.60 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, hAPP( hAPP(
% 1.02/1.60 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.02/1.60 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.02/1.60 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_w____ ) ),
% 1.02/1.60 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, v_k____,
% 1.02/1.60 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), v_m____ ) ) ),
% 1.02/1.60 v_thesis____ }.
% 1.02/1.60 { ! v_thesis____ }.
% 1.02/1.60
% 1.02/1.60 *** allocated 15000 integers for clauses
% 1.02/1.60 *** allocated 22500 integers for clauses
% 1.02/1.60 *** allocated 33750 integers for clauses
% 1.02/1.60 *** allocated 50625 integers for clauses
% 1.02/1.60 *** allocated 75937 integers for clauses
% 1.02/1.60 percentage equality = 0.261674, percentage horn = 0.916276
% 1.02/1.60 This is a problem with some equality
% 1.02/1.60
% 1.02/1.60
% 1.02/1.60
% 1.02/1.60 Options Used:
% 1.02/1.60
% 1.02/1.60 useres = 1
% 1.02/1.60 useparamod = 1
% 1.02/1.60 useeqrefl = 1
% 1.02/1.60 useeqfact = 1
% 1.02/1.60 usefactor = 1
% 1.02/1.60 usesimpsplitting = 0
% 1.02/1.60 usesimpdemod = 5
% 1.02/1.60 usesimpres = 3
% 1.02/1.60
% 1.02/1.60 resimpinuse = 1000
% 1.02/1.60 resimpclauses = 20000
% 1.02/1.60 substype = eqrewr
% 1.02/1.60 backwardsubs = 1
% 1.02/1.60 selectoldest = 5
% 1.02/1.60
% 1.02/1.60 litorderings [0] = split
% 1.02/1.60 litorderings [1] = extend the termordering, first sorting on arguments
% 1.02/1.60
% 1.02/1.60 termordering = kbo
% 1.02/1.60
% 1.02/1.60 litapriori = 0
% 1.02/1.60 termapriori = 1
% 1.02/1.60 litaposteriori = 0
% 1.02/1.60 termaposteriori = 0
% 1.02/1.60 demodaposteriori = 0
% 1.02/1.60 ordereqreflfact = 0
% 1.02/1.60
% 1.02/1.60 litselect = negord
% 1.02/1.60
% 1.02/1.60 maxweight = 15
% 1.02/1.60 maxdepth = 30000
% 1.02/1.60 maxlength = 115
% 1.02/1.60 maxnrvars = 195
% 1.02/1.60 excuselevel = 1
% 1.02/1.60 increasemaxweight = 1
% 1.02/1.60
% 1.02/1.60 maxselected = 10000000
% 1.02/1.60 maxnrclauses = 10000000
% 1.02/1.60
% 1.02/1.60 showgenerated = 0
% 1.02/1.60 showkept = 0
% 1.02/1.60 showselected = 0
% 1.02/1.60 showdeleted = 0
% 1.02/1.60 showresimp = 1
% 1.02/1.60 showstatus = 2000
% 1.02/1.60
% 1.02/1.60 prologoutput = 0
% 1.02/1.60 nrgoals = 5000000
% 1.02/1.60 totalproof = 1
% 1.02/1.60
% 1.02/1.60 Symbols occurring in the translation:
% 1.02/1.60
% 1.02/1.60 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.02/1.60 . [1, 2] (w:1, o:211, a:1, s:1, b:0),
% 1.02/1.60 ! [4, 1] (w:0, o:126, a:1, s:1, b:0),
% 1.02/1.60 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.02/1.60 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.02/1.60 hAPP [38, 2] (w:1, o:235, a:1, s:1, b:0),
% 1.02/1.60 tc_RealDef_Oreal [40, 0] (w:1, o:31, a:1, s:1, b:0),
% 1.02/1.60 c_Groups_Ozero__class_Ozero [41, 1] (w:1, o:131, a:1, s:1, b:0),
% 1.02/1.60 c_Orderings_Oord__class_Oless [42, 3] (w:1, o:261, a:1, s:1, b:0),
% 1.02/1.60 c_Groups_Oone__class_Oone [44, 1] (w:1, o:132, a:1, s:1, b:0),
% 1.02/1.60 v_m____ [45, 0] (w:1, o:34, a:1, s:1, b:0),
% 1.02/1.60 c_Groups_Otimes__class_Otimes [46, 1] (w:1, o:133, a:1, s:1, b:0),
% 1.02/1.60 c_Power_Opower__class_Opower [47, 1] (w:1, o:134, a:1, s:1, b:0),
% 1.02/1.60 tc_Complex_Ocomplex [48, 0] (w:1, o:35, a:1, s:1, b:0),
% 1.02/1.60 v_w____ [49, 0] (w:1, o:36, a:1, s:1, b:0),
% 1.02/1.60 c_RealVector_Onorm__class_Onorm [50, 2] (w:1, o:236, a:1, s:1, b:0),
% 1.02/1.60
% 1.02/1.60 tc_Nat_Onat [51, 0] (w:1, o:37, a:1, s:1, b:0),
% 1.02/1.60 v_k____ [52, 0] (w:1, o:38, a:1, s:1, b:0),
% 1.02/1.60 c_Groups_Oplus__class_Oplus [53, 3] (w:1, o:263, a:1, s:1, b:0),
% 1.02/1.60 c_Rings_Oinverse__class_Oinverse [54, 2] (w:1, o:237, a:1, s:1, b:0)
% 1.02/1.60 ,
% 1.02/1.60 class_Rings_Olinordered__semidom [58, 1] (w:1, o:137, a:1, s:1, b:0)
% 1.02/1.60 ,
% 1.02/1.60 class_RealVector_Oreal__normed__div__algebra [63, 1] (w:1, o:138, a:1
% 1.02/1.60 , s:1, b:0),
% 1.02/1.60 class_RealVector_Oreal__normed__algebra [66, 1] (w:1, o:139, a:1, s:1
% 1.02/1.60 , b:0),
% 1.02/1.60 class_RealVector_Oreal__normed__vector [68, 1] (w:1, o:140, a:1, s:1
% 1.02/1.60 , b:0),
% 1.02/1.60 class_Rings_Odivision__ring [69, 1] (w:1, o:146, a:1, s:1, b:0),
% 1.02/1.60 class_Fields_Ofield [70, 1] (w:1, o:147, a:1, s:1, b:0),
% 1.02/1.60 class_Fields_Olinordered__field__inverse__zero [71, 1] (w:1, o:148
% 1.02/1.60 , a:1, s:1, b:0),
% 1.02/1.60 class_Fields_Olinordered__field [72, 1] (w:1, o:149, a:1, s:1, b:0),
% 1.02/1.60
% 1.02/1.60 v_a____ [73, 0] (w:1, o:73, a:1, s:1, b:0),
% 1.02/1.60 class_Groups_Omonoid__mult [77, 1] (w:1, o:152, a:1, s:1, b:0),
% 1.02/1.60 class_Power_Opower [78, 1] (w:1, o:157, a:1, s:1, b:0),
% 1.02/1.60 class_Rings_Olinordered__idom [79, 1] (w:1, o:158, a:1, s:1, b:0),
% 1.02/1.60 class_Rings_Odivision__ring__inverse__zero [86, 1] (w:1, o:159, a:1
% 1.02/1.60 , s:1, b:0),
% 1.02/1.60 class_Rings_Ono__zero__divisors [89, 1] (w:1, o:166, a:1, s:1, b:0),
% 1.02/1.60
% 1.02/1.60 class_Rings_Oring__no__zero__divisors [90, 1] (w:1, o:167, a:1, s:1
% 1.02/1.60 , b:0),
% 1.02/1.60 class_Rings_Omult__zero [91, 1] (w:1, o:165, a:1, s:1, b:0),
% 1.02/1.60 class_Rings_Ozero__neq__one [92, 1] (w:1, o:168, a:1, s:1, b:0),
% 1.02/1.60 class_Rings_Osemiring [95, 1] (w:1, o:172, a:1, s:1, b:0),
% 1.02/1.60 class_Rings_Ocomm__semiring [98, 1] (w:1, o:143, a:1, s:1, b:0),
% 1.02/1.60 class_Rings_Oring__1__no__zero__divisors [101, 1] (w:1, o:169, a:1
% 1.02/1.60 , s:1, b:0),
% 1.02/1.60 class_Groups_Ocomm__monoid__mult [102, 1] (w:1, o:173, a:1, s:1, b:0)
% 1.02/1.60 ,
% 1.02/1.60 class_Fields_Ofield__inverse__zero [103, 1] (w:1, o:150, a:1, s:1, b:
% 1.02/1.60 0),
% 1.02/1.60 class_Rings_Olinordered__ring__strict [105, 1] (w:1, o:135, a:1, s:1
% 1.02/1.60 , b:0),
% 1.02/1.60 class_Rings_Olinordered__comm__semiring__strict [106, 1] (w:1, o:160
% 1.02/1.60 , a:1, s:1, b:0),
% 1.02/1.60 class_Rings_Olinordered__semiring__strict [107, 1] (w:1, o:161, a:1
% 1.02/1.60 , s:1, b:0),
% 1.02/1.60 class_Rings_Olinordered__ring [108, 1] (w:1, o:136, a:1, s:1, b:0),
% 1.02/1.60 class_Rings_Osemiring__0 [109, 1] (w:1, o:174, a:1, s:1, b:0),
% 1.02/1.60 class_RealVector_Oreal__normed__algebra__1 [114, 1] (w:1, o:175, a:1
% 1.02/1.60 , s:1, b:0),
% 1.02/1.60 class_Rings_Ocomm__semiring__1 [117, 1] (w:1, o:145, a:1, s:1, b:0),
% 1.02/1.60
% 1.02/1.60 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 1.02/1.60 119, 1] (w:1, o:182, a:1, s:1, b:0),
% 1.02/1.60 class_Groups_Oordered__comm__monoid__add [120, 1] (w:1, o:183, a:1
% 1.02/1.60 , s:1, b:0),
% 1.02/1.60 class_Groups_Ozero [121, 1] (w:1, o:184, a:1, s:1, b:0),
% 1.02/1.60 class_Groups_Oab__semigroup__mult [125, 1] (w:1, o:185, a:1, s:1, b:0
% 1.02/1.60 ),
% 1.02/1.60 class_Groups_Oab__semigroup__add [127, 1] (w:1, o:186, a:1, s:1, b:0)
% 1.02/1.60 ,
% 1.02/1.60 class_Groups_Ocancel__semigroup__add [128, 1] (w:1, o:187, a:1, s:1
% 1.02/1.60 , b:0),
% 1.02/1.60 class_Groups_Ocancel__ab__semigroup__add [129, 1] (w:1, o:188, a:1
% 1.02/1.60 , s:1, b:0),
% 1.02/1.60 class_Groups_Oone [130, 1] (w:1, o:189, a:1, s:1, b:0),
% 1.02/1.60 class_Groups_Omonoid__add [131, 1] (w:1, o:190, a:1, s:1, b:0),
% 1.02/1.60 class_Groups_Ocomm__monoid__add [132, 1] (w:1, o:191, a:1, s:1, b:0)
% 1.02/1.60 ,
% 1.02/1.60 class_Groups_Olinordered__ab__group__add [133, 1] (w:1, o:151, a:1
% 1.02/1.60 , s:1, b:0),
% 1.02/1.60 class_Groups_Oordered__ab__semigroup__add__imp__le [134, 1] (w:1, o:
% 1.02/1.60 192, a:1, s:1, b:0),
% 1.02/1.60 class_Groups_Oordered__cancel__ab__semigroup__add [135, 1] (w:1, o:
% 1.02/1.60 193, a:1, s:1, b:0),
% 1.02/1.60 c_Groups_Ominus__class_Ominus [139, 3] (w:1, o:264, a:1, s:1, b:0),
% 1.02/1.60 c_Groups_Ouminus__class_Ouminus [140, 2] (w:1, o:239, a:1, s:1, b:0)
% 1.02/1.60 ,
% 1.02/1.60 class_Groups_Ogroup__add [144, 1] (w:1, o:194, a:1, s:1, b:0),
% 1.02/1.60 class_Groups_Oab__group__add [145, 1] (w:1, o:195, a:1, s:1, b:0),
% 1.02/1.60 class_Rings_Ocomm__ring__1 [146, 1] (w:1, o:141, a:1, s:1, b:0),
% 1.02/1.60 class_Groups_Oordered__ab__group__add [147, 1] (w:1, o:196, a:1, s:1
% 1.02/1.60 , b:0),
% 1.02/1.60 class_Rings_Oidom [148, 1] (w:1, o:176, a:1, s:1, b:0),
% 1.02/1.60 class_Rings_Oring [149, 1] (w:1, o:170, a:1, s:1, b:0),
% 1.02/1.60 class_Rings_Oordered__ring [151, 1] (w:1, o:177, a:1, s:1, b:0),
% 1.02/1.60 class_Rings_Oring__1 [152, 1] (w:1, o:171, a:1, s:1, b:0),
% 4.27/4.62 hBOOL [154, 1] (w:1, o:197, a:1, s:1, b:0),
% 4.27/4.62 c_Complex_Oii [158, 0] (w:1, o:100, a:1, s:1, b:0),
% 4.27/4.62 c_Power_Opower_Opower [159, 3] (w:1, o:266, a:1, s:1, b:0),
% 4.27/4.62 tc_Int_Oint [165, 0] (w:1, o:102, a:1, s:1, b:0),
% 4.27/4.62 v_pa____ [168, 0] (w:1, o:105, a:1, s:1, b:0),
% 4.27/4.62 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [169, 2] (w:1, o:
% 4.27/4.62 238, a:1, s:1, b:0),
% 4.27/4.62 c_Complex_Oexpi [170, 1] (w:1, o:198, a:1, s:1, b:0),
% 4.27/4.62 tc_Polynomial_Opoly [172, 1] (w:1, o:205, a:1, s:1, b:0),
% 4.27/4.62 v_q____ [173, 0] (w:1, o:107, a:1, s:1, b:0),
% 4.27/4.62 c_Polynomial_Omonom [174, 3] (w:1, o:267, a:1, s:1, b:0),
% 4.27/4.62 c_Polynomial_OpCons [175, 3] (w:1, o:269, a:1, s:1, b:0),
% 4.27/4.62 c_Polynomial_Opoly [176, 2] (w:1, o:240, a:1, s:1, b:0),
% 4.27/4.62 v_c____ [177, 0] (w:1, o:108, a:1, s:1, b:0),
% 4.27/4.62 c_Orderings_Oord__class_Oless__eq [178, 3] (w:1, o:265, a:1, s:1, b:0
% 4.27/4.62 ),
% 4.27/4.62 c_Nat_OSuc [179, 1] (w:1, o:206, a:1, s:1, b:0),
% 4.27/4.62 v_p [180, 0] (w:1, o:106, a:1, s:1, b:0),
% 4.27/4.62 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant [181, 3] (w:1
% 4.27/4.62 , o:262, a:1, s:1, b:0),
% 4.27/4.62 v_s____ [182, 0] (w:1, o:109, a:1, s:1, b:0),
% 4.27/4.62 class_Groups_Oordered__ab__semigroup__add [184, 1] (w:1, o:207, a:1
% 4.27/4.62 , s:1, b:0),
% 4.27/4.62 class_Rings_Oordered__cancel__semiring [192, 1] (w:1, o:178, a:1, s:1
% 4.27/4.62 , b:0),
% 4.27/4.62 class_Rings_Oordered__semiring [193, 1] (w:1, o:179, a:1, s:1, b:0),
% 4.27/4.62
% 4.27/4.62 class_Rings_Oordered__comm__semiring [194, 1] (w:1, o:180, a:1, s:1
% 4.27/4.62 , b:0),
% 4.27/4.62 class_Rings_Olinordered__semiring [197, 1] (w:1, o:162, a:1, s:1, b:0
% 4.27/4.62 ),
% 4.27/4.62 class_Rings_Olinordered__semiring__1 [200, 1] (w:1, o:163, a:1, s:1
% 4.27/4.62 , b:0),
% 4.27/4.62 class_Rings_Olinordered__semiring__1__strict [201, 1] (w:1, o:164, a:
% 4.27/4.62 1, s:1, b:0),
% 4.27/4.62 c_Polynomial_Osmult [203, 3] (w:1, o:270, a:1, s:1, b:0),
% 4.27/4.62 class_Rings_Ocomm__semiring__0 [205, 1] (w:1, o:144, a:1, s:1, b:0),
% 4.27/4.62
% 4.27/4.62 class_Int_Oring__char__0 [209, 1] (w:1, o:208, a:1, s:1, b:0),
% 4.27/4.62 class_Rings_Ocomm__ring [210, 1] (w:1, o:142, a:1, s:1, b:0),
% 4.27/4.62 c_Polynomial_Osynthetic__div [211, 3] (w:1, o:271, a:1, s:1, b:0),
% 4.27/4.62 c_Polynomial_Opcompose [213, 3] (w:1, o:272, a:1, s:1, b:0),
% 4.27/4.62 c_Polynomial_Oorder [214, 3] (w:1, o:268, a:1, s:1, b:0),
% 4.27/4.62 class_Orderings_Opreorder [216, 1] (w:1, o:155, a:1, s:1, b:0),
% 4.27/4.62 c_Rings_Odvd__class_Odvd [217, 3] (w:1, o:273, a:1, s:1, b:0),
% 4.27/4.62 class_Rings_Odvd [218, 1] (w:1, o:181, a:1, s:1, b:0),
% 4.27/4.62 class_Orderings_Olinorder [219, 1] (w:1, o:156, a:1, s:1, b:0),
% 4.27/4.62 class_Orderings_Oord [220, 1] (w:1, o:153, a:1, s:1, b:0),
% 4.27/4.62 tc_fun [221, 2] (w:1, o:251, a:1, s:1, b:0),
% 4.27/4.62 class_Orderings_Oorder [222, 1] (w:1, o:154, a:1, s:1, b:0),
% 4.27/4.62 c_Nat__Transfer_Otsub [229, 2] (w:1, o:252, a:1, s:1, b:0),
% 4.27/4.62 c_Polynomial_Opos__poly [230, 2] (w:1, o:253, a:1, s:1, b:0),
% 4.27/4.62 c_Divides_Odiv__class_Odiv [231, 3] (w:1, o:274, a:1, s:1, b:0),
% 4.27/4.62 class_Divides_Osemiring__div [232, 1] (w:1, o:209, a:1, s:1, b:0),
% 4.27/4.62 class_Groups_Ocancel__comm__monoid__add [234, 1] (w:1, o:210, a:1, s:
% 4.27/4.62 1, b:0),
% 4.27/4.62 tc_HOL_Obool [236, 0] (w:1, o:101, a:1, s:1, b:0),
% 4.27/4.62 v_thesis____ [238, 0] (w:1, o:125, a:1, s:1, b:0),
% 4.27/4.62 alpha1 [239, 4] (w:1, o:292, a:1, s:1, b:1),
% 4.27/4.62 alpha2 [240, 4] (w:1, o:295, a:1, s:1, b:1),
% 4.27/4.62 alpha3 [241, 3] (w:1, o:277, a:1, s:1, b:1),
% 4.27/4.62 alpha4 [242, 3] (w:1, o:278, a:1, s:1, b:1),
% 4.27/4.62 alpha5 [243, 3] (w:1, o:279, a:1, s:1, b:1),
% 4.27/4.62 alpha6 [244, 3] (w:1, o:280, a:1, s:1, b:1),
% 4.27/4.62 alpha7 [245, 2] (w:1, o:254, a:1, s:1, b:1),
% 4.27/4.62 alpha8 [246, 2] (w:1, o:255, a:1, s:1, b:1),
% 4.27/4.62 alpha9 [247, 2] (w:1, o:256, a:1, s:1, b:1),
% 4.27/4.62 alpha10 [248, 3] (w:1, o:281, a:1, s:1, b:1),
% 4.27/4.62 alpha11 [249, 2] (w:1, o:257, a:1, s:1, b:1),
% 4.27/4.62 alpha12 [250, 2] (w:1, o:258, a:1, s:1, b:1),
% 4.27/4.62 alpha13 [251, 3] (w:1, o:282, a:1, s:1, b:1),
% 4.27/4.62 alpha14 [252, 4] (w:1, o:293, a:1, s:1, b:1),
% 4.27/4.62 alpha15 [253, 4] (w:1, o:294, a:1, s:1, b:1),
% 4.27/4.62 alpha16 [254, 3] (w:1, o:283, a:1, s:1, b:1),
% 4.27/4.62 alpha17 [255, 3] (w:1, o:284, a:1, s:1, b:1),
% 34.78/35.16 alpha18 [256, 3] (w:1, o:285, a:1, s:1, b:1),
% 34.78/35.16 alpha19 [257, 3] (w:1, o:286, a:1, s:1, b:1),
% 34.78/35.16 alpha20 [258, 2] (w:1, o:259, a:1, s:1, b:1),
% 34.78/35.16 alpha21 [259, 2] (w:1, o:260, a:1, s:1, b:1),
% 34.78/35.16 alpha22 [260, 4] (w:1, o:296, a:1, s:1, b:1),
% 34.78/35.16 alpha23 [261, 3] (w:1, o:275, a:1, s:1, b:1),
% 34.78/35.16 alpha24 [262, 3] (w:1, o:276, a:1, s:1, b:1),
% 34.78/35.16 skol1 [263, 2] (w:1, o:241, a:1, s:1, b:1),
% 34.78/35.16 skol2 [264, 1] (w:1, o:202, a:1, s:1, b:1),
% 34.78/35.16 skol3 [265, 0] (w:1, o:22, a:1, s:1, b:1),
% 34.78/35.16 skol4 [266, 2] (w:1, o:242, a:1, s:1, b:1),
% 34.78/35.16 skol5 [267, 3] (w:1, o:287, a:1, s:1, b:1),
% 34.78/35.16 skol6 [268, 3] (w:1, o:288, a:1, s:1, b:1),
% 34.78/35.16 skol7 [269, 2] (w:1, o:243, a:1, s:1, b:1),
% 34.78/35.16 skol8 [270, 2] (w:1, o:244, a:1, s:1, b:1),
% 34.78/35.16 skol9 [271, 2] (w:1, o:245, a:1, s:1, b:1),
% 34.78/35.16 skol10 [272, 2] (w:1, o:246, a:1, s:1, b:1),
% 34.78/35.16 skol11 [273, 1] (w:1, o:199, a:1, s:1, b:1),
% 34.78/35.16 skol12 [274, 2] (w:1, o:247, a:1, s:1, b:1),
% 34.78/35.16 skol13 [275, 0] (w:1, o:23, a:1, s:1, b:1),
% 34.78/35.16 skol14 [276, 0] (w:1, o:24, a:1, s:1, b:1),
% 34.78/35.16 skol15 [277, 0] (w:1, o:25, a:1, s:1, b:1),
% 34.78/35.16 skol16 [278, 1] (w:1, o:200, a:1, s:1, b:1),
% 34.78/35.16 skol17 [279, 0] (w:1, o:26, a:1, s:1, b:1),
% 34.78/35.16 skol18 [280, 0] (w:1, o:27, a:1, s:1, b:1),
% 34.78/35.16 skol19 [281, 1] (w:1, o:201, a:1, s:1, b:1),
% 34.78/35.16 skol20 [282, 0] (w:1, o:18, a:1, s:1, b:1),
% 34.78/35.16 skol21 [283, 2] (w:1, o:248, a:1, s:1, b:1),
% 34.78/35.16 skol22 [284, 0] (w:1, o:19, a:1, s:1, b:1),
% 34.78/35.16 skol23 [285, 0] (w:1, o:20, a:1, s:1, b:1),
% 34.78/35.16 skol24 [286, 3] (w:1, o:289, a:1, s:1, b:1),
% 34.78/35.16 skol25 [287, 3] (w:1, o:290, a:1, s:1, b:1),
% 34.78/35.16 skol26 [288, 4] (w:1, o:297, a:1, s:1, b:1),
% 34.78/35.16 skol27 [289, 0] (w:1, o:21, a:1, s:1, b:1),
% 34.78/35.16 skol28 [290, 2] (w:1, o:249, a:1, s:1, b:1),
% 34.78/35.16 skol29 [291, 2] (w:1, o:250, a:1, s:1, b:1),
% 34.78/35.16 skol30 [292, 1] (w:1, o:203, a:1, s:1, b:1),
% 34.78/35.16 skol31 [293, 1] (w:1, o:204, a:1, s:1, b:1),
% 34.78/35.16 skol32 [294, 0] (w:1, o:28, a:1, s:1, b:1),
% 34.78/35.16 skol33 [295, 0] (w:1, o:29, a:1, s:1, b:1),
% 34.78/35.16 skol34 [296, 3] (w:1, o:291, a:1, s:1, b:1),
% 34.78/35.16 skol35 [297, 0] (w:1, o:30, a:1, s:1, b:1).
% 34.78/35.16
% 34.78/35.16
% 34.78/35.16 Starting Search:
% 34.78/35.16
% 34.78/35.16 *** allocated 113905 integers for clauses
% 34.78/35.16 *** allocated 170857 integers for clauses
% 34.78/35.16 Resimplifying inuse:
% 34.78/35.16 Done
% 34.78/35.16
% 34.78/35.16
% 34.78/35.16 Intermediate Status:
% 34.78/35.16 Generated: 3330
% 34.78/35.16 Kept: 2049
% 34.78/35.16 Inuse: 55
% 34.78/35.16 Deleted: 1
% 34.78/35.16 Deletedinuse: 0
% 34.78/35.16
% 34.78/35.16 *** allocated 256285 integers for clauses
% 34.78/35.16 *** allocated 170857 integers for termspace/termends
% 34.78/35.16 Resimplifying inuse:
% 34.78/35.16 Done
% 34.78/35.16
% 34.78/35.16 Resimplifying inuse:
% 34.78/35.16 Done
% 34.78/35.16
% 34.78/35.16
% 34.78/35.16 Intermediate Status:
% 34.78/35.16 Generated: 7238
% 34.78/35.16 Kept: 4056
% 34.78/35.16 Inuse: 142
% 34.78/35.16 Deleted: 5
% 34.78/35.16 Deletedinuse: 2
% 34.78/35.16
% 34.78/35.16 *** allocated 384427 integers for clauses
% 34.78/35.16 *** allocated 256285 integers for termspace/termends
% 34.78/35.16 Resimplifying inuse:
% 34.78/35.16 Done
% 34.78/35.16
% 34.78/35.16
% 34.78/35.16 Intermediate Status:
% 34.78/35.16 Generated: 14034
% 34.78/35.16 Kept: 6139
% 34.78/35.16 Inuse: 188
% 34.78/35.16 Deleted: 5
% 34.78/35.16 Deletedinuse: 2
% 34.78/35.16
% 34.78/35.16 Resimplifying inuse:
% 34.78/35.16 Done
% 34.78/35.16
% 34.78/35.16 *** allocated 576640 integers for clauses
% 34.78/35.16 Resimplifying inuse:
% 34.78/35.16 Done
% 34.78/35.16
% 34.78/35.16 *** allocated 384427 integers for termspace/termends
% 34.78/35.16
% 34.78/35.16 Intermediate Status:
% 34.78/35.16 Generated: 20665
% 34.78/35.16 Kept: 8208
% 34.78/35.16 Inuse: 243
% 34.78/35.16 Deleted: 5
% 34.78/35.16 Deletedinuse: 2
% 34.78/35.16
% 34.78/35.16 Resimplifying inuse:
% 34.78/35.16 Done
% 34.78/35.16
% 34.78/35.16 Resimplifying inuse:
% 34.78/35.16 Done
% 34.78/35.16
% 34.78/35.16
% 34.78/35.16 Intermediate Status:
% 34.78/35.16 Generated: 26619
% 34.78/35.16 Kept: 10366
% 34.78/35.16 Inuse: 267
% 34.78/35.16 Deleted: 6
% 34.78/35.16 Deletedinuse: 2
% 34.78/35.16
% 34.78/35.16 Resimplifying inuse:
% 34.78/35.16 Done
% 34.78/35.16
% 34.78/35.16 *** allocated 864960 integers for clauses
% 34.78/35.16 *** allocated 576640 integers for termspace/termends
% 34.78/35.16 Resimplifying inuse:
% 34.78/35.16 Done
% 34.78/35.16
% 34.78/35.16
% 34.78/35.16 Intermediate Status:
% 34.78/35.16 Generated: 45291
% 34.78/35.16 Kept: 12713
% 34.78/35.16 Inuse: 291
% 34.78/35.16 Deleted: 7
% 34.78/35.16 Deletedinuse: 2
% 34.78/35.16
% 34.78/35.16 Resimplifying inuse:
% 34.78/35.16 Done
% 34.78/35.16
% 34.78/35.16 Resimplifying inuse:
% 34.78/35.16 Done
% 34.78/35.16
% 34.78/35.16
% 34.78/35.16 Intermediate Status:
% 34.78/35.16 Generated: 52388
% 34.78/35.16 Kept: 15279
% 34.78/35.16 Inuse: 326
% 34.78/35.16 Deleted: 7
% 34.78/35.16 Deletedinuse: 2
% 34.78/35.16
% 34.78/35.16 Resimplifying inuse:
% 34.78/35.16 Done
% 34.78/35.16
% 34.78/35.16 Resimplifying inuse:
% 34.78/35.16 Done
% 34.78/35.16
% 34.78/35.16 *** allocated 1297440 integers for clauses
% 34.78/35.16
% 34.78/35.16 Intermediate Status:
% 34.78/35.16 Generated: 67154
% 34.78/35.16 Kept: 17540
% 34.78/35.16 Inuse: 346
% 34.78/35.16 Deleted: 7
% 34.78/35.16 Deletedinuse: 2
% 34.78/35.16
% 34.78/35.16 Resimplifying inuse:
% 34.78/35.16 Done
% 34.78/35.16
% 34.78/35.16 *** allocated 864960 integers for termspace/termends
% 34.78/35.16
% 34.78/35.16 Intermediate Status:
% 122.05/122.48 Generated: 82407
% 122.05/122.48 Kept: 19599
% 122.05/122.48 Inuse: 356
% 122.05/122.48 Deleted: 7
% 122.05/122.48 Deletedinuse: 2
% 122.05/122.48
% 122.05/122.48 Resimplifying inuse:
% 122.05/122.48 Done
% 122.05/122.48
% 122.05/122.48 Resimplifying clauses:
% 122.05/122.48 Done
% 122.05/122.48
% 122.05/122.48 Resimplifying inuse:
% 122.05/122.48 Done
% 122.05/122.48
% 122.05/122.48
% 122.05/122.48 Intermediate Status:
% 122.05/122.48 Generated: 89984
% 122.05/122.48 Kept: 21732
% 122.05/122.48 Inuse: 396
% 122.05/122.48 Deleted: 344
% 122.05/122.48 Deletedinuse: 2
% 122.05/122.48
% 122.05/122.48 Resimplifying inuse:
% 122.05/122.48 Done
% 122.05/122.48
% 122.05/122.48 Resimplifying inuse:
% 122.05/122.48 Done
% 122.05/122.48
% 122.05/122.48
% 122.05/122.48 Intermediate Status:
% 122.05/122.48 Generated: 96963
% 122.05/122.48 Kept: 23799
% 122.05/122.48 Inuse: 431
% 122.05/122.48 Deleted: 344
% 122.05/122.48 Deletedinuse: 2
% 122.05/122.48
% 122.05/122.48 Resimplifying inuse:
% 122.05/122.48 Done
% 122.05/122.48
% 122.05/122.48 Resimplifying inuse:
% 122.05/122.48 Done
% 122.05/122.48
% 122.05/122.48
% 122.05/122.48 Intermediate Status:
% 122.05/122.48 Generated: 103718
% 122.05/122.48 Kept: 25812
% 122.05/122.48 Inuse: 472
% 122.05/122.48 Deleted: 344
% 122.05/122.48 Deletedinuse: 2
% 122.05/122.48
% 122.05/122.48 Resimplifying inuse:
% 122.05/122.48 Done
% 122.05/122.48
% 122.05/122.48 Resimplifying inuse:
% 122.05/122.48 Done
% 122.05/122.48
% 122.05/122.48 *** allocated 1946160 integers for clauses
% 122.05/122.48
% 122.05/122.48 Intermediate Status:
% 122.05/122.48 Generated: 110222
% 122.05/122.48 Kept: 27819
% 122.05/122.48 Inuse: 523
% 122.05/122.48 Deleted: 344
% 122.05/122.48 Deletedinuse: 2
% 122.05/122.48
% 122.05/122.48 Resimplifying inuse:
% 122.05/122.48 Done
% 122.05/122.48
% 122.05/122.48 *** allocated 1297440 integers for termspace/termends
% 122.05/122.48 Resimplifying inuse:
% 122.05/122.48 Done
% 122.05/122.48
% 122.05/122.48
% 122.05/122.48 Intermediate Status:
% 122.05/122.48 Generated: 116544
% 122.05/122.48 Kept: 29900
% 122.05/122.48 Inuse: 571
% 122.05/122.48 Deleted: 344
% 122.05/122.48 Deletedinuse: 2
% 122.05/122.48
% 122.05/122.48 Resimplifying inuse:
% 122.05/122.48 Done
% 122.05/122.48
% 122.05/122.48
% 122.05/122.48 Intermediate Status:
% 122.05/122.48 Generated: 128866
% 122.05/122.48 Kept: 32546
% 122.05/122.48 Inuse: 591
% 122.05/122.48 Deleted: 344
% 122.05/122.48 Deletedinuse: 2
% 122.05/122.48
% 122.05/122.48 Resimplifying inuse:
% 122.05/122.48 Done
% 122.05/122.48
% 122.05/122.48 Resimplifying inuse:
% 122.05/122.48 Done
% 122.05/122.48
% 122.05/122.48
% 122.05/122.48 Intermediate Status:
% 122.05/122.48 Generated: 136062
% 122.05/122.48 Kept: 34561
% 122.05/122.48 Inuse: 615
% 122.05/122.48 Deleted: 344
% 122.05/122.48 Deletedinuse: 2
% 122.05/122.48
% 122.05/122.48 Resimplifying inuse:
% 122.05/122.48 Done
% 122.05/122.48
% 122.05/122.48
% 122.05/122.48 Intermediate Status:
% 122.05/122.48 Generated: 142932
% 122.05/122.48 Kept: 36671
% 122.05/122.48 Inuse: 636
% 122.05/122.48 Deleted: 344
% 122.05/122.48 Deletedinuse: 2
% 122.05/122.48
% 122.05/122.48 Resimplifying inuse:
% 122.05/122.48 Done
% 122.05/122.48
% 122.05/122.48
% 122.05/122.48 Intermediate Status:
% 122.05/122.48 Generated: 160645
% 122.05/122.48 Kept: 39655
% 122.05/122.48 Inuse: 661
% 122.05/122.48 Deleted: 344
% 122.05/122.48 Deletedinuse: 2
% 122.05/122.48
% 122.05/122.48 Resimplifying inuse:
% 122.05/122.48 Done
% 122.05/122.48
% 122.05/122.48 Resimplifying inuse:
% 122.05/122.48 Done
% 122.05/122.48
% 122.05/122.48 Resimplifying clauses:
% 122.05/122.48 Done
% 122.05/122.48
% 122.05/122.48
% 122.05/122.48 Intermediate Status:
% 122.05/122.48 Generated: 165460
% 122.05/122.48 Kept: 41669
% 122.05/122.48 Inuse: 675
% 122.05/122.48 Deleted: 589
% 122.05/122.48 Deletedinuse: 2
% 122.05/122.48
% 122.05/122.48 *** allocated 1946160 integers for termspace/termends
% 122.05/122.48 *** allocated 2919240 integers for clauses
% 122.05/122.48 Resimplifying inuse:
% 122.05/122.48 Done
% 122.05/122.48
% 122.05/122.48
% 122.05/122.48 Intermediate Status:
% 122.05/122.48 Generated: 175403
% 122.05/122.49 Kept: 44320
% 122.05/122.49 Inuse: 691
% 122.05/122.49 Deleted: 589
% 122.05/122.49 Deletedinuse: 2
% 122.05/122.49
% 122.05/122.49 Resimplifying inuse:
% 122.05/122.49 Done
% 122.05/122.49
% 122.05/122.49 Resimplifying inuse:
% 122.05/122.49 Done
% 122.05/122.49
% 122.05/122.49
% 122.05/122.49 Intermediate Status:
% 122.05/122.49 Generated: 182946
% 122.05/122.49 Kept: 46336
% 122.05/122.49 Inuse: 717
% 122.05/122.49 Deleted: 589
% 122.05/122.49 Deletedinuse: 2
% 122.05/122.49
% 122.05/122.49 Resimplifying inuse:
% 122.05/122.49 Done
% 122.05/122.49
% 122.05/122.49 Resimplifying inuse:
% 122.05/122.49 Done
% 122.05/122.49
% 122.05/122.49
% 122.05/122.49 Intermediate Status:
% 122.05/122.49 Generated: 189924
% 122.05/122.49 Kept: 48346
% 122.05/122.49 Inuse: 746
% 122.05/122.49 Deleted: 589
% 122.05/122.49 Deletedinuse: 2
% 122.05/122.49
% 122.05/122.49 Resimplifying inuse:
% 122.05/122.49 Done
% 122.05/122.49
% 122.05/122.49
% 122.05/122.49 Intermediate Status:
% 122.05/122.49 Generated: 213841
% 122.05/122.49 Kept: 52155
% 122.05/122.49 Inuse: 766
% 122.05/122.49 Deleted: 589
% 122.05/122.49 Deletedinuse: 2
% 122.05/122.49
% 122.05/122.49 Resimplifying inuse:
% 122.05/122.49 Done
% 122.05/122.49
% 122.05/122.49
% 122.05/122.49 Intermediate Status:
% 122.05/122.49 Generated: 235098
% 122.05/122.49 Kept: 54648
% 122.05/122.49 Inuse: 771
% 122.05/122.49 Deleted: 589
% 122.05/122.49 Deletedinuse: 2
% 122.05/122.49
% 122.05/122.49 Resimplifying inuse:
% 122.05/122.49 Done
% 122.05/122.49
% 122.05/122.49 Resimplifying inuse:
% 122.05/122.49 Done
% 122.05/122.49
% 122.05/122.49
% 122.05/122.49 Intermediate Status:
% 122.05/122.49 Generated: 247243
% 122.05/122.49 Kept: 57637
% 122.05/122.49 Inuse: 781
% 122.05/122.49 Deleted: 589
% 122.05/122.49 Deletedinuse: 2
% 122.05/122.49
% 122.05/122.49 Resimplifying inuse:
% 122.05/122.49 Done
% 122.05/122.49
% 122.05/122.49 *** allocated 2919240 integers for termspace/termends
% 122.05/122.49
% 122.05/122.49 Intermediate Status:
% 122.05/122.49 Generated: 254207
% 122.05/122.49 Kept: 59913
% 122.05/122.49 Inuse: 791
% 122.05/122.49 Deleted: 589
% 122.05/122.49 Deletedinuse: 2
% 122.05/122.49
% 122.05/122.49 Resimplifying inuse:
% 122.05/122.49 Done
% 122.05/122.49
% 122.05/122.49 Resimplifying inuse:
% 122.05/122.49 Done
% 122.05/122.49
% 122.05/122.49 Resimplifying clauses:
% 122.05/122.49 Done
% 122.05/122.49
% 122.05/122.49
% 122.05/122.49 Intermediate Status:
% 122.05/122.49 Generated: 263310
% 122.05/122.49 Kept: 61935
% 122.05/122.49 Inuse: 813
% 122.05/122.49 Deleted: 706
% 122.05/122.49 Deletedinuse: 2
% 122.05/122.49
% 122.05/122.49 Resimplifying inuse:
% 122.05/122.49 Done
% 122.05/122.49
% 122.05/122.49 *** allocated 4378860 integers for clauses
% 122.05/122.49
% 122.05/122.49 Intermediate Status:
% 122.05/122.49 Generated: 290682
% 122.05/122.49 Kept: 64303
% 122.05/122.49 Inuse: 816
% 122.05/122.49 Deleted: 706
% 122.05/122.49 Deletedinuse: 2
% 122.05/122.49
% 122.05/122.49 Resimplifying inuse:
% 122.05/122.49 Done
% 122.05/122.49
% 122.05/122.49 Resimplifying inuse:
% 122.05/122.49 Done
% 122.05/122.49
% 122.05/122.49
% 122.05/122.49 Intermediate Status:
% 122.05/122.49 Generated: 304271
% 122.05/122.49 Kept: 67425
% 122.05/122.49 Inuse: 826
% 122.05/122.49 Deleted: 706
% 122.05/122.49 Deletedinuse: 2
% 122.05/122.49
% 122.05/122.49 Resimplifying inuse:
% 122.05/122.49 Done
% 122.05/122.49
% 122.05/122.49 Resimplifying inuse:
% 122.05/122.49 Done
% 122.05/122.49
% 122.05/122.49
% 122.05/122.49 Intermediate Status:
% 122.05/122.49 Generated: 320743
% 122.05/122.49 Kept: 70547
% 122.05/122.49 Inuse: 851
% 122.05/122.49 Deleted: 706
% 122.05/122.49 Deletedinuse: 2
% 122.05/122.49
% 122.05/122.49 Resimplifying inuse:
% 122.05/122.49 Done
% 122.05/122.49
% 122.05/122.49 Resimplifying inuse:
% 122.05/122.49 Done
% 122.05/122.49
% 122.05/122.49
% 122.05/122.49 Intermediate Status:
% 122.05/122.49 Generated: 331690
% 122.05/122.49 Kept: 72741
% 122.05/122.49 Inuse: 866
% 122.05/122.49 Deleted: 706
% 122.05/122.49 Deletedinuse: 2
% 122.05/122.49
% 122.05/122.49 Resimplifying inuse:
% 122.05/122.49 Done
% 122.05/122.49
% 122.05/122.49 Resimplifying inuse:
% 122.05/122.49 Done
% 122.05/122.49
% 122.05/122.49
% 122.05/122.49 Intermediate Status:
% 122.05/122.49 GeneratedCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------