TSTP Solution File: SWW204+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW204+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Wed Jul 20 23:21:12 EDT 2022
% Result : Timeout 300.05s 300.49s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SWW204+1 : TPTP v8.1.0. Released v5.2.0.
% 0.00/0.08 % Command : bliksem %s
% 0.07/0.27 % Computer : n032.cluster.edu
% 0.07/0.27 % Model : x86_64 x86_64
% 0.07/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27 % Memory : 8042.1875MB
% 0.07/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27 % CPULimit : 300
% 0.07/0.27 % DateTime : Sat Jun 4 10:25:32 EDT 2022
% 0.07/0.27 % CPUTime :
% 1.08/1.65 *** allocated 10000 integers for termspace/termends
% 1.08/1.65 *** allocated 10000 integers for clauses
% 1.08/1.65 *** allocated 10000 integers for justifications
% 1.08/1.65 *** allocated 15000 integers for termspace/termends
% 1.08/1.65 *** allocated 22500 integers for termspace/termends
% 1.08/1.65 *** allocated 33750 integers for termspace/termends
% 1.08/1.65 Bliksem 1.12
% 1.08/1.65
% 1.08/1.65
% 1.08/1.65 Automatic Strategy Selection
% 1.08/1.65
% 1.08/1.65 *** allocated 50625 integers for termspace/termends
% 1.08/1.65 *** allocated 75937 integers for termspace/termends
% 1.08/1.65 *** allocated 113905 integers for termspace/termends
% 1.08/1.65
% 1.08/1.65 Clauses:
% 1.08/1.65
% 1.08/1.65 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 1.08/1.65 { c_SEQ_Osubseq( v_ga____ ) }.
% 1.08/1.65 { ! class_Orderings_Opreorder( X ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ), Y ) ) }.
% 1.08/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( v_s, X ) ) )
% 1.08/1.65 , v_r ) ) }.
% 1.08/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( v_s,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), v_r ) ) }.
% 1.08/1.65 { c_SEQ_Osubseq( v_f____ ) }.
% 1.08/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ), X
% 1.08/1.65 ) ) }.
% 1.08/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ), X
% 1.08/1.65 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X
% 1.08/1.65 ), Y ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 1.08/1.65 X ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal
% 1.08/1.65 , X ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.08/1.65 tc_RealDef_Oreal, Y ), Z ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 1.08/1.65 X ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal
% 1.08/1.65 , X ), Y ) ), Y = X }.
% 1.08/1.65 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ), hBOOL(
% 1.08/1.65 hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ) ), hAPP( Y, U )
% 1.08/1.65 ) ) }.
% 1.08/1.65 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, skol2( X, Y, Z ) ) ), hAPP
% 1.08/1.65 ( Y, skol2( X, Y, Z ) ) ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ) }.
% 1.08/1.65 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 1.08/1.65 { ! class_Orderings_Oorder( X ), ! Z = Y, hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.08/1.65 { ! class_Orderings_Oorder( X ), ! Z = Y, hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 1.08/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), Z = Y }.
% 1.08/1.65 { ! class_Orderings_Opreorder( X ), ! Z = Y, hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.08/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( v_s,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) }.
% 1.08/1.65 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 1.08/1.65 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ), hBOOL(
% 1.08/1.65 hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ) ), hAPP( Y, U )
% 1.08/1.65 ) ) }.
% 1.08/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ) }.
% 1.08/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), Y = Z }.
% 1.08/1.65 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ), T ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), T ) ) }.
% 1.08/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), Z = Y }.
% 1.08/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! Z = T, hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ) }.
% 1.08/1.65 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! Y = T, hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), T ) ) }.
% 1.08/1.65 { ! class_Orderings_Oorder( X ), ! Z = Y, ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ) }.
% 1.08/1.65 { ! class_Orderings_Oord( X ), ! Z = Y, ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ), T ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), T ) ) }.
% 1.08/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), Y = Z }.
% 1.08/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! Y = Z, hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 1.08/1.65 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ), hBOOL(
% 1.08/1.65 hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ) ), hAPP( Y, U )
% 1.08/1.65 ) ) }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, Y ) ), c_Groups_Ozero__class_Ozero(
% 1.08/1.65 tc_RealDef_Oreal ) ) ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, Y ) ), c_Groups_Ozero__class_Ozero(
% 1.08/1.65 tc_RealDef_Oreal ) ) ) }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__vector( X ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, Y ) = c_Groups_Ozero__class_Ozero(
% 1.08/1.65 tc_RealDef_Oreal ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X, Y )
% 1.08/1.65 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.08/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ) }.
% 1.08/1.65 { ! c_SEQ_Osubseq( X ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.08/1.65 tc_Nat_Onat, Y ), hAPP( X, Y ) ) ) }.
% 1.08/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ),
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.08/1.65 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ),
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.08/1.65 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.08/1.65 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_RealDef_Oreal( tc_Nat_Onat, X ) ), c_Groups_Ozero__class_Ozero(
% 1.08/1.65 tc_RealDef_Oreal ) ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 1.08/1.65 .
% 1.08/1.65 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.08/1.65 tc_Nat_Onat, X ) ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ) }
% 1.08/1.65 .
% 1.08/1.65 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, Z ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ),
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, T ) ) ) ), Z =
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.08/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_RealDef_Oreal(
% 1.08/1.65 tc_Nat_Onat, X ) ) ) }.
% 1.08/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), X ) ) }
% 1.08/1.65 .
% 1.08/1.65 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 1.08/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) =
% 1.08/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y )
% 1.08/1.65 }.
% 1.08/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ),
% 1.08/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Y ) ) }
% 1.08/1.65 .
% 1.08/1.65 { ! c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat, X ),
% 1.08/1.65 Y = X }.
% 1.08/1.65 { ! Y = X, c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat
% 1.08/1.65 , X ) }.
% 1.08/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP
% 1.08/1.65 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) ), X ) =
% 1.08/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), hAPP
% 1.08/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.08/1.65 { ! Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y )
% 1.08/1.65 , X ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.65 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Z )
% 1.08/1.65 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 1.08/1.65 ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.65 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Y )
% 1.08/1.65 ), Y = X }.
% 1.08/1.65 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.08/1.65 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.08/1.65 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.08/1.65 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.08/1.65 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal( tc_Nat_Onat, X ) )
% 1.08/1.65 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X )
% 1.08/1.65 ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.65 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal( tc_Nat_Onat, X ) )
% 1.08/1.65 ) }.
% 1.08/1.65 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP( hAPP
% 1.08/1.65 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), Z = Y }.
% 1.08/1.65 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 1.08/1.65 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP(
% 1.08/1.65 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) }.
% 1.08/1.65 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP( hAPP
% 1.08/1.65 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ), Z = Y }.
% 1.08/1.65 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 1.08/1.65 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP(
% 1.08/1.65 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) }.
% 1.08/1.65 { ! c_RealDef_Oreal( tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero(
% 1.08/1.65 tc_RealDef_Oreal ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.08/1.65 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RealDef_Oreal(
% 1.08/1.65 tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.08/1.65 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.08/1.65 ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.08/1.65 { ! class_Rings_Olinordered__ring( X ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.65 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.08/1.65 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.65 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ), alpha1( X
% 1.08/1.65 , Y, Z ), alpha16( X, Y, Z ) }.
% 1.08/1.65 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha1( X, Y, Z ), hBOOL
% 1.08/1.65 ( hAPP( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.08/1.65 ( X ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.08/1.65 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha16( X, Y, Z ), hBOOL
% 1.08/1.65 ( hAPP( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.08/1.65 ( X ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.08/1.65 { ! alpha16( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.08/1.65 Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.08/1.65 { ! alpha16( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.08/1.65 Y ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.08/1.65 ) ) ), alpha16( X, Y, Z ) }.
% 1.08/1.65 { ! alpha1( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) ), Z ) ) }.
% 1.08/1.65 { ! alpha1( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) ), Y ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.65 , Y ) ), alpha1( X, Y, Z ) }.
% 1.08/1.65 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) ) ), alpha2( X, Y, Z ), alpha17( X, Y, Z
% 1.08/1.65 ) }.
% 1.08/1.65 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha2( X, Y, Z ), hBOOL
% 1.08/1.65 ( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.08/1.65 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha17( X, Y, Z ), hBOOL
% 1.08/1.65 ( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.08/1.65 { ! alpha17( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.08/1.65 Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.08/1.65 { ! alpha17( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) ), Y ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.65 , Y ) ), alpha17( X, Y, Z ) }.
% 1.08/1.65 { ! alpha2( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) ), Z ) ) }.
% 1.08/1.65 { ! alpha2( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y
% 1.08/1.65 ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.08/1.65 ) ) ), alpha2( X, Y, Z ) }.
% 1.08/1.65 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.65 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.65 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.08/1.65 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.65 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.08/1.65 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.65 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.08/1.65 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.08/1.65 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.08/1.65 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.08/1.65 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.65 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.08/1.65 { ! class_Rings_Oordered__semiring( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.65 , T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 1.08/1.65 { ! class_Rings_Oordered__semiring( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.65 , T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 1.08/1.65 { ! class_Rings_Oordered__comm__semiring( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.65 , T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 1.08/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.08/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.08/1.65 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.08/1.65 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.08/1.65 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.08/1.65 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.08/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 1.08/1.65 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.08/1.65 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.08/1.65 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.08/1.65 .
% 1.08/1.65 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.08/1.65 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.08/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 1.08/1.65 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.08/1.65 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.08/1.65 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 1.08/1.65 .
% 1.08/1.65 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.65 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), Z )
% 1.08/1.65 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.08/1.65 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ) ), hAPP(
% 1.08/1.65 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.65 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.08/1.65 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.65 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.08/1.65 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) ) }.
% 1.08/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), hAPP(
% 1.08/1.65 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) ) }.
% 1.08/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), hAPP(
% 1.08/1.65 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 1.08/1.65 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.08/1.65 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.08/1.65 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal
% 1.08/1.65 ( tc_Nat_Onat, X ) ) }.
% 1.08/1.65 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.08/1.65 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.08/1.65 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.08/1.65 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.08/1.65 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.08/1.65 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.08/1.65 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.08/1.65 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.08/1.65 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.08/1.65 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.08/1.65 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.08/1.65 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.08/1.65 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.65 , Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ),
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.08/1.65 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), c_Groups_Ozero__class_Ozero( X
% 1.08/1.65 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) ), Y ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.08/1.65 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.65 , Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) ), Y ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.65 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.08/1.65 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), c_Groups_Ozero__class_Ozero( X
% 1.08/1.65 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ),
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.65 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.08/1.65 { ! class_Rings_Oordered__semiring( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.65 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) ), U ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 1.08/1.65 { ! class_Rings_Oordered__semiring( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.65 , Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) ), U ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 1.08/1.65 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, T ), c_Groups_Ozero__class_Ozero( X
% 1.08/1.65 ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) ) }.
% 1.08/1.65 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, T ), c_Groups_Ozero__class_Ozero( X
% 1.08/1.65 ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) ) }.
% 1.08/1.65 { ! class_Orderings_Oorder( X ), ! c_SEQ_Odecseq( X, Y ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), T ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ) ), hAPP( Y, Z ) ) ) }
% 1.08/1.65 .
% 1.08/1.65 { ! class_Orderings_Oorder( X ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol3( X, Y ) ), skol62(
% 1.08/1.65 X, Y ) ) ), c_SEQ_Odecseq( X, Y ) }.
% 1.08/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, skol62( X, Y ) ) ), hAPP(
% 1.08/1.65 Y, skol3( X, Y ) ) ) ), c_SEQ_Odecseq( X, Y ) }.
% 1.08/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.08/1.65 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.08/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.08/1.65 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol4( Y ) ) ) }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol4( X ) ) ) ) }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol5( Z, T ) ) ) }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol5( X, Y ) ) ) ) }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol6( Z, T ) ) ) }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol6( X, Y ) ) ) ) }.
% 1.08/1.65 { ! class_Orderings_Oorder( X ), ! c_SEQ_Oincseq( X, Y ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), T ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, Z ) ), hAPP( Y, T ) ) ) }
% 1.08/1.65 .
% 1.08/1.65 { ! class_Orderings_Oorder( X ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol7( X, Y ) ), skol63(
% 1.08/1.65 X, Y ) ) ), c_SEQ_Oincseq( X, Y ) }.
% 1.08/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, skol7( X, Y ) ) ), hAPP( Y
% 1.08/1.65 , skol63( X, Y ) ) ) ), c_SEQ_Oincseq( X, Y ) }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol8( X ) ) ) ) }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol9( X, Y ) ) ) ) }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol10( X, Y ) ) ) ) }.
% 1.08/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 1.08/1.65 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.08/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 1.08/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.08/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.08/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 1.08/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.08/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 1.08/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.08/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 1.08/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.08/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 1.08/1.65 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.08/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.08/1.65 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.08/1.65 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.08/1.65 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.08/1.65 .
% 1.08/1.65 { ! class_Groups_Ozero( X ), !
% 1.08/1.65 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.65 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.08/1.65 tc_Polynomial_Opoly( X ) ),
% 1.08/1.65 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_RComplete_Onatfloor( X )
% 1.08/1.65 ), c_RComplete_Onatfloor( Y ) ) ), c_RComplete_Onatfloor( hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ) ) }.
% 1.08/1.65 { ! class_Orderings_Oorder( X ), ! c_SEQ_Omonoseq( X, Y ), alpha3( X, Y ),
% 1.08/1.65 alpha18( X, Y ) }.
% 1.08/1.65 { ! class_Orderings_Oorder( X ), ! alpha3( X, Y ), c_SEQ_Omonoseq( X, Y ) }
% 1.08/1.65 .
% 1.08/1.65 { ! class_Orderings_Oorder( X ), ! alpha18( X, Y ), c_SEQ_Omonoseq( X, Y )
% 1.08/1.65 }.
% 1.08/1.65 { ! alpha18( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.08/1.65 tc_Nat_Onat, Z ), T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.08/1.65 X, hAPP( Y, T ) ), hAPP( Y, Z ) ) ) }.
% 1.08/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol11( X, Y
% 1.08/1.65 ) ), skol64( X, Y ) ) ), alpha18( X, Y ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, skol64( X,
% 1.08/1.65 Y ) ) ), hAPP( Y, skol11( X, Y ) ) ) ), alpha18( X, Y ) }.
% 1.08/1.65 { ! alpha3( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.08/1.65 tc_Nat_Onat, Z ), T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.08/1.65 X, hAPP( Y, Z ) ), hAPP( Y, T ) ) ) }.
% 1.08/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol12( X, Y
% 1.08/1.65 ) ), skol65( X, Y ) ) ), alpha3( X, Y ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, skol12( X,
% 1.08/1.65 Y ) ) ), hAPP( Y, skol65( X, Y ) ) ) ), alpha3( X, Y ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 1.08/1.65 X ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.08/1.65 tc_RealDef_Oreal, X ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ), c_RealDef_Oreal
% 1.08/1.65 ( tc_Nat_Onat, Y ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.08/1.65 tc_Nat_Onat, c_RComplete_Onatceiling( X ) ), Y ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ),
% 1.08/1.65 c_RComplete_Onatfloor( X ) ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.08/1.65 tc_Nat_Onat, Y ) ), X ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.08/1.65 tc_Nat_Onat, Y ) ), X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.08/1.65 ( tc_Nat_Onat, Y ), c_RComplete_Onatfloor( X ) ) ) }.
% 1.08/1.65 { ! class_Orderings_Oorder( X ), ! c_SEQ_Odecseq( X, Y ), c_SEQ_Omonoseq( X
% 1.08/1.65 , Y ) }.
% 1.08/1.65 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 1.08/1.65 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 1.08/1.65 { c_RComplete_Onatfloor( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 1.08/1.65 { c_RComplete_Onatceiling( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 1.08/1.65 { c_RComplete_Onatfloor( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) )
% 1.08/1.65 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.08/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), c_RComplete_Onatfloor( X )
% 1.08/1.65 ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 1.08/1.65 X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.08/1.65 c_RComplete_Onatfloor( Y ) ), c_RComplete_Onatfloor( X ) ) ) }.
% 1.08/1.65 { c_RComplete_Onatceiling( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 1.08/1.65 ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.08/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), c_RComplete_Onatceiling( X
% 1.08/1.65 ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 1.08/1.65 X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.08/1.65 c_RComplete_Onatceiling( Y ) ), c_RComplete_Onatceiling( X ) ) ) }.
% 1.08/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ),
% 1.08/1.65 c_RealDef_Oreal( tc_Nat_Onat, c_RComplete_Onatceiling( X ) ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ),
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ),
% 1.08/1.65 c_RComplete_Onatfloor( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 1.08/1.65 .
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.08/1.65 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ) ), X ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ),
% 1.08/1.65 c_RComplete_Onatfloor( X ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ),
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ),
% 1.08/1.65 c_RComplete_Onatceiling( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.08/1.65 }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 1.08/1.65 c_RealDef_Oreal( tc_Nat_Onat, X ) ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 1.08/1.65 Y ) ), X ) ) }.
% 1.08/1.65 { ! class_Orderings_Oorder( X ), ! c_SEQ_Oincseq( X, Y ), c_SEQ_Omonoseq( X
% 1.08/1.65 , Y ) }.
% 1.08/1.65 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 1.08/1.65 { ! class_Orderings_Oorder( X ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol13( X, Y ) ), skol66
% 1.08/1.65 ( X, Y ) ) ), c_SEQ_Omonoseq( X, Y ) }.
% 1.08/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, skol13( X, Y ) ) ), hAPP(
% 1.08/1.65 Y, skol66( X, Y ) ) ) ), c_SEQ_Omonoseq( X, Y ) }.
% 1.08/1.65 { ! class_Orderings_Oorder( X ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol14( X, Y ) ), skol67
% 1.08/1.65 ( X, Y ) ) ), c_SEQ_Omonoseq( X, Y ) }.
% 1.08/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, skol67( X, Y ) ) ), hAPP(
% 1.08/1.65 Y, skol14( X, Y ) ) ) ), c_SEQ_Omonoseq( X, Y ) }.
% 1.08/1.65 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.65 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.65 { c_SEQ_Omonoseq( tc_RealDef_Oreal, c_COMBB( tc_Complex_Ocomplex,
% 1.08/1.65 tc_RealDef_Oreal, tc_Nat_Onat, c_Complex_OIm, c_COMBB( tc_Nat_Onat,
% 1.08/1.65 tc_Complex_Ocomplex, tc_Nat_Onat, v_s, c_COMBB( tc_Nat_Onat, tc_Nat_Onat
% 1.08/1.65 , tc_Nat_Onat, v_f____, v_ga____ ) ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.08/1.65 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ), ! hBOOL( hAPP
% 1.08/1.65 ( c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.08/1.65 ( tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.08/1.65 ( tc_Nat_Onat, Z ), X ) ) }.
% 1.08/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), X ) )
% 1.08/1.65 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.08/1.65 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.08/1.65 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), ! hBOOL( hAPP
% 1.08/1.65 ( c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.08/1.65 ( tc_Nat_Onat ) ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.08/1.65 ( tc_Nat_Onat, Y ), X ) ) }.
% 1.08/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.65 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.08/1.65 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__algebra( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, U ) ), T ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ),
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.08/1.65 { c_SEQ_Omonoseq( tc_RealDef_Oreal, c_COMBB( tc_Complex_Ocomplex,
% 1.08/1.65 tc_RealDef_Oreal, tc_Nat_Onat, c_Complex_ORe, c_COMBB( tc_Nat_Onat,
% 1.08/1.65 tc_Complex_Ocomplex, tc_Nat_Onat, v_s, v_f____ ) ) ) }.
% 1.08/1.65 { ! class_Rings_Olinordered__idom( X ), Z = Y, hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 1.08/1.65 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Y ), Y ) ) }.
% 1.08/1.65 { ! class_Orderings_Olinorder( X ), Z = Y, hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 1.08/1.65 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! Z = Y }.
% 1.08/1.65 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Y ), Z ) ), ! Z = Y }.
% 1.08/1.65 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Y ), Z ) ), Z = Y }.
% 1.08/1.65 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Y ), Z ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.08/1.65 { ! class_Orderings_Olinorder( X ), ! Z = Y, ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.08/1.65 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), Z = Y, hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 1.08/1.65 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Y ), Z ) ), Y = Z }.
% 1.08/1.65 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! Y = Z, ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 1.08/1.65 { ! class_Orderings_Olinorder( X ), Z = Y, hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 1.08/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! Z = Y }.
% 1.08/1.65 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 1.08/1.65 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 1.08/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! Z = Y }.
% 1.08/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! Y = Z }.
% 1.08/1.65 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 1.08/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 1.08/1.65 { ! class_Orderings_Oord( X ), ! Z = Y, ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Y ), T ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), T ) ) }.
% 1.08/1.65 { ! class_Orderings_Oorder( X ), ! Z = Y, ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, T ), Y ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, T ), Z ) ) }.
% 1.08/1.65 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless
% 1.08/1.65 ( X, Z ), Y ) ), ! Y = T, hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.08/1.65 Z ), T ) ) }.
% 1.08/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! Z = T, hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, T ), Y ) ) }.
% 1.08/1.65 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Y ), T ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), T ) ) }.
% 1.08/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, T ), Z ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, T ), Y ) ) }.
% 1.08/1.65 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 1.08/1.65 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), Z = Y, hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), X ) ) }.
% 1.08/1.65 { Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X )
% 1.08/1.65 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Y ) ) }
% 1.08/1.65 .
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 1.08/1.65 Y = X }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Y ) ), !
% 1.08/1.65 Y = X }.
% 1.08/1.65 { Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X )
% 1.08/1.65 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Y ) ) }
% 1.08/1.65 .
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), X ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 1.08/1.65 X = Y }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 1.08/1.65 Y = X }.
% 1.08/1.65 { alpha42( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.08/1.65 tc_Nat_Onat, Y ), Z ) ), hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.08/1.65 { alpha42( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 1.08/1.65 ( X, Y ), Z ) ) }.
% 1.08/1.65 { ! alpha42( X, Y, Z ), alpha45( X, Y, Z ), Z = Y }.
% 1.08/1.65 { ! alpha42( X, Y, Z ), alpha45( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 1.08/1.65 ) ) }.
% 1.08/1.65 { ! alpha45( X, Y, Z ), alpha42( X, Y, Z ) }.
% 1.08/1.65 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha42( X, Y, Z ) }.
% 1.08/1.65 { ! alpha45( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.08/1.65 tc_Nat_Onat, Z ), Y ) ) }.
% 1.08/1.65 { ! alpha45( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), Y ) ),
% 1.08/1.65 hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha45( X, Y, Z ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal( tc_Nat_Onat, X ) )
% 1.08/1.65 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ) }
% 1.08/1.65 .
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.08/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal( tc_Nat_Onat, X ) )
% 1.08/1.65 ) }.
% 1.08/1.65 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 1.08/1.65 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.08/1.65 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 1.08/1.65 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Y ), Z ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.08/1.65 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 1.08/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.08/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! Z = Y }.
% 1.08/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), Z = Y, hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.08/1.65 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.08/1.65 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 1.08/1.65 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.08/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), Z = Y }.
% 1.08/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.08/1.65 { ! class_Orderings_Oorder( X ), ! Z = Y, hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.08/1.65 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 1.08/1.65 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 1.08/1.65 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), Z = Y }.
% 1.08/1.65 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! Z = Y, hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.08/1.65 { ! class_Orderings_Oorder( X ), Z = Y, ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.08/1.65 { ! class_Orderings_Oorder( X ), Z = Y, ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 1.08/1.65 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Y ), Z ) ) }.
% 1.08/1.65 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.08/1.65 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), Z = Y }.
% 1.08/1.65 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! Z = Y, ! hBOOL( hAPP
% 1.08/1.65 ( c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.08/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), Z = Y }.
% 1.08/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), Z = Y, hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.08/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), Y = Z, hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.08/1.65 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Y ), T ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), T ) ) }.
% 1.08/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, T ), Y ) ) }.
% 1.08/1.65 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Y ), T ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), T ) ) }.
% 1.08/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, T ), Z ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, T ), Y ) ) }.
% 1.08/1.65 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.08/1.65 tc_Nat_Onat ) ), X ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 1.08/1.65 X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ),
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.08/1.65 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.08/1.65 tc_Nat_Onat ) ), X ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! X =
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ),
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y ), X )
% 1.08/1.65 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y )
% 1.08/1.65 , X ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y ), X )
% 1.08/1.65 ), ! Y = X }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 1.08/1.65 X ) ), Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.08/1.65 tc_RealDef_Oreal, Y ), X ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 1.08/1.65 X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y )
% 1.08/1.65 , X ) ), Y = X }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y ), X )
% 1.08/1.65 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y )
% 1.08/1.65 , X ) ) }.
% 1.08/1.65 { ! Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal
% 1.08/1.65 , Y ), X ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.08/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }
% 1.08/1.65 .
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 1.08/1.65 Y = X }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.65 , Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X
% 1.08/1.65 ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.65 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), Y
% 1.08/1.65 = X }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.08/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }
% 1.08/1.65 .
% 1.08/1.65 { ! Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y )
% 1.08/1.65 , X ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.08/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }
% 1.08/1.65 .
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.65 , Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X
% 1.08/1.65 ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.08/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }
% 1.08/1.65 .
% 1.08/1.65 { ! Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y )
% 1.08/1.65 , X ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_RealDef_Oreal(
% 1.08/1.65 tc_Nat_Onat, X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.08/1.65 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_RealDef_Oreal(
% 1.08/1.65 tc_Nat_Onat, X ) ) ) }.
% 1.08/1.65 { ! c_SEQ_Osubseq( X ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.08/1.65 tc_Nat_Onat, Y ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.08/1.65 tc_Nat_Onat, hAPP( X, Y ) ), hAPP( X, Z ) ) ) }.
% 1.08/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol15( X ) ),
% 1.08/1.65 skol68( X ) ) ), c_SEQ_Osubseq( X ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( X,
% 1.08/1.65 skol15( X ) ) ), hAPP( X, skol68( X ) ) ) ), c_SEQ_Osubseq( X ) }.
% 1.08/1.65 { ! class_Rings_Olinordered__ring( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.08/1.65 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), alpha4( X, Y, Z, T ),
% 1.08/1.65 alpha19( X, Y, Z, T ) }.
% 1.08/1.65 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha4( X, Y, Z, T ),
% 1.08/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.08/1.65 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha19( X, Y, Z, T ),
% 1.08/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.08/1.65 { ! alpha19( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z
% 1.08/1.65 ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.08/1.65 { ! alpha19( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Y
% 1.08/1.65 ), T ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ),
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Y ), T ) ), alpha19( X, Y, Z, T ) }.
% 1.08/1.65 { ! alpha4( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) ), Z ) ) }.
% 1.08/1.65 { ! alpha4( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T
% 1.08/1.65 ), Y ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, T ), Y ) ), alpha4( X, Y, Z, T ) }.
% 1.08/1.65 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), alpha5( X, Y, Z, T ),
% 1.08/1.65 alpha20( X, Y, Z, T ) }.
% 1.08/1.65 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha5( X, Y, Z, T ),
% 1.08/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 1.08/1.65 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha20( X, Y, Z, T ),
% 1.08/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 1.08/1.65 { ! alpha20( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T
% 1.08/1.65 ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.08/1.65 { ! alpha20( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Y
% 1.08/1.65 ), Z ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ),
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Y ), Z ) ), alpha20( X, Y, Z, T ) }.
% 1.08/1.65 { ! alpha5( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) ), T ) ) }.
% 1.08/1.65 { ! alpha5( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z
% 1.08/1.65 ), Y ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) ), T ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), alpha5( X, Y, Z, T ) }.
% 1.08/1.65 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.08/1.65 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, T ), Z ) ) }.
% 1.08/1.65 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.08/1.65 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ), Z ) ), hBOOL(
% 1.08/1.65 hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.08/1.65 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.08/1.65 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 1.08/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.08/1.65 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.08/1.65 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ),
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.08/1.65 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.08/1.65 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ),
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.08/1.65 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 1.08/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ), ! hBOOL(
% 1.08/1.65 hAPP( c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.08/1.65 ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) ), Y ) ) }.
% 1.08/1.65 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 1.08/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ), ! hBOOL(
% 1.08/1.65 hAPP( c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.08/1.65 ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) ), Z ) ) }.
% 1.08/1.65 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.65 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), T ) ) }.
% 1.08/1.65 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.65 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ), T ) ), hBOOL(
% 1.08/1.65 hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.08/1.65 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.65 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.08/1.65 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.65 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ),
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 1.08/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.08/1.65 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), T )
% 1.08/1.65 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 1.08/1.65 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), T )
% 1.08/1.65 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 1.08/1.65 { ! class_Rings_Olinordered__comm__semiring__strict( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), T )
% 1.08/1.65 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 1.08/1.65 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, T ), c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.65 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) ) }.
% 1.08/1.65 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, T ), c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.65 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X ), c_RealDef_Oreal(
% 1.08/1.65 tc_Nat_Onat, Y ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.08/1.65 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ), Y ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.08/1.65 tc_Nat_Onat ) ), Y ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.08/1.65 tc_Nat_Onat ) ), X ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.08/1.65 tc_Nat_Onat ) ), X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.08/1.65 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.08/1.65 tc_Nat_Onat ) ), Z ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.08/1.65 tc_Nat_Onat ) ), Y ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), X ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), X ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 1.08/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 1.08/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), Y ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), Y ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = Y }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! Z = Y, hAPP( hAPP
% 1.08/1.65 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z ), Y ) ), hBOOL( hAPP
% 1.08/1.65 ( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) ), hAPP( hAPP
% 1.08/1.65 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) ), hAPP( hAPP
% 1.08/1.65 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) ), hBOOL
% 1.08/1.65 ( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z ), Y ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z ), Y ) ), hBOOL( hAPP
% 1.08/1.65 ( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) ), hAPP( hAPP
% 1.08/1.65 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) ) }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, Y ) ), c_Groups_Ozero__class_Ozero(
% 1.08/1.65 tc_RealDef_Oreal ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_RealDef_Oreal( tc_Nat_Onat, X ) ), c_Groups_Ozero__class_Ozero(
% 1.08/1.65 tc_RealDef_Oreal ) ) ) }.
% 1.08/1.65 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.08/1.65 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ) }.
% 1.08/1.65 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.08/1.65 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ),
% 1.08/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.08/1.65 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.65 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), T ) ) }.
% 1.08/1.65 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.65 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), T ) ),
% 1.08/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.08/1.65 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, U ), T ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.08/1.65 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) ), U ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 1.08/1.65 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, U ), T ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.65 , Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) ), U ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 1.08/1.65 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.65 , Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) ), U ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 1.08/1.65 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, U ), T ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Z )
% 1.08/1.65 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) ), U ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 1.08/1.65 { ! class_Rings_Olinordered__semiring( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.65 , Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ), Y ) ) }.
% 1.08/1.65 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.65 , Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ), Y ) ) }.
% 1.08/1.65 { ! class_Rings_Olinordered__semiring( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.65 , T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.08/1.65 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.65 , T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.08/1.65 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Z )
% 1.08/1.65 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ) }.
% 1.08/1.65 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), T )
% 1.08/1.65 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, Y ) ) ), ! Y =
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) ), hAPP( hAPP
% 1.08/1.65 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) ), hBOOL
% 1.08/1.65 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z ), Y ) ) }
% 1.08/1.65 .
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z ), Y ) ), hBOOL(
% 1.08/1.65 hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) ), hAPP( hAPP
% 1.08/1.65 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) ), hAPP( hAPP
% 1.08/1.65 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ), hBOOL
% 1.08/1.65 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z ), Y ) ) }
% 1.08/1.65 .
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z ), Y ) ), hBOOL(
% 1.08/1.65 hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) ), hAPP( hAPP
% 1.08/1.65 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ) }.
% 1.08/1.65 { c_SEQ_Osubseq( skol16 ) }.
% 1.08/1.65 { c_SEQ_Omonoseq( tc_RealDef_Oreal, c_COMBB( tc_Complex_Ocomplex,
% 1.08/1.65 tc_RealDef_Oreal, tc_Nat_Onat, c_Complex_OIm, c_COMBB( tc_Nat_Onat,
% 1.08/1.65 tc_Complex_Ocomplex, tc_Nat_Onat, v_s, c_COMBB( tc_Nat_Onat, tc_Nat_Onat
% 1.08/1.65 , tc_Nat_Onat, v_f____, skol16 ) ) ) ) }.
% 1.08/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) ), X =
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.08/1.65 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) ) }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol17( Z, T ) ) ) }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol17( X, Y ) ) ) ) }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol18( Z, T ) ) ) }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol18( X, Y ) ) ) ) }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol19( Y ) ) ) }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol19( X ) ) ) ) }.
% 1.08/1.65 { hAPP( c_Complex_OIm, c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) )
% 1.08/1.65 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.08/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }
% 1.08/1.65 .
% 1.08/1.65 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.08/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol20( Z, T ) ) ) }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.08/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ) ), skol20( X, Y ) ) )
% 1.08/1.65 }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Z ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol69( X, Y, Z ) ) ) ), Z )
% 1.08/1.65 ), c_SEQ_OBseq( X, Y ) }.
% 1.08/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol21 ) ) }.
% 1.08/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, hAPP( c_Complex_OIm, X
% 1.08/1.65 ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ), skol21 ) ) )
% 1.08/1.65 }.
% 1.08/1.65 { ! hAPP( c_Complex_ORe, Y ) = hAPP( c_Complex_ORe, X ), ! hAPP(
% 1.08/1.65 c_Complex_OIm, Y ) = hAPP( c_Complex_OIm, X ), Y = X }.
% 1.08/1.65 { ! Y = X, hAPP( c_Complex_ORe, Y ) = hAPP( c_Complex_ORe, X ) }.
% 1.08/1.65 { ! Y = X, hAPP( c_Complex_OIm, Y ) = hAPP( c_Complex_OIm, X ) }.
% 1.08/1.65 { ! hAPP( c_Complex_ORe, Y ) = hAPP( c_Complex_ORe, X ), ! hAPP(
% 1.08/1.65 c_Complex_OIm, Y ) = hAPP( c_Complex_OIm, X ), Y = X }.
% 1.08/1.65 { hAPP( c_Complex_ORe, c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) )
% 1.08/1.65 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.08/1.65 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless
% 1.08/1.65 ( tc_fun( T, X ), Z ), Y ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ) }.
% 1.08/1.65 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless
% 1.08/1.65 ( tc_fun( T, X ), Z ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y ), Z ) ) }.
% 1.08/1.65 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ), hBOOL(
% 1.08/1.65 hAPP( c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y ), Z ) ),
% 1.08/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z ), Y ) ) }
% 1.08/1.65 .
% 1.08/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 1.08/1.65 c_Complex_ORe, X ) ), c_RealVector_Onorm__class_Onorm(
% 1.08/1.65 tc_Complex_Ocomplex, X ) ) ) }.
% 1.08/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol22 ) ) }.
% 1.08/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, hAPP( c_Complex_ORe, X
% 1.08/1.65 ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ), skol22 ) ) )
% 1.08/1.65 }.
% 1.08/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol23 ) ) }.
% 1.08/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, hAPP( c_Complex_OIm, X
% 1.08/1.65 ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ), skol23 ) ) )
% 1.08/1.65 }.
% 1.08/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol24 ) ) }.
% 1.08/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, hAPP( c_Complex_ORe, X
% 1.08/1.65 ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ), skol24 ) ) )
% 1.08/1.65 }.
% 1.08/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, hAPP( c_Complex_OIm, X
% 1.08/1.65 ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ), skol25 ) ) )
% 1.08/1.65 }.
% 1.08/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, hAPP( c_Complex_ORe, X
% 1.08/1.65 ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ), skol26 ) ) )
% 1.08/1.65 }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.08/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol27( Z, T ) ) ) }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.08/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ) ), skol27( X, Y ) ) )
% 1.08/1.65 }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( Z, skol28( X, Y, Z ) ) ) ), Y )
% 1.08/1.65 ), c_SEQ_OBseq( X, Z ) }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__vector( X ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), skol29( U, W, V0, T
% 1.08/1.65 ) ) ), c_SEQ_OBseq( X, Y ) }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol29( X, Y, Z, T ) ) ) ),
% 1.08/1.65 Z ) ), c_SEQ_OBseq( X, Y ) }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Z ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol30( X, Y, Z ) ) ) ), Z )
% 1.08/1.65 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ) ), c_RealDef_Oreal(
% 1.08/1.65 tc_Nat_Onat, c_Nat_OSuc( skol70( X, Y ) ) ) ) ) }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol75( X, Y, Z ) ) ) ),
% 1.08/1.65 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol77( T, U ) ) ) }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol75( X, Y, Z ) ) ) ),
% 1.08/1.65 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ) ), skol77( X, Y ) ) )
% 1.08/1.65 }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Z ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol31( X, Y, Z ) ) ) ), Z )
% 1.08/1.65 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ) ), c_RealDef_Oreal(
% 1.08/1.65 tc_Nat_Onat, c_Nat_OSuc( skol71( X, Y ) ) ) ) ) }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol76( X, Y, Z ) ) ) ),
% 1.08/1.65 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol78( T, U ) ) ) }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol76( X, Y, Z ) ) ) ),
% 1.08/1.65 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ) ), skol78( X, Y ) ) )
% 1.08/1.65 }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.08/1.65 tc_Nat_Onat, skol32( X, Y ) ) ), X ) ) ) }.
% 1.08/1.65 { c_SEQ_Osubseq( skol33 ) }.
% 1.08/1.65 { c_SEQ_Omonoseq( tc_RealDef_Oreal, c_COMBB( tc_Nat_Onat, tc_RealDef_Oreal
% 1.08/1.65 , tc_Nat_Onat, c_Fun_Ocomp( tc_Complex_Ocomplex, tc_RealDef_Oreal,
% 1.08/1.65 tc_Nat_Onat, c_Complex_ORe, v_s ), skol33 ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.08/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y )
% 1.08/1.65 ), c_Nat_OSuc( X ) ) ) }.
% 1.08/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), c_Nat_OSuc
% 1.08/1.65 ( X ) ) ) }.
% 1.08/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), c_Nat_OSuc( X ) ) ) }.
% 1.08/1.65 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 1.08/1.65 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 1.08/1.65 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 1.08/1.65 { ! c_Nat_OSuc( X ) = X }.
% 1.08/1.65 { ! X = c_Nat_OSuc( X ) }.
% 1.08/1.65 { ! hAPP( W, hAPP( U, T ) ) = hAPP( Z, hAPP( Y, X ) ), hAPP( c_Fun_Ocomp(
% 1.08/1.65 V4, V3, V2, W, U ), T ) = hAPP( c_Fun_Ocomp( V1, V3, V0, Z, Y ), X ) }.
% 1.08/1.65 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.08/1.65 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.08/1.65 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.08/1.65 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.08/1.65 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.08/1.65 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y
% 1.08/1.65 ) ), c_Nat_OSuc( X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.08/1.65 tc_Nat_Onat, Y ), X ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y
% 1.08/1.65 ) ), X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y )
% 1.08/1.65 , X ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ),
% 1.08/1.65 c_Nat_OSuc( X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.08/1.65 tc_Nat_Onat, Y ), X ) ), Y = X }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 1.08/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Z ) ),
% 1.08/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y )
% 1.08/1.65 ), Z ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.08/1.65 c_Nat_OSuc( Y ) = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.08/1.65 tc_Nat_Onat, c_Nat_OSuc( Y ) ), X ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.08/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), c_Nat_OSuc
% 1.08/1.65 ( X ) ) ) }.
% 1.08/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 1.08/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), c_Nat_OSuc
% 1.08/1.65 ( X ) ) ), X = Y }.
% 1.08/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 1.08/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), c_Nat_OSuc
% 1.08/1.65 ( X ) ) ), Y = X }.
% 1.08/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), ! Y
% 1.08/1.65 = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ),
% 1.08/1.65 c_Nat_OSuc( X ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y
% 1.08/1.65 ) ), c_Nat_OSuc( X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.08/1.65 tc_Nat_Onat, Y ), X ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.08/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y )
% 1.08/1.65 ), c_Nat_OSuc( X ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ),
% 1.08/1.65 c_Nat_OSuc( X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.08/1.65 tc_Nat_Onat, Y ), X ) ), Y = X }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.08/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), c_Nat_OSuc
% 1.08/1.65 ( X ) ) ) }.
% 1.08/1.65 { ! Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ),
% 1.08/1.65 c_Nat_OSuc( X ) ) ) }.
% 1.08/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.08/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), c_Nat_OSuc
% 1.08/1.65 ( Y ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ),
% 1.08/1.65 c_Nat_OSuc( Y ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.08/1.65 tc_Nat_Onat, Y ), X ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 1.08/1.65 ( Y ) ), X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.08/1.65 tc_Nat_Onat, Y ), X ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ),
% 1.08/1.65 c_Nat_OSuc( X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.08/1.65 tc_Nat_Onat, Y ), X ) ), Y = c_Nat_OSuc( X ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.65 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ),
% 1.08/1.65 c_Nat_OSuc( X ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 1.08/1.65 ( Y ) ), c_Nat_OSuc( X ) ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.65 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 1.08/1.65 ( Y ) ), c_Nat_OSuc( X ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ),
% 1.08/1.65 c_Nat_OSuc( X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.08/1.65 tc_Nat_Onat, Y ), X ) ), Y = c_Nat_OSuc( X ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.65 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ),
% 1.08/1.65 c_Nat_OSuc( X ) ) ) }.
% 1.08/1.65 { ! Y = c_Nat_OSuc( X ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.08/1.65 tc_Nat_Onat, Y ), c_Nat_OSuc( X ) ) ) }.
% 1.08/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ),
% 1.08/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.08/1.65 X ) ), Y ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 1.08/1.65 ( X ) ), Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.08/1.65 tc_Nat_Onat, Y ), X ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 1.08/1.65 ( X ) ), X ) ) }.
% 1.08/1.65 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 1.08/1.65 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.08/1.65 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 1.08/1.65 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.08/1.65 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.08/1.65 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ),
% 1.08/1.65 c_Nat_OSuc( X ) ) ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.08/1.65 alpha6( X, Y ) }.
% 1.08/1.65 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), c_Nat_OSuc( X ) ) ) }.
% 1.08/1.65 { ! alpha6( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 1.08/1.65 , Y ), c_Nat_OSuc( X ) ) ) }.
% 1.08/1.65 { ! alpha6( X, Y ), Y = c_Nat_OSuc( skol34( Z, Y ) ) }.
% 1.08/1.65 { ! alpha6( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 1.08/1.65 , skol34( X, Y ) ), X ) ) }.
% 1.08/1.65 { ! Y = c_Nat_OSuc( Z ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.08/1.65 tc_Nat_Onat, Z ), X ) ), alpha6( X, Y ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ),
% 1.08/1.65 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.08/1.65 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), c_Nat_OSuc(
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), X = c_Nat_OSuc(
% 1.08/1.65 skol35( X ) ) }.
% 1.08/1.65 { ! X = c_Nat_OSuc( Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.08/1.65 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ) }.
% 1.08/1.65 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.08/1.65 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 1.08/1.65 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.08/1.65 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.08/1.65 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 1.08/1.65 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.08/1.65 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.08/1.65 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.08/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.08/1.65 Y ) ), X ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 1.08/1.65 ( Y ) ), X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 Y ), X ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ),
% 1.08/1.65 c_Nat_OSuc( X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.08/1.65 tc_Nat_Onat, Y ), X ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.65 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ),
% 1.08/1.65 c_Nat_OSuc( X ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 1.08/1.65 ( Y ) ), X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 Y ), X ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.08/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.08/1.65 Y ) ), X ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.65 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ),
% 1.08/1.65 c_Nat_OSuc( X ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.08/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.08/1.65 Y ) ), X ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.65 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ),
% 1.08/1.65 c_Nat_OSuc( Y ) ) ), X = Y }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.65 , ! X = Y, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ),
% 1.08/1.65 c_Nat_OSuc( Y ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 1.08/1.65 ( Y ) ), X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 Y ), X ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ) ),
% 1.08/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.08/1.65 ), X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y )
% 1.08/1.65 , X ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.08/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ) ),
% 1.08/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.08/1.65 ), X ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.08/1.65 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ) )
% 1.08/1.65 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 1.08/1.65 ) ), X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.08/1.65 tc_Nat_Onat, Y ), X ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.65 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.08/1.65 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ) )
% 1.08/1.65 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 1.08/1.65 ) ), X ) ) ) }.
% 1.08/1.65 { ! class_Orderings_Oorder( X ), ! c_SEQ_Omonoseq( X, Y ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, Z ) ), hAPP( Y, c_Nat_OSuc
% 1.08/1.65 ( Z ) ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( Y,
% 1.08/1.65 c_Nat_OSuc( T ) ) ), hAPP( Y, T ) ) ) }.
% 1.08/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, skol36( X, Y ) ) ), hAPP(
% 1.08/1.65 Y, c_Nat_OSuc( skol36( X, Y ) ) ) ) ), c_SEQ_Omonoseq( X, Y ) }.
% 1.08/1.65 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, c_Nat_OSuc( skol72( X, Y )
% 1.08/1.65 ) ) ), hAPP( Y, skol72( X, Y ) ) ) ), c_SEQ_Omonoseq( X, Y ) }.
% 1.08/1.65 { ! c_SEQ_Osubseq( X ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.08/1.65 tc_Nat_Onat, hAPP( X, Y ) ), hAPP( X, c_Nat_OSuc( Y ) ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( X,
% 1.08/1.65 skol37( X ) ) ), hAPP( X, c_Nat_OSuc( skol37( X ) ) ) ) ), c_SEQ_Osubseq
% 1.08/1.65 ( X ) }.
% 1.08/1.65 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ) =
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), Y ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), Y ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), Y ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 1.08/1.65 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), Y ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 1.08/1.65 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 1.08/1.65 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ) }.
% 1.08/1.65 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_RealDef_Oreal(
% 1.08/1.65 tc_Nat_Onat, c_Nat_OSuc( X ) ) ) ) }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.08/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ) ), c_RealDef_Oreal(
% 1.08/1.65 tc_Nat_Onat, c_Nat_OSuc( skol38( X, Y ) ) ) ) ) }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol73( X, Y, Z ) ) ) ),
% 1.08/1.65 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ) ), c_SEQ_OBseq( X, Y )
% 1.08/1.65 }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.08/1.65 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ) ), c_RealDef_Oreal(
% 1.08/1.65 tc_Nat_Onat, c_Nat_OSuc( skol39( X, Y ) ) ) ) ) }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol74( X, Y, Z ) ) ) ),
% 1.08/1.65 c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Z ) ) ) ), c_SEQ_OBseq( X, Y )
% 1.08/1.65 }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ),
% 1.08/1.65 c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) )
% 1.08/1.65 ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.08/1.65 { c_SEQ_Osubseq( skol40 ) }.
% 1.08/1.65 { c_SEQ_Omonoseq( tc_RealDef_Oreal, c_COMBB( tc_Nat_Onat, tc_RealDef_Oreal
% 1.08/1.65 , tc_Nat_Onat, c_Fun_Ocomp( tc_Nat_Onat, tc_RealDef_Oreal, tc_Nat_Onat,
% 1.08/1.65 c_Fun_Ocomp( tc_Complex_Ocomplex, tc_RealDef_Oreal, tc_Nat_Onat,
% 1.08/1.65 c_Complex_OIm, v_s ), v_f____ ), skol40 ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.08/1.65 tc_Nat_Onat, skol41( X ) ) ), X ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X ), c_RealDef_Oreal(
% 1.08/1.65 tc_Nat_Onat, c_Nat_OSuc( skol41( X ) ) ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.08/1.65 tc_Nat_Onat, skol42( X, Y ) ) ), X ) ), Y ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.08/1.65 tc_Nat_Onat, c_Nat_OSuc( skol42( X, Y ) ) ) ), X ) ) ) }.
% 1.08/1.65 { hAPP( c_Fun_Ocomp( W, U, T, c_COMBK( U, W, Z ), Y ), X ) = Z }.
% 1.08/1.65 { ! c_Fun_Ocomp( W, U, T, Z, Y ) = X, hAPP( Z, hAPP( Y, V0 ) ) = hAPP( X,
% 1.08/1.65 V0 ) }.
% 1.08/1.65 { hAPP( c_Fun_Ocomp( W, U, T, Z, Y ), X ) = hAPP( Z, hAPP( Y, X ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.08/1.65 tc_Nat_Onat ) ), Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.08/1.65 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Z )
% 1.08/1.65 ), c_NthRoot_Oroot( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.08/1.65 tc_Nat_Onat ), X ), Y ), Z ) = c_NthRoot_Oroot( X, c_NthRoot_Oroot( Y, Z
% 1.08/1.65 ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Z ) ), c_NthRoot_Oroot
% 1.08/1.65 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ),
% 1.08/1.65 Z ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.08/1.65 c_NthRoot_Oroot( X, Y ) ), c_NthRoot_Oroot( X, Z ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y ), Z ) ), hBOOL( hAPP
% 1.08/1.65 ( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Oroot( X, Y
% 1.08/1.65 ) ), c_NthRoot_Oroot( X, Z ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_NthRoot_Oroot( X, Y
% 1.08/1.65 ) ) ) }.
% 1.08/1.65 { c_NthRoot_Oroot( X, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.08/1.65 { c_NthRoot_Oroot( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 1.08/1.65 , X ) = X }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.08/1.65 tc_Nat_Onat ) ), Y ) ), c_NthRoot_Oroot( X, c_NthRoot_Oroot( Y, Z ) ) =
% 1.08/1.65 c_NthRoot_Oroot( Y, c_NthRoot_Oroot( X, Z ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! c_NthRoot_Oroot( X
% 1.08/1.65 , Z ) = c_NthRoot_Oroot( X, Y ), Z = Y }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! Z = Y,
% 1.08/1.65 c_NthRoot_Oroot( X, Z ) = c_NthRoot_Oroot( X, Y ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Oroot( X,
% 1.08/1.65 Z ) ), c_NthRoot_Oroot( X, Y ) ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z ), Y ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z ), Y ) ), hBOOL(
% 1.08/1.65 hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_NthRoot_Oroot( X, Z ) ), c_NthRoot_Oroot( X, Y ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z ), Y ) ), hBOOL(
% 1.08/1.65 hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_NthRoot_Oroot( X, Z ) ), c_NthRoot_Oroot( X, Y ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! c_NthRoot_Oroot( X
% 1.08/1.65 , Y ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! Y =
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y )
% 1.08/1.65 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z ), Y ) ), hBOOL( hAPP
% 1.08/1.65 ( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Oroot( X, Z
% 1.08/1.65 ) ), c_NthRoot_Oroot( X, Y ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Oroot( X, Z )
% 1.08/1.65 ), c_NthRoot_Oroot( X, Y ) ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z ), Y ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z ), Y ) ), hBOOL( hAPP
% 1.08/1.65 ( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Oroot( X, Z
% 1.08/1.65 ) ), c_NthRoot_Oroot( X, Y ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), c_NthRoot_Oroot( X,
% 1.08/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) )
% 1.08/1.65 = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.08/1.65 c_NthRoot_Oroot( X, Z ) ), c_NthRoot_Oroot( X, Y ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.08/1.65 tc_Nat_Onat ) ), Y ) ), c_NthRoot_Oroot( hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z ) =
% 1.08/1.65 c_NthRoot_Oroot( X, c_NthRoot_Oroot( Y, Z ) ) }.
% 1.08/1.65 { c_Fun_Ocomp( V0, W, U, T, c_Fun_Ocomp( Z, V0, U, Y, X ) ) = c_Fun_Ocomp(
% 1.08/1.65 Z, W, U, c_Fun_Ocomp( V0, W, Z, T, Y ), X ) }.
% 1.08/1.65 { hAPP( c_Fun_Ocomp( W, U, T, Z, Y ), X ) = hAPP( Z, hAPP( Y, X ) ) }.
% 1.08/1.65 { ! c_Fun_Ocomp( V1, V0, W, T, Z ) = c_Fun_Ocomp( U, V0, W, Y, X ), hAPP( T
% 1.08/1.65 , hAPP( Z, V2 ) ) = hAPP( Y, hAPP( X, V2 ) ) }.
% 1.08/1.65 { ! c_Fun_Ocomp( V1, V0, W, T, Z ) = c_Fun_Ocomp( U, V0, W, Y, X ), hAPP( T
% 1.08/1.65 , hAPP( Z, V2 ) ) = hAPP( Y, hAPP( X, V2 ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_NthRoot_Oroot( X, Y
% 1.08/1.65 ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Oroot( X,
% 1.08/1.65 Y ) ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Oroot( X,
% 1.08/1.65 Y ) ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_NthRoot_Oroot( X, Y
% 1.08/1.65 ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal
% 1.08/1.65 , c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_NthRoot_Oroot( X, Y
% 1.08/1.65 ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_NthRoot_Oroot( X, Y
% 1.08/1.65 ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_NthRoot_Oroot( X, Y
% 1.08/1.65 ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Oroot( X, Y )
% 1.08/1.65 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y ),
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y ),
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Oroot( X, Y )
% 1.08/1.65 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_NthRoot_Oroot( X, Y
% 1.08/1.65 ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Z ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z ),
% 1.08/1.65 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Oroot( X, Z )
% 1.08/1.65 ), c_NthRoot_Oroot( Y, Z ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Z ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z ),
% 1.08/1.65 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Oroot( X,
% 1.08/1.65 Z ) ), c_NthRoot_Oroot( Y, Z ) ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), hAPP( hAPP(
% 1.08/1.65 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y )
% 1.08/1.65 ), X ) = Y }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), c_NthRoot_Oroot
% 1.08/1.65 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ), X
% 1.08/1.65 ) ) = Y }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), hAPP( hAPP(
% 1.08/1.65 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y )
% 1.08/1.65 ), X ) = Y }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.08/1.65 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.08/1.65 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oone__class_Oone( X ) ) =
% 1.08/1.65 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.08/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.08/1.65 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 1.08/1.65 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.08/1.65 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 1.08/1.65 c_Groups_Oone__class_Oone( X ) }.
% 1.08/1.65 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 1.08/1.65 c_Groups_Oone__class_Oone( X ) = Y }.
% 1.08/1.65 { ! class_RealVector_Oreal__normed__algebra__1( X ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.08/1.65 c_Power_Opower__class_Opower( X ), Z ), Y ) ) ), hAPP( hAPP(
% 1.08/1.65 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.08/1.65 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) ) ) }.
% 1.08/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.08/1.65 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.08/1.65 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.08/1.65 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.08/1.65 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.08/1.65 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 1.08/1.65 c_Groups_Oone__class_Oone( X ) }.
% 1.08/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.08/1.65 = Y }.
% 1.08/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.08/1.65 = Y }.
% 1.08/1.65 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.08/1.65 = Y }.
% 1.08/1.65 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.08/1.65 = Y }.
% 1.08/1.65 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.08/1.65 = Y }.
% 1.08/1.65 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.08/1.65 = Y }.
% 1.08/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.08/1.65 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.08/1.65 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.08/1.65 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ),
% 1.08/1.65 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), c_SEQ_OBseq(
% 1.08/1.65 tc_RealDef_Oreal, hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal )
% 1.08/1.65 , X ) ) }.
% 1.08/1.65 { ! c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) =
% 1.08/1.65 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.08/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.08/1.65 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) = X }.
% 1.08/1.65 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.65 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ),
% 1.08/1.65 c_Groups_Oone__class_Oone( X ) ) ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.65 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ), Y ) ) }.
% 1.08/1.65 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ),
% 1.08/1.65 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), c_SEQ_Omonoseq(
% 1.08/1.65 tc_RealDef_Oreal, hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal )
% 1.08/1.65 , X ) ) }.
% 1.08/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.08/1.65 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.08/1.65 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 1.08/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.08/1.65 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.08/1.65 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 1.08/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.08/1.65 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 1.08/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.08/1.65 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.08/1.65 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ) ),
% 1.08/1.65 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.08/1.65 { ! class_Rings_Olinordered__semidom( X ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.65 , c_Groups_Oone__class_Oone( X ) ) ) }.
% 1.08/1.65 { ! class_Rings_Olinordered__semidom( X ), hBOOL( hAPP(
% 1.08/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 1.08/1.66 c_Groups_Oone__class_Oone( X ) ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 1.08/1.66 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.08/1.66 c_Groups_Oone__class_Oone( X ) ), Z ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), hAPP
% 1.08/1.66 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.66 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, Z ), c_Groups_Oone__class_Oone( X )
% 1.08/1.66 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.66 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, Z ), c_Groups_Oone__class_Oone( X )
% 1.08/1.66 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), c_NthRoot_Oroot( X,
% 1.08/1.66 hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), Y ) )
% 1.08/1.66 = hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.08/1.66 c_NthRoot_Oroot( X, Z ) ), Y ) }.
% 1.08/1.66 { c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_Nat_Onat ) ) ) = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! c_NthRoot_Oroot( X
% 1.08/1.66 , Y ) = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), Y =
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! Y =
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Oroot( X, Y ) =
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), c_NthRoot_Oroot( X,
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), c_NthRoot_Oroot
% 1.08/1.66 ( c_Nat_OSuc( Y ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.08/1.66 tc_RealDef_Oreal ), X ), c_Nat_OSuc( Y ) ) ) = X }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), Z ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Oroot( Y,
% 1.08/1.66 Z ) ), c_NthRoot_Oroot( X, Z ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Oroot( X,
% 1.08/1.66 Y ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Oroot( X,
% 1.08/1.66 Y ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), c_NthRoot_Oroot( X, Y )
% 1.08/1.66 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), Y ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), Y ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), c_NthRoot_Oroot( X, Y )
% 1.08/1.66 ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), c_NthRoot_Oroot( X, Y )
% 1.08/1.66 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), Y ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), Y ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), c_NthRoot_Oroot( X, Y )
% 1.08/1.66 ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Oroot( X, Y )
% 1.08/1.66 ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y ),
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y ),
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Oroot( X, Y )
% 1.08/1.66 ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), Z ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Oroot( Y, Z )
% 1.08/1.66 ), c_NthRoot_Oroot( X, Z ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), ! hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ), X ) = Z,
% 1.08/1.66 c_NthRoot_Oroot( X, Z ) = Y }.
% 1.08/1.66 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.66 , Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), T ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), Z ), T ) ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), Y ), T ) ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 1.08/1.66 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Z ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), hAPP
% 1.08/1.66 ( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 1.08/1.66 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), Z ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 1.08/1.66 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), Z )
% 1.08/1.66 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 1.08/1.66 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), Z ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ), ! hBOOL( hAPP
% 1.08/1.66 ( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.08/1.66 ), T ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ),
% 1.08/1.66 c_Groups_Oone__class_Oone( X ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), T ), Z ) ) ) }.
% 1.08/1.66 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.08/1.66 tc_Nat_Onat ) ) = Y }.
% 1.08/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.08/1.66 tc_Nat_Onat ) ) = Y }.
% 1.08/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 1.08/1.66 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.08/1.66 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.08/1.66 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 1.08/1.66 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.08/1.66 , Y ), X ) }.
% 1.08/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.08/1.66 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 1.08/1.66 tc_Nat_Onat ) }.
% 1.08/1.66 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 1.08/1.66 tc_Nat_Onat ) }.
% 1.08/1.66 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.08/1.66 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.08/1.66 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 1.08/1.66 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.08/1.66 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.08/1.66 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 1.08/1.66 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 1.08/1.66 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ) ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), Y ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_Nat_Onat ) ), Y ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 1.08/1.66 .
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_Nat_Onat ) ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.08/1.66 , Y ), X ) ) ) }.
% 1.08/1.66 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_Nat_Onat ) ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.08/1.66 , Y ), X ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 1.08/1.66 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) ), X =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_Nat_Onat ) ), Y ) ) }.
% 1.08/1.66 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_Nat_Onat ) ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.08/1.66 , Y ), X ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_Nat_Onat ) ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.08/1.66 , Y ), X ) ) ) }.
% 1.08/1.66 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.08/1.66 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.08/1.66 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) }.
% 1.08/1.66 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.08/1.66 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) = c_RealDef_Oreal( tc_Nat_Onat,
% 1.08/1.66 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.08/1.66 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.08/1.66 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 1.08/1.66 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.08/1.66 { hAPP( c_Complex_OIm, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.08/1.66 { hAPP( c_Complex_ORe, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) =
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.08/1.66 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Oone__class_Oone( tc_Nat_Onat ) )
% 1.08/1.66 = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.08/1.66 { c_RComplete_Onatfloor( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.08/1.66 { c_RComplete_Onatceiling( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 1.08/1.66 = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.08/1.66 { ! X = c_RealDef_Oreal( tc_Nat_Onat, c_RComplete_Onatfloor( X ) ),
% 1.08/1.66 c_RComplete_Onatfloor( hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.08/1.66 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP( c_Power_Opower__class_Opower
% 1.08/1.66 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ), Y ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), c_RComplete_Onatfloor( X ) )
% 1.08/1.66 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Groups_Oone__class_Oone
% 1.08/1.66 ( tc_Nat_Onat ) ), c_RComplete_Onatfloor( X ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.08/1.66 c_RComplete_Onatceiling( X ) ), c_Groups_Oone__class_Oone( tc_Nat_Onat )
% 1.08/1.66 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X
% 1.08/1.66 ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ),
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 1.08/1.66 X ) ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 1.08/1.66 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 1.08/1.66 ( X ) }.
% 1.08/1.66 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.08/1.66 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.08/1.66 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.08/1.66 = c_Groups_Oone__class_Oone( X ) }.
% 1.08/1.66 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.66 , Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), Z ), T ) ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), Y ), T ) ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.66 , Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ) ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.08/1.66 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ) ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ) ), Y
% 1.08/1.66 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.08/1.66 c_Groups_Oone__class_Oone( X ) ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.08/1.66 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.08/1.66 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.08/1.66 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.08/1.66 .
% 1.08/1.66 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.08/1.66 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.08/1.66 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_Nat_Onat ) }.
% 1.08/1.66 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.08/1.66 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.08/1.66 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 1.08/1.66 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 1.08/1.66 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 1.08/1.66 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP
% 1.08/1.66 ( c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 1.08/1.66 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 1.08/1.66 , ! T = Z, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP
% 1.08/1.66 ( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 1.08/1.66 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.08/1.66 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.08/1.66 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.08/1.66 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.08/1.66 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.08/1.66 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 1.08/1.66 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.08/1.66 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.08/1.66 c_Groups_Oone__class_Oone( X ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), Z ), T ) ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), Y ), T ) ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.66 , Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), ! hBOOL( hAPP
% 1.08/1.66 ( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.08/1.66 ), Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ) ), Y ) ), Z = Y }.
% 1.08/1.66 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ) ), ! hBOOL(
% 1.08/1.66 hAPP( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.08/1.66 X ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), Y )
% 1.08/1.66 ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 1.08/1.66 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 1.08/1.66 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.08/1.66 c_Groups_Oone__class_Oone( X ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) ) }.
% 1.08/1.66 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.08/1.66 ) = c_Groups_Oone__class_Oone( X ) }.
% 1.08/1.66 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.08/1.66 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 1.08/1.66 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.08/1.66 c_Groups_Oone__class_Oone( X ) ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 1.08/1.66 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T ), Z ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 1.08/1.66 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, T ), Z ) ),
% 1.08/1.66 hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), Y ) )
% 1.08/1.66 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T ), Z ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ) ), T ) )
% 1.08/1.66 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), T ), Y ) ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ), ! hBOOL( hAPP
% 1.08/1.66 ( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ) )
% 1.08/1.66 , T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), T ), Y ) ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.08/1.66 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Y ),
% 1.08/1.66 c_Groups_Oone__class_Oone( X ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.08/1.66 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Y ),
% 1.08/1.66 c_Groups_Oone__class_Oone( X ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ),
% 1.08/1.66 c_Groups_Oone__class_Oone( X ) ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), T )
% 1.08/1.66 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ),
% 1.08/1.66 c_Groups_Oone__class_Oone( X ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), T ), Z ) ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), Y ), Z ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.66 , T ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ) ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_Nat_Onat ) ), Z ) ), T = Y }.
% 1.08/1.66 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 1.08/1.66 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol43( Z, T ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol43( X, Y ) ), X ) =
% 1.08/1.66 Y }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Z ) ), ! hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), X ) = Y, Z =
% 1.08/1.66 skol43( X, Y ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol44( Z, T ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol44( X, Y ) ), X ) =
% 1.08/1.66 Y }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.08/1.66 tc_Nat_Onat, Y ) ), X ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal )
% 1.08/1.66 ) ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), hAPP
% 1.08/1.66 ( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), X ),
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), Y ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ),
% 1.08/1.66 c_Transcendental_Oln( hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.08/1.66 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.08/1.66 tc_Nat_Onat, Y ) ), c_Transcendental_Oln( X ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 1.08/1.66 X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Z ), Y ) ),
% 1.08/1.66 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Z ), X ) ) )
% 1.08/1.66 }.
% 1.08/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP
% 1.08/1.66 ( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Z ), Y ) ), X ) = hAPP
% 1.08/1.66 ( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) ), hAPP( hAPP
% 1.08/1.66 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.08/1.66 { ! class_Groups_Oab__semigroup__add( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.08/1.66 ( X ), T ), Z ) ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T
% 1.08/1.66 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) }.
% 1.08/1.66 { ! class_Groups_Ocancel__semigroup__add( X ), ! hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Y ), Z = Y }.
% 1.08/1.66 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Y ) }.
% 1.08/1.66 { ! class_Groups_Ocancel__semigroup__add( X ), ! hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Y ), Z ), T = Y }.
% 1.08/1.66 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) }.
% 1.08/1.66 { ! class_Groups_Ocancel__semigroup__add( X ), ! hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Y ), Z = Y }.
% 1.08/1.66 { ! class_Groups_Ocancel__ab__semigroup__add( X ), ! hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Y ), Z = Y }.
% 1.08/1.66 { ! class_Groups_Ocancel__semigroup__add( X ), ! hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Z ), T ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Y ), T ), Z = Y }.
% 1.08/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) }.
% 1.08/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), T ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Z ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) }.
% 1.08/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), T ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.08/1.66 ( X ), T ), Z ) ), Y ) }.
% 1.08/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.08/1.66 ( X ), T ), Z ) ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T
% 1.08/1.66 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) }.
% 1.08/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.08/1.66 ( X ), T ), Z ) ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ),
% 1.08/1.66 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Y ) ), Z ) }.
% 1.08/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.08/1.66 ( X ), U ), T ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y )
% 1.08/1.66 ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), U ), Z ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) }.
% 1.08/1.66 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_RealVector_Onorm__class_Onorm( X, U ) ), T ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Z ), U ) ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Y ), T ) ) ) }.
% 1.08/1.66 { ! class_RealVector_Oreal__normed__vector( X ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 1.08/1.66 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 1.08/1.66 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) ) }.
% 1.08/1.66 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.08/1.66 { ! class_Rings_Osemiring( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X
% 1.08/1.66 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP(
% 1.08/1.66 hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ), Y ) ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), U ), Z ) ), T ) ), Y ) }.
% 1.08/1.66 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.08/1.66 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.08/1.66 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.08/1.66 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.08/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.08/1.66 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.08/1.66 ( X ), U = T, Z = Y, ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP
% 1.08/1.66 ( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.08/1.66 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.08/1.66 ( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), ! U = T }.
% 1.08/1.66 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.08/1.66 ( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), ! Z = Y }.
% 1.08/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.08/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ), Z ) }.
% 1.08/1.66 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.08/1.66 ( X ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ), U = Z, T = Y }.
% 1.08/1.66 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.08/1.66 ( X ), ! U = Z, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP
% 1.08/1.66 ( c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.08/1.66 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.08/1.66 ( X ), ! T = Y, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP
% 1.08/1.66 ( c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.08/1.66 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.08/1.66 ( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.08/1.66 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.08/1.66 ( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Z ), T ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.08/1.66 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, U ), T ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.08/1.66 ( X ), Z ), U ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), T )
% 1.08/1.66 ) ) }.
% 1.08/1.66 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.08/1.66 ( X ), T ), Z ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Y )
% 1.08/1.66 ) ) }.
% 1.08/1.66 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.08/1.66 ( X ), Z ), T ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), T )
% 1.08/1.66 ) ) }.
% 1.08/1.66 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.08/1.66 ( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.08/1.66 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.08/1.66 ( c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.08/1.66 ( X ), T ), Z ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Y )
% 1.08/1.66 ) ) }.
% 1.08/1.66 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.08/1.66 ( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, T ), Y ) ) }.
% 1.08/1.66 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.08/1.66 ( c_Orderings_Oord__class_Oless( X, T ), Y ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.08/1.66 ( X ), T ), Z ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z )
% 1.08/1.66 ) ) }.
% 1.08/1.66 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.08/1.66 ( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.08/1.66 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.08/1.66 ( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Z ), T ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.08/1.66 { ! class_Groups_Oordered__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Z ), U ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) ) }.
% 1.08/1.66 { ! class_Groups_Oordered__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) ) }.
% 1.08/1.66 { ! class_Groups_Oordered__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Z ), T ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) ) }.
% 1.08/1.66 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.08/1.66 ( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.08/1.66 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.08/1.66 ( c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) ) }.
% 1.08/1.66 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.08/1.66 ( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ) }.
% 1.08/1.66 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.08/1.66 ( c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 1.08/1.66 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.66 = Y }.
% 1.08/1.66 { ! class_Groups_Omonoid__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.08/1.66 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.08/1.66 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Y ), Y ), Y =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.08/1.66 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) = hAPP
% 1.08/1.66 ( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Y ) }.
% 1.08/1.66 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.08/1.66 = Y }.
% 1.08/1.66 { ! class_Groups_Omonoid__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.08/1.66 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) = Y }.
% 1.08/1.66 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.08/1.66 ( X ), ! Z = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ), Y =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.08/1.66 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.08/1.66 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z = hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) }.
% 1.08/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.66 = Y }.
% 1.08/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.08/1.66 = Y }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ),
% 1.08/1.66 c_Transcendental_Oln( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.08/1.66 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.08/1.66 ( tc_RealDef_Oreal ), c_Transcendental_Oln( X ) ), c_Transcendental_Oln(
% 1.08/1.66 Y ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_Transcendental_Oln
% 1.08/1.66 ( hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ) ), X ) ) }.
% 1.08/1.66 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.66 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ) ), hBOOL( hAPP
% 1.08/1.66 ( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.08/1.66 ), Y ) ) }.
% 1.08/1.66 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.66 , Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ) ) }.
% 1.08/1.66 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ), c_Groups_Ozero__class_Ozero
% 1.08/1.66 ( X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.08/1.66 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.08/1.66 ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ), c_Groups_Ozero__class_Ozero
% 1.08/1.66 ( X ) ) ) }.
% 1.08/1.66 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.66 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.66 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 1.08/1.66 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.66 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 1.08/1.66 ( X ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.08/1.66 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.66 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 1.08/1.66 ( X ), Z = c_Groups_Ozero__class_Ozero( X ) }.
% 1.08/1.66 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.66 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! Y =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X )
% 1.08/1.66 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.08/1.66 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.66 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), Z ) )
% 1.08/1.66 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 1.08/1.66 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.66 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), Z ) )
% 1.08/1.66 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) ) }.
% 1.08/1.66 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.08/1.66 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ), c_Groups_Ozero__class_Ozero
% 1.08/1.66 ( X ) ) ) }.
% 1.08/1.66 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 1.08/1.66 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.08/1.66 ) }.
% 1.08/1.66 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.08/1.66 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ) ) }.
% 1.08/1.66 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.08/1.66 ( X ), Y ), Y ) ), c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.66 ) }.
% 1.08/1.66 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.66 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ), c_Groups_Ozero__class_Ozero
% 1.08/1.66 ( X ) ) ) }.
% 1.08/1.66 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.08/1.66 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 1.08/1.66 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 1.08/1.66 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.66 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.08/1.66 ( X ), Y ), Z ) ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.08/1.66 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ), Z ) ), hBOOL(
% 1.08/1.66 hAPP( c_Orderings_Oord__class_Oless( X, T ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 1.08/1.66 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, U ), T ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.08/1.66 ( X ), Z ), U ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), T )
% 1.08/1.66 ) ) }.
% 1.08/1.66 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.08/1.66 ( X ), Z ), U ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), T )
% 1.08/1.66 ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__ring__strict( X ), ! hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.08/1.66 .
% 1.08/1.66 { ! class_Rings_Olinordered__ring__strict( X ), ! hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 1.08/1.66 .
% 1.08/1.66 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.08/1.66 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.08/1.66 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.08/1.66 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, ! hAPP( hAPP
% 1.08/1.66 ( c_Groups_Oplus__class_Oplus( X ), W ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), U ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__semidom( X ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, Y ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Oone__class_Oone( X ) ) )
% 1.08/1.66 ) }.
% 1.08/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Z ), c_Groups_Oone__class_Oone( X ) ) )
% 1.08/1.66 , Y ) }.
% 1.08/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Z ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Oone__class_Oone( X ) ) )
% 1.08/1.66 , Z ) }.
% 1.08/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.08/1.66 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.08/1.66 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( hAPP
% 1.08/1.66 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ), hAPP(
% 1.08/1.66 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.08/1.66 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( hAPP
% 1.08/1.66 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ), hAPP(
% 1.08/1.66 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.08/1.66 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ), hAPP( hAPP
% 1.08/1.66 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 1.08/1.66 ) ), X ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), !
% 1.08/1.66 c_Transcendental_Oln( X ) = c_Transcendental_Oln( Y ), X = Y }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), ! X = Y,
% 1.08/1.66 c_Transcendental_Oln( X ) = c_Transcendental_Oln( Y ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 1.08/1.66 ) ), c_Transcendental_Oln( Y ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X ), Y ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X ), Y ) ), hBOOL( hAPP
% 1.08/1.66 ( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln(
% 1.08/1.66 X ) ), c_Transcendental_Oln( Y ) ) ) }.
% 1.08/1.66 { c_Transcendental_Oln( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.08/1.66 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.08/1.66 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 1.08/1.66 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 1.08/1.66 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.66 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 1.08/1.66 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 1.08/1.66 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.08/1.66 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ),
% 1.08/1.66 hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 1.08/1.66 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.66 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ), Z ) ),
% 1.08/1.66 hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ) }.
% 1.08/1.66 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.66 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.08/1.66 ( X ), Y ), Z ) ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.08/1.66 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.08/1.66 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.08/1.66 ( X ), Y ), Z ) ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__ring( X ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.66 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ) ) ), Z = c_Groups_Ozero__class_Ozero( X
% 1.08/1.66 ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ) ) ), Y = c_Groups_Ozero__class_Ozero( X
% 1.08/1.66 ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.08/1.66 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__ring( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.08/1.66 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP(
% 1.08/1.66 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 1.08/1.66 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) ), ! Z =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.08/1.66 }.
% 1.08/1.66 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 1.08/1.66 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 1.08/1.66 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__semidom( X ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 1.08/1.66 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), c_Groups_Oone__class_Oone(
% 1.08/1.66 X ) ), c_Groups_Oone__class_Oone( X ) ) ) ) }.
% 1.08/1.66 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 1.08/1.66 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 1.08/1.66 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 1.08/1.66 ) ) }.
% 1.08/1.66 { c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( X ) ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.08/1.66 tc_Nat_Onat, X ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.08/1.66 { hAPP( c_Complex_OIm, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.08/1.66 tc_Complex_Ocomplex ), Y ), X ) ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( c_Complex_ORe, Y
% 1.08/1.66 ) ), hAPP( c_Complex_OIm, X ) ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( c_Complex_OIm, Y
% 1.08/1.66 ) ), hAPP( c_Complex_ORe, X ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_Transcendental_Oln
% 1.08/1.66 ( X ) ), c_Transcendental_Oln( Y ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ), Y ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ), Y ) ), hBOOL(
% 1.08/1.66 hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_Transcendental_Oln( X ) ), c_Transcendental_Oln( Y ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_Transcendental_Oln(
% 1.08/1.66 X ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_Transcendental_Oln(
% 1.08/1.66 X ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X ),
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 1.08/1.66 ) ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 1.08/1.66 ) ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X ),
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X ),
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 1.08/1.66 ) ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), !
% 1.08/1.66 c_Transcendental_Oln( X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 1.08/1.66 ), X = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! X =
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_Transcendental_Oln( X )
% 1.08/1.66 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_Transcendental_Oln(
% 1.08/1.66 X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_Transcendental_Oln(
% 1.08/1.66 X ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_Transcendental_Oln(
% 1.08/1.66 X ) ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__semiring__1( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.66 , U ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ) ), W ) ), ! hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), U ), W ) = c_Groups_Oone__class_Oone( X
% 1.08/1.66 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), W ), T ) ) ), Y ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.08/1.66 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 1.08/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.08/1.66 tc_Nat_Onat, Y ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ),
% 1.08/1.66 c_RealDef_Oreal( tc_Nat_Onat, X ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP
% 1.08/1.66 ( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), c_RealDef_Oreal
% 1.08/1.66 ( tc_Nat_Onat, Y ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ),
% 1.08/1.66 c_RealDef_Oreal( tc_Nat_Onat, X ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.08/1.66 tc_Nat_Onat, X ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) ) }
% 1.08/1.66 .
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.08/1.66 tc_Nat_Onat, X ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) ),
% 1.08/1.66 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }
% 1.08/1.66 .
% 1.08/1.66 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X ), hAPP(
% 1.08/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.08/1.66 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ) ), c_Groups_Oone__class_Oone(
% 1.08/1.66 tc_RealDef_Oreal ) ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_Transcendental_Oln(
% 1.08/1.66 X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal
% 1.08/1.66 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_Transcendental_Oln(
% 1.08/1.66 X ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_Transcendental_Oln(
% 1.08/1.66 X ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__semiring__1__strict( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, T ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.66 , U ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ) ), W ) ), ! hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), U ), W ) = c_Groups_Oone__class_Oone( X
% 1.08/1.66 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), W ), T ) ) ), Y ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.08/1.66 tc_Nat_Onat, Y ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) ),
% 1.08/1.66 c_RComplete_Onatfloor( X ) = Y }.
% 1.08/1.66 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.08/1.66 ( X ), Y ), Y ) ), c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.66 ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.66 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ), c_Groups_Ozero__class_Ozero
% 1.08/1.66 ( X ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.08/1.66 tc_Nat_Onat, Y ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) ),
% 1.08/1.66 c_RComplete_Onatceiling( X ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.08/1.66 tc_Nat_Onat ), Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.08/1.66 { ! class_Groups_Olinordered__ab__group__add( X ), ! hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) = c_Groups_Ozero__class_Ozero
% 1.08/1.66 ( X ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.08/1.66 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.08/1.66 ( X ), Y ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ),
% 1.08/1.66 c_RComplete_Onatceiling( hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.08/1.66 tc_RealDef_Oreal ), X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 1.08/1.66 ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.08/1.66 c_RComplete_Onatceiling( X ) ), c_Groups_Oone__class_Oone( tc_Nat_Onat )
% 1.08/1.66 ) }.
% 1.08/1.66 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP
% 1.08/1.66 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 1.08/1.66 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) = X }.
% 1.08/1.66 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 1.08/1.66 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.08/1.66 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.08/1.66 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.08/1.66 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) = Y, X
% 1.08/1.66 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.08/1.66 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), c_Nat_OSuc( Y ) )
% 1.08/1.66 , X ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ),
% 1.08/1.66 c_Nat_OSuc( X ) ) }.
% 1.08/1.66 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), c_Nat_OSuc( Y ) )
% 1.08/1.66 , X ) = c_Nat_OSuc( hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 1.08/1.66 ), Y ), X ) ) }.
% 1.08/1.66 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), c_Nat_OSuc(
% 1.08/1.66 X ) ) = c_Nat_OSuc( hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 1.08/1.66 ), Y ), X ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.08/1.66 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP( hAPP
% 1.08/1.66 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.08/1.66 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP( hAPP
% 1.08/1.66 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ) ), X ) ), hBOOL(
% 1.08/1.66 hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 1.08/1.66 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), T ), X ) = hAPP(
% 1.08/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T ), Z ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 1.08/1.66 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, T ), Z ) ),
% 1.08/1.66 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), T ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.08/1.66 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.08/1.66 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP( hAPP
% 1.08/1.66 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.08/1.66 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP( hAPP
% 1.08/1.66 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.08/1.66 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ), X ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ), Y ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP
% 1.08/1.66 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP
% 1.08/1.66 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.08/1.66 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) ), hBOOL(
% 1.08/1.66 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), X ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.08/1.66 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) ), hBOOL(
% 1.08/1.66 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.08/1.66 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ) ), X ) ), hBOOL(
% 1.08/1.66 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.08/1.66 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) ), hBOOL(
% 1.08/1.66 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), Z )
% 1.08/1.66 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.08/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), T ) ), hAPP( hAPP
% 1.08/1.66 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.08/1.66 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP
% 1.08/1.66 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP
% 1.08/1.66 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.08/1.66 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.08/1.66 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , X = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), skol45
% 1.08/1.66 ( X, Y ) ) }.
% 1.08/1.66 { ! X = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ),
% 1.08/1.66 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }
% 1.08/1.66 .
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , X = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), skol46
% 1.08/1.66 ( X, Y ) ) }.
% 1.08/1.66 { ! X = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ),
% 1.08/1.66 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }
% 1.08/1.66 .
% 1.08/1.66 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP(
% 1.08/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) ) }.
% 1.08/1.66 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), hAPP(
% 1.08/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) ) }.
% 1.08/1.66 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ) ), X ) ) = hAPP(
% 1.08/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), T ), Y ) ), Z ) ), X ) }.
% 1.08/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP
% 1.08/1.66 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.08/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.08/1.66 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.08/1.66 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) = Y }.
% 1.08/1.66 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), Y ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.08/1.66 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) = hAPP(
% 1.08/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) }.
% 1.08/1.66 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) }.
% 1.08/1.66 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.08/1.66 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) }.
% 1.08/1.66 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) = hAPP
% 1.08/1.66 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ), Y = X }.
% 1.08/1.66 { ! Y = X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y )
% 1.08/1.66 = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) }.
% 1.08/1.66 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) = hAPP
% 1.08/1.66 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ), Z = X }.
% 1.08/1.66 { ! Z = X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y )
% 1.08/1.66 = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) }.
% 1.08/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ), T ), Z ) ), Y )
% 1.08/1.66 = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ) ),
% 1.08/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T
% 1.08/1.66 ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly
% 1.08/1.66 ( X ) ), Z ), Y ) ) }.
% 1.08/1.66 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.08/1.66 c_SEQ_OBseq( X, c_COMBB( tc_Nat_Onat, X, tc_Nat_Onat, Y, c_COMBC(
% 1.08/1.66 tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.08/1.66 tc_Nat_Onat ), Z ) ) ) }.
% 1.08/1.66 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, c_COMBB
% 1.08/1.66 ( tc_Nat_Onat, X, tc_Nat_Onat, Y, c_COMBC( tc_Nat_Onat, tc_Nat_Onat,
% 1.08/1.66 tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ) ) ),
% 1.08/1.66 c_SEQ_OBseq( X, Y ) }.
% 1.08/1.66 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.08/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ) }.
% 1.08/1.66 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ), alpha7( X, Y ),
% 1.08/1.66 alpha21( X, Y ) }.
% 1.08/1.66 { ! alpha7( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.08/1.66 ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) }.
% 1.08/1.66 { ! alpha21( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.08/1.66 ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) }.
% 1.08/1.66 { ! alpha21( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.08/1.66 { ! alpha21( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_Nat_Onat ) ) }.
% 1.08/1.66 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha21( X, Y ) }.
% 1.08/1.66 { ! alpha7( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_Nat_Onat ) ) }.
% 1.08/1.66 { ! alpha7( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.08/1.66 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha7( X, Y ) }.
% 1.08/1.66 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) =
% 1.08/1.66 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha8( X, Y )
% 1.08/1.66 , alpha22( X, Y ) }.
% 1.08/1.66 { ! alpha8( X, Y ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat )
% 1.08/1.66 , Y ), X ) = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.08/1.66 { ! alpha22( X, Y ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat )
% 1.08/1.66 , Y ), X ) = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.08/1.66 { ! alpha22( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.08/1.66 { ! alpha22( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_Nat_Onat ) ) }.
% 1.08/1.66 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha22( X, Y ) }.
% 1.08/1.66 { ! alpha8( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_Nat_Onat ) ) }.
% 1.08/1.66 { ! alpha8( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.08/1.66 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha8( X, Y ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.08/1.66 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_Nat_Onat ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.08/1.66 Y ), X ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_Nat_Onat ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.08/1.66 Y ), X ) ) ) }.
% 1.08/1.66 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), c_Nat_OSuc
% 1.08/1.66 ( hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) ) )
% 1.08/1.66 }.
% 1.08/1.66 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), c_Nat_OSuc
% 1.08/1.66 ( hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) ) )
% 1.08/1.66 }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), X
% 1.08/1.66 = c_Nat_OSuc( hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y )
% 1.08/1.66 , skol47( X, Y ) ) ) }.
% 1.08/1.66 { ! X = c_Nat_OSuc( hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat )
% 1.08/1.66 , Y ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 1.08/1.66 ), X ) ) }.
% 1.08/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 1.08/1.66 ( X ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ),
% 1.08/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.08/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 1.08/1.66 ), X ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ),
% 1.08/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.08/1.66 { c_Nat_OSuc( X ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat )
% 1.08/1.66 , c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 1.08/1.66 { c_Nat_OSuc( X ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat )
% 1.08/1.66 , X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.08/1.66 { hAPP( c_Complex_ORe, hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.08/1.66 tc_Complex_Ocomplex ), Y ), X ) ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( c_Complex_ORe, Y )
% 1.08/1.66 ), hAPP( c_Complex_ORe, X ) ) }.
% 1.08/1.66 { hAPP( c_Complex_OIm, hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.08/1.66 tc_Complex_Ocomplex ), Y ), X ) ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( c_Complex_OIm, Y )
% 1.08/1.66 ), hAPP( c_Complex_OIm, X ) ) }.
% 1.08/1.66 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.08/1.66 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.08/1.66 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal
% 1.08/1.66 ( tc_Nat_Onat, X ) ) }.
% 1.08/1.66 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 1.08/1.66 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex ), Y ), X ) ) ),
% 1.08/1.66 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) ) }.
% 1.08/1.66 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.08/1.66 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ),
% 1.08/1.66 c_RComplete_Onatfloor( hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.08/1.66 tc_RealDef_Oreal ), X ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = hAPP(
% 1.08/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), c_RComplete_Onatfloor(
% 1.08/1.66 X ) ), Y ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.08/1.66 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), c_RComplete_Onatfloor( Y )
% 1.08/1.66 ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), X ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y ), c_RealDef_Oreal(
% 1.08/1.66 tc_Nat_Onat, X ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ),
% 1.08/1.66 c_RComplete_Onatceiling( hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.08/1.66 tc_RealDef_Oreal ), X ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = hAPP(
% 1.08/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), c_RComplete_Onatceiling
% 1.08/1.66 ( X ) ), Y ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ),
% 1.08/1.66 c_RComplete_Onatfloor( hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.08/1.66 tc_RealDef_Oreal ), X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 1.08/1.66 ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.08/1.66 c_RComplete_Onatfloor( X ) ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) )
% 1.08/1.66 }.
% 1.08/1.66 { X = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), Y =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex ),
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), X ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol48( X, Y ) ), Y
% 1.08/1.66 ) ) ) ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) }.
% 1.08/1.66 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.08/1.66 hAPP( X, Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 skol49( Z, Y ) ), Y ) ) }.
% 1.08/1.66 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.08/1.66 hAPP( X, Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.08/1.66 tc_Nat_Onat, Z ), skol49( X, Y ) ) ), ! hBOOL( hAPP( X, Z ) ) }.
% 1.08/1.66 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.08/1.66 hAPP( X, Y ) ), hBOOL( hAPP( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.08/1.66 tc_Nat_Onat ), skol49( X, Y ) ), c_Groups_Oone__class_Oone( tc_Nat_Onat )
% 1.08/1.66 ) ) ) }.
% 1.08/1.66 { c_Complex_Ocis( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.08/1.66 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Y ) ) ), X
% 1.08/1.66 ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.08/1.66 c_Complex_Ocis( X ) ), c_Complex_Ocis( hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.08/1.66 tc_Nat_Onat, Y ) ), X ) ) ) }.
% 1.08/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 1.08/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_Int_Oint ), X = c_Groups_Oone__class_Oone(
% 1.08/1.66 tc_Int_Oint ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_Int_Oint ), Y = c_Groups_Oone__class_Oone(
% 1.08/1.66 tc_Int_Oint ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! X =
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y = c_Groups_Oone__class_Oone
% 1.08/1.66 ( tc_Int_Oint ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 1.08/1.66 , X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.08/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.08/1.66 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.08/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP
% 1.08/1.66 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ), !
% 1.08/1.66 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) }.
% 1.08/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 1.08/1.66 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 1.08/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 1.08/1.66 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.08/1.66 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ),
% 1.08/1.66 c_Complex_Ocis( Y ) ), X ) = c_Complex_Ocis( hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.08/1.66 tc_Nat_Onat, X ) ), Y ) ) }.
% 1.08/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.08/1.66 c_Complex_Ocis( Y ) ), c_Complex_Ocis( X ) ) = c_Complex_Ocis( hAPP( hAPP
% 1.08/1.66 ( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.08/1.66 { c_Complex_Ocis( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 1.08/1.66 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ),
% 1.08/1.66 c_Complex_Orcis( Z, Y ) ), X ) = c_Complex_Orcis( hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.08/1.66 tc_Nat_Onat, X ) ), Y ) ) }.
% 1.08/1.66 { c_Complex_Oexpi( c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) =
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 1.08/1.66 { c_Transcendental_Ocos( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.08/1.66 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) ) = hAPP(
% 1.08/1.66 c_Complex_ORe, hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.08/1.66 tc_Complex_Ocomplex ), c_Complex_Ocis( X ) ), Y ) ) }.
% 1.08/1.66 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 1.08/1.66 tc_Int_Oint ) ), X ) ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint )
% 1.08/1.66 }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), hAPP(
% 1.08/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 1.08/1.66 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), hAPP(
% 1.08/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP
% 1.08/1.66 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ),
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ),
% 1.08/1.66 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ),
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ),
% 1.08/1.66 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ),
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), hAPP(
% 1.08/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ), Y = X }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ),
% 1.08/1.66 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), hAPP( hAPP
% 1.08/1.66 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) ) }.
% 1.08/1.66 { ! Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ),
% 1.08/1.66 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_Int_Oint ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ),
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 1.08/1.66 tc_Int_Oint ) ), X ) ), X ) ), c_Groups_Ozero__class_Ozero( tc_Int_Oint )
% 1.08/1.66 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 1.08/1.66 tc_Int_Oint ) ), X ) ), X ) ), c_Groups_Ozero__class_Ozero( tc_Int_Oint )
% 1.08/1.66 ) ) }.
% 1.08/1.66 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) = X }.
% 1.08/1.66 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) = X }.
% 1.08/1.66 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.08/1.66 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) ) }.
% 1.08/1.66 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), X ) ) }.
% 1.08/1.66 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) = hAPP(
% 1.08/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ), Y ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 1.08/1.66 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP
% 1.08/1.66 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), X ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ), !
% 1.08/1.66 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T ), Z ) ),
% 1.08/1.66 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), T ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ), Z ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ),
% 1.08/1.66 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), Z ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ), Z ) ) ) }.
% 1.08/1.66 { hAPP( c_Complex_ORe, c_Complex_Orcis( Y, X ) ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ),
% 1.08/1.66 c_Transcendental_Ocos( X ) ) }.
% 1.08/1.66 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_Transcendental_Ocos( X ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal
% 1.08/1.66 ) ) ) }.
% 1.08/1.66 { c_Transcendental_Ocos( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) )
% 1.08/1.66 = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ),
% 1.08/1.66 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ) }
% 1.08/1.66 .
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ), !
% 1.08/1.66 Y = X }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 1.08/1.66 , Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X
% 1.08/1.66 ) ) }.
% 1.08/1.66 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ), Y =
% 1.08/1.66 X, hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), Y ) ) }
% 1.08/1.66 .
% 1.08/1.66 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oone__class_Oone(
% 1.08/1.66 tc_Int_Oint ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_Int_Oint ) ), X ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 1.08/1.66 ( tc_Int_Oint ) ), X ) ) }.
% 1.08/1.66 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 1.08/1.66 ( tc_Int_Oint ) }.
% 1.08/1.66 { hAPP( c_Complex_ORe, c_Complex_Ocis( X ) ) = c_Transcendental_Ocos( X ) }
% 1.08/1.66 .
% 1.08/1.66 { c_Complex_Ocis( X ) = c_Complex_Orcis( c_Groups_Oone__class_Oone(
% 1.08/1.66 tc_RealDef_Oreal ), X ) }.
% 1.08/1.66 { c_Complex_Orcis( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.08/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.08/1.66 c_Complex_Orcis( T, Z ) ), c_Complex_Orcis( Y, X ) ) = c_Complex_Orcis(
% 1.08/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), T ), Y ),
% 1.08/1.66 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Z ), X ) ) }
% 1.08/1.66 .
% 1.08/1.66 { c_Complex_Oexpi( hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.08/1.66 tc_Complex_Ocomplex ), Y ), X ) ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), c_Complex_Oexpi( Y
% 1.08/1.66 ) ), c_Complex_Oexpi( X ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! X = hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ),
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! X = hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z ), X ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 1.08/1.66 ( tc_Int_Oint ) ), Y ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) ) ), !
% 1.08/1.66 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), Z ) ), !
% 1.08/1.66 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ) }.
% 1.08/1.66 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), X ) ) }
% 1.08/1.66 .
% 1.08/1.66 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ),
% 1.08/1.66 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), Y ) ) }
% 1.08/1.66 .
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 1.08/1.66 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), Z )
% 1.08/1.66 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), Z )
% 1.08/1.66 ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 1.08/1.66 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), Y )
% 1.08/1.66 ), Y = X }.
% 1.08/1.66 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ) ), T ) = hAPP(
% 1.08/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ), ! hBOOL(
% 1.08/1.66 hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, T ), W ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_Int_Oint ) ), Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.08/1.66 ( tc_Int_Oint, Z ), W ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.08/1.66 ( tc_Int_Oint, Y ), U ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP
% 1.08/1.66 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ) ), Z ) ), hAPP(
% 1.08/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ) ), X ) ) ), !
% 1.08/1.66 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, U ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, U ), Z ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), T ) ) }.
% 1.08/1.66 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ) ), T ) = hAPP(
% 1.08/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ), ! hBOOL(
% 1.08/1.66 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) ) ), !
% 1.08/1.66 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), Z ) ), !
% 1.08/1.66 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), T ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_Int_Oint ) ), Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.08/1.66 ( tc_Int_Oint, Z ), W ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.08/1.66 ( tc_Int_Oint, U ), Y ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP
% 1.08/1.66 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ) ), Z ) ), hAPP(
% 1.08/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ) ), X ) ) ), !
% 1.08/1.66 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z ), U ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), U ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T ), Y ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_Int_Oint ) ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.08/1.66 tc_Int_Oint, Y ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ), Y ) ) ) }.
% 1.08/1.66 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Ozero__class_Ozero
% 1.08/1.66 ( tc_Int_Oint ) ) ) }.
% 1.08/1.66 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oone__class_Oone(
% 1.08/1.66 tc_Int_Oint ) ) ) }.
% 1.08/1.66 { c_Transcendental_Osin( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.08/1.66 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) ) = hAPP(
% 1.08/1.66 c_Complex_OIm, hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.08/1.66 tc_Complex_Ocomplex ), c_Complex_Ocis( X ) ), Y ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), skol50( Z, T ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol50( X, Y ) ),
% 1.08/1.66 c_Nat_OSuc( Y ) ) = X }.
% 1.08/1.66 { c_Transcendental_Osin( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) )
% 1.08/1.66 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.08/1.66 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_Transcendental_Osin( X ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal
% 1.08/1.66 ) ) ) }.
% 1.08/1.66 { hAPP( c_Complex_OIm, c_Complex_Ocis( X ) ) = c_Transcendental_Osin( X ) }
% 1.08/1.66 .
% 1.08/1.66 { ! c_Transcendental_Ocos( X ) = c_Groups_Oone__class_Oone(
% 1.08/1.66 tc_RealDef_Oreal ), c_Transcendental_Osin( X ) =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.08/1.66 { c_Transcendental_Osin( hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.08/1.66 tc_RealDef_Oreal ), Y ), X ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.08/1.66 ( tc_RealDef_Oreal ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.08/1.66 tc_RealDef_Oreal ), c_Transcendental_Osin( Y ) ), c_Transcendental_Ocos(
% 1.08/1.66 X ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.08/1.66 c_Transcendental_Ocos( Y ) ), c_Transcendental_Osin( X ) ) ) }.
% 1.08/1.66 { hAPP( c_Complex_OIm, c_Complex_Orcis( Y, X ) ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ),
% 1.08/1.66 c_Transcendental_Osin( X ) ) }.
% 1.08/1.66 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_Transcendental_Ocos
% 1.08/1.66 ( X ) ), c_Transcendental_Ocos( X ) ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_Transcendental_Osin
% 1.08/1.66 ( X ) ), c_Transcendental_Osin( X ) ) ) = c_Groups_Oone__class_Oone(
% 1.08/1.66 tc_RealDef_Oreal ) }.
% 1.08/1.66 { ! class_Groups_Omonoid__mult( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_Nat_Onat ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.08/1.66 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 1.08/1.66 ( tc_Nat_Onat ) ) ) ), Z ) = hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.08/1.66 ), Z ), Y ) }.
% 1.08/1.66 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 1.08/1.66 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 1.08/1.66 c_Groups_Oone__class_Oone( X ) }.
% 1.08/1.66 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.08/1.66 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 1.08/1.66 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 1.08/1.66 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 1.08/1.66 , Y ) ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.08/1.66 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 1.08/1.66 , Y ) ), c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 1.08/1.66 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Z ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 1.08/1.66 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Z
% 1.08/1.66 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 1.08/1.66 ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) =
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 1.08/1.66 ), ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 1.08/1.66 ), ! X = Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ) ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) ) }.
% 1.08/1.66 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ), Y ) ) }.
% 1.08/1.66 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.08/1.66 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.08/1.66 ( X, Z, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, U ), T
% 1.08/1.66 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.08/1.66 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.08/1.66 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.08/1.66 ( X, Z, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), Y
% 1.08/1.66 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, U ), T ) ) }.
% 1.08/1.66 { ! class_RealVector_Oreal__normed__vector( X ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.08/1.66 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.08/1.66 ( X, Y ) ) ), c_RealVector_Onorm__class_Onorm( X,
% 1.08/1.66 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) ) }.
% 1.08/1.66 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ), c_Nat_OSuc( Y ) ) )
% 1.08/1.66 }.
% 1.08/1.66 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.08/1.66 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 1.08/1.66 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ), Y ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ), Y ) ), hBOOL(
% 1.08/1.66 hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.08/1.66 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), hAPP
% 1.08/1.66 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 1.08/1.66 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Z ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 1.08/1.66 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Z ) )
% 1.08/1.66 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 1.08/1.66 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ),
% 1.08/1.66 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ) ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ), X ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) ), hBOOL( hAPP
% 1.08/1.66 ( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), hAPP
% 1.08/1.66 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) ), hBOOL(
% 1.08/1.66 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ), Y ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ), Y ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.08/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) ),
% 1.08/1.66 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Y ) = X }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X = hAPP(
% 1.08/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , ! X = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y )
% 1.08/1.66 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ), Y ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Z ) =
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ), Y ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ), Y ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus
% 1.08/1.66 ( tc_Nat_Onat, X, Y ) ), Z ) }.
% 1.08/1.66 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.08/1.66 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.08/1.66 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 1.08/1.66 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 1.08/1.66 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.08/1.66 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 1.08/1.66 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.08/1.66 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 1.08/1.66 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.08/1.66 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 1.08/1.66 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.08/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.08/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.08/1.66 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.08/1.66 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 1.08/1.66 Y ) ) = c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 1.08/1.66 ( X, Y, Z ) ) }.
% 1.08/1.66 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.08/1.66 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 1.08/1.66 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.08/1.66 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.08/1.66 ( tc_Nat_Onat, Z, Y ), X ) }.
% 1.08/1.66 { ! class_Groups_Ominus( X ), hAPP( c_Groups_Ominus__class_Ominus( tc_fun(
% 1.08/1.66 U, X ), T, Z ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( T, Y ),
% 1.08/1.66 hAPP( Z, Y ) ) }.
% 1.08/1.66 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.08/1.66 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 1.08/1.66 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.08/1.66 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 1.08/1.66 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.08/1.66 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 1.08/1.66 { ! class_Groups_Ominus( X ), hAPP( c_Groups_Ominus__class_Ominus( tc_fun(
% 1.08/1.66 U, X ), T, Z ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( T, Y ),
% 1.08/1.66 hAPP( Z, Y ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Y ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, X ), Y ) ),
% 1.08/1.66 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.08/1.66 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ), Y ) )
% 1.08/1.66 }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ), !
% 1.08/1.66 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), Z ) ),
% 1.08/1.66 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.08/1.66 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ) ), X ) ) }.
% 1.08/1.66 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.08/1.66 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.08/1.66 ( X, Z, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, U ), T ) )
% 1.08/1.66 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.08/1.66 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.08/1.66 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.08/1.66 ( X, Z, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, Z ), Y ) )
% 1.08/1.66 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, U ), T ) ) }.
% 1.08/1.66 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.08/1.66 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.08/1.66 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 1.08/1.66 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.08/1.66 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 1.08/1.66 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.08/1.66 ) }.
% 1.08/1.66 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.08/1.66 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.08/1.66 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 1.08/1.66 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.08/1.66 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.08/1.66 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.08/1.66 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 1.08/1.66 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.08/1.66 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.08/1.66 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), U ), c_Groups_Ominus__class_Ominus( X
% 1.08/1.66 , T, Y ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( X, U, Z ) ), Y ) ) }.
% 1.08/1.66 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.08/1.66 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( X, U, Z ) ), c_Groups_Ominus__class_Ominus
% 1.08/1.66 ( X, T, Y ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( X, U, Z ) ), Y ) ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ominus__class_Ominus( X
% 1.08/1.66 , T, Y ) ) ) }.
% 1.08/1.66 { ! class_Rings_Oring( X ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X )
% 1.08/1.66 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) = hAPP
% 1.08/1.66 ( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ), T = hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.08/1.66 W ) ), U ) ), Y ) }.
% 1.08/1.66 { ! class_Rings_Oring( X ), ! T = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.08/1.66 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ) ), Y ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) }.
% 1.08/1.66 { ! class_Rings_Oring( X ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X )
% 1.08/1.66 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) = hAPP
% 1.08/1.66 ( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.08/1.66 Z ) ), U ) ), T ) = Y }.
% 1.08/1.66 { ! class_Rings_Oring( X ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X )
% 1.08/1.66 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ) ), T ) = Y, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) }.
% 1.08/1.66 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, Z ), Y ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.08/1.66 ) ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.08/1.66 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.08/1.66 ) ), c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, Z ), Y ) ) }.
% 1.08/1.66 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) =
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 1.08/1.66 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) =
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 1.08/1.66 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.08/1.66 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.08/1.66 Z, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) }.
% 1.08/1.66 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ), Y ) = X }.
% 1.08/1.66 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ), X ) = Y }.
% 1.08/1.66 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, hAPP(
% 1.08/1.66 hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ), Y ) = Z }.
% 1.08/1.66 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.08/1.66 ( X ), c_Groups_Ominus__class_Ominus( X, Z, Y ) ), Y ) = Z }.
% 1.08/1.66 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, T ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.08/1.66 W ) ), U ) ), Y ) ) ) }.
% 1.08/1.66 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, T ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.08/1.66 W ) ), U ) ), Y ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X
% 1.08/1.66 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ) }.
% 1.08/1.66 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.08/1.66 Z ) ), U ) ), T ) ), Y ) ) }.
% 1.08/1.66 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.08/1.66 Z ) ), U ) ), T ) ), Y ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ) }.
% 1.08/1.66 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.08/1.66 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) )
% 1.08/1.66 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, T ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.08/1.66 W ) ), U ) ), Y ) ) ) }.
% 1.08/1.66 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, T ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.08/1.66 W ) ), U ) ), Y ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.08/1.66 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ) }.
% 1.08/1.66 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.08/1.66 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) )
% 1.08/1.66 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.08/1.66 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ) ), T ) ), Y ) ) }.
% 1.08/1.66 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.08/1.66 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ) ), T ) ), Y ) ), hBOOL(
% 1.08/1.66 hAPP( c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) ) }.
% 1.08/1.66 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 1.08/1.66 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 1.08/1.66 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Oone__class_Oone( X ) ) )
% 1.08/1.66 , c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) )
% 1.08/1.66 }.
% 1.08/1.66 { ! class_RealVector_Oreal__normed__vector( X ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 1.08/1.66 Y ) ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 1.08/1.66 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 1.08/1.66 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.08/1.66 ( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) ), X ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), c_Nat_OSuc(
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = X }.
% 1.08/1.66 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.08/1.66 , alpha9( X, Y, Z ) }.
% 1.08/1.66 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.08/1.66 , alpha23( X, Y, Z ) }.
% 1.08/1.66 { ! alpha9( X, Y, Z ), ! alpha23( X, Y, Z ), hBOOL( hAPP( Z,
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.08/1.66 { ! alpha23( X, Y, Z ), ! Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.08/1.66 tc_Nat_Onat ), X ), T ), hBOOL( hAPP( Z, T ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( Z, skol51( T, U, Z ) ) ), alpha23( X, Y, Z ) }.
% 1.08/1.66 { Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), skol51(
% 1.08/1.66 X, Y, Z ) ), alpha23( X, Y, Z ) }.
% 1.08/1.66 { ! alpha9( X, Y, Z ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.08/1.66 tc_Nat_Onat, Y ), X ) ), hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_Nat_Onat ) ) ) }.
% 1.08/1.66 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.08/1.66 alpha9( X, Y, Z ) }.
% 1.08/1.66 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha9
% 1.08/1.66 ( X, Y, Z ) }.
% 1.08/1.66 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.08/1.66 , ! alpha10( X, Y, Z ) }.
% 1.08/1.66 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.08/1.66 , ! alpha24( X, Y, Z ) }.
% 1.08/1.66 { alpha10( X, Y, Z ), alpha24( X, Y, Z ), hBOOL( hAPP( Z,
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.08/1.66 { ! alpha24( X, Y, Z ), ! hBOOL( hAPP( Z, skol52( T, U, Z ) ) ) }.
% 1.08/1.66 { ! alpha24( X, Y, Z ), Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.08/1.66 tc_Nat_Onat ), X ), skol52( X, Y, Z ) ) }.
% 1.08/1.66 { ! Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), T ),
% 1.08/1.66 hBOOL( hAPP( Z, T ) ), alpha24( X, Y, Z ) }.
% 1.08/1.66 { ! alpha10( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.08/1.66 tc_Nat_Onat, Y ), X ) ) }.
% 1.08/1.66 { ! alpha10( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_Nat_Onat ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.08/1.66 hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha10(
% 1.08/1.66 X, Y, Z ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, c_Nat_OSuc(
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) =
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ), c_Nat_OSuc( X ) ) }
% 1.08/1.66 .
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc(
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Z ) =
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.08/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ) ), hAPP(
% 1.08/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ) ) ), hBOOL
% 1.08/1.66 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), T ) ), Z ) )
% 1.08/1.66 }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.08/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), T ) ), Z ) )
% 1.08/1.66 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.08/1.66 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ) ), hAPP(
% 1.08/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ), hAPP( hAPP
% 1.08/1.66 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ) ) =
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), T ), Z ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ) = hAPP(
% 1.08/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ), hAPP( hAPP
% 1.08/1.66 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), T ) = Z }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), T ) = Z,
% 1.08/1.66 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ) = hAPP(
% 1.08/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.08/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ) ), hAPP(
% 1.08/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ) ) ), hBOOL
% 1.08/1.66 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), Z ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ),
% 1.08/1.66 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), Z ) ) ),
% 1.08/1.66 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ) ), hAPP(
% 1.08/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ), hAPP( hAPP
% 1.08/1.66 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ) ) =
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, T, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), Z ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ) = hAPP(
% 1.08/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ), T = hAPP(
% 1.08/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), Z ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , ! T = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP(
% 1.08/1.66 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), Z ), hAPP(
% 1.08/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ) = hAPP(
% 1.08/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ) }.
% 1.08/1.66 { ! class_RealVector_Oreal__normed__vector( X ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X,
% 1.08/1.66 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), U ), T ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 1.08/1.66 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, U,
% 1.08/1.66 Z ) ) ), c_RealVector_Onorm__class_Onorm( X,
% 1.08/1.66 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) ) ) }.
% 1.08/1.66 { ! class_Groups_Omonoid__mult( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), T ), c_Groups_Ominus__class_Ominus(
% 1.08/1.66 tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), T ), c_Groups_Ominus__class_Ominus(
% 1.08/1.66 tc_Nat_Onat, Y, Z ) ) ), T ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), c_Nat_OSuc(
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Groups_Oone__class_Oone
% 1.08/1.66 ( tc_Nat_Onat ) ) ) = X }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), X = c_Nat_OSuc(
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Groups_Oone__class_Oone
% 1.08/1.66 ( tc_Nat_Onat ) ) ) }.
% 1.08/1.66 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) = X }.
% 1.08/1.66 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc( hAPP(
% 1.08/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 1.08/1.66 ( tc_Nat_Onat ) ) ), X ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ) ), hAPP(
% 1.08/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ) ) ), hBOOL
% 1.08/1.66 ( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, T ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), Z ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, T ), hAPP(
% 1.08/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), Z ) ) ),
% 1.08/1.66 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ) ), hAPP(
% 1.08/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ) ), hAPP(
% 1.08/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ) ) ), hBOOL
% 1.08/1.66 ( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), T ) ), Z ) )
% 1.08/1.66 }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ) ), T ) ), Z ) )
% 1.08/1.66 , hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ) ), hAPP(
% 1.08/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ) ) ) }.
% 1.08/1.66 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.08/1.66 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 1.08/1.66 ( tc_Nat_Onat ) ) ), X ) ) }.
% 1.08/1.66 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.08/1.66 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 1.08/1.66 ( tc_Nat_Onat ) ) ) ) }.
% 1.08/1.66 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP
% 1.08/1.66 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.08/1.66 Y ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.08/1.66 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, skol53( X ),
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), X ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X ), c_RealDef_Oreal(
% 1.08/1.66 tc_Nat_Onat, skol53( X ) ) ) ) }.
% 1.08/1.66 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 1.08/1.66 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), skol54( X, U
% 1.08/1.66 , W, T ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ),
% 1.08/1.66 V0 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, V0 ) ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.08/1.66 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) ) ) ) ) }.
% 1.08/1.66 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 1.08/1.66 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_RealVector_Onorm__class_Onorm( Y, c_Groups_Ominus__class_Ominus( Y,
% 1.08/1.66 hAPP( Z, T ), hAPP( Z, skol54( X, Y, Z, T ) ) ) ) ),
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, T ), U ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, U ) ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.08/1.66 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) ) ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 1.08/1.66 X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ), X ) ) }.
% 1.08/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.08/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.08/1.66 { hAPP( c_Complex_ORe, c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex,
% 1.08/1.66 Y, X ) ) = c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP(
% 1.08/1.66 c_Complex_ORe, Y ), hAPP( c_Complex_ORe, X ) ) }.
% 1.08/1.66 { hAPP( c_Complex_OIm, c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex,
% 1.08/1.66 Y, X ) ) = c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP(
% 1.08/1.66 c_Complex_OIm, Y ), hAPP( c_Complex_OIm, X ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ),
% 1.08/1.66 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ) }.
% 1.08/1.66 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.08/1.66 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.08/1.66 { ! class_RealVector_Oreal__normed__vector( X ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.08/1.66 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.08/1.66 ( X, Y ) ) ), c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 1.08/1.66 ( tc_Int_Oint ) ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.08/1.66 tc_Int_Oint, Y ), X ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ),
% 1.08/1.66 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 1.08/1.66 ( tc_Int_Oint ) ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.08/1.66 tc_Nat_Onat, X, Y ) ) = c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.08/1.66 c_RealDef_Oreal( tc_Nat_Onat, X ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ) }
% 1.08/1.66 .
% 1.08/1.66 { c_Transcendental_Osin( c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y
% 1.08/1.66 , X ) ) = c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_Transcendental_Osin
% 1.08/1.66 ( Y ) ), c_Transcendental_Ocos( X ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_Transcendental_Ocos
% 1.08/1.66 ( Y ) ), c_Transcendental_Osin( X ) ) ) }.
% 1.08/1.66 { c_Transcendental_Osin( c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y
% 1.08/1.66 , X ) ) = c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_Transcendental_Ocos
% 1.08/1.66 ( X ) ), c_Transcendental_Osin( Y ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_Transcendental_Osin
% 1.08/1.66 ( X ) ), c_Transcendental_Ocos( Y ) ) ) }.
% 1.08/1.66 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.08/1.66 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex ), Y ), X ) ),
% 1.08/1.66 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ) ) ),
% 1.08/1.66 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) }.
% 1.08/1.66 { c_Transcendental_Ocos( hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.08/1.66 tc_RealDef_Oreal ), Y ), X ) ) = c_Groups_Ominus__class_Ominus(
% 1.08/1.66 tc_RealDef_Oreal, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.08/1.66 tc_RealDef_Oreal ), c_Transcendental_Ocos( Y ) ), c_Transcendental_Ocos(
% 1.08/1.66 X ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.08/1.66 c_Transcendental_Osin( Y ) ), c_Transcendental_Osin( X ) ) ) }.
% 1.08/1.66 { c_Transcendental_Ocos( c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y
% 1.08/1.66 , X ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 1.08/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.08/1.66 c_Transcendental_Ocos( Y ) ), c_Transcendental_Ocos( X ) ) ), hAPP( hAPP
% 1.08/1.66 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.08/1.66 c_Transcendental_Osin( Y ) ), c_Transcendental_Osin( X ) ) ) }.
% 1.08/1.66 { c_Transcendental_Ocos( c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y
% 1.08/1.66 , X ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 1.08/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.08/1.66 c_Transcendental_Ocos( X ) ), c_Transcendental_Ocos( Y ) ) ), hAPP( hAPP
% 1.08/1.66 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.08/1.66 c_Transcendental_Osin( X ) ), c_Transcendental_Osin( Y ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) ), c_RComplete_Onatfloor(
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 1.08/1.66 tc_Nat_Onat, Y ) ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.08/1.66 c_RComplete_Onatfloor( X ), Y ) }.
% 1.08/1.66 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X,
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), c_RealDef_Oreal(
% 1.08/1.66 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) ), c_RComplete_Onatceiling(
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 1.08/1.66 tc_Nat_Onat, Y ) ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.08/1.66 c_RComplete_Onatceiling( X ), Y ) }.
% 1.08/1.66 { hAPP( c_Complex_ORe, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.08/1.66 tc_Complex_Ocomplex ), Y ), X ) ) = c_Groups_Ominus__class_Ominus(
% 1.08/1.66 tc_RealDef_Oreal, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.08/1.66 tc_RealDef_Oreal ), hAPP( c_Complex_ORe, Y ) ), hAPP( c_Complex_ORe, X )
% 1.08/1.66 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP(
% 1.08/1.66 c_Complex_OIm, Y ) ), hAPP( c_Complex_OIm, X ) ) ) }.
% 1.08/1.66 { ! c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) =
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex ), X ),
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) ) ),
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, X,
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) ) ),
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex ), X ), c_Complex_Oii )
% 1.08/1.66 ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, X, c_Complex_Oii ) )
% 1.08/1.66 ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_Int_Oint ) ), Y ) ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP(
% 1.08/1.66 hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ), Y ) = hAPP(
% 1.08/1.66 hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Y ),
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.08/1.66 { ! class_Divides_Osemiring__div( X ), ! T = c_Groups_Ozero__class_Ozero( X
% 1.08/1.66 ), c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.08/1.66 { ! class_Divides_Osemiring__div( X ), T = c_Groups_Ozero__class_Ozero( X )
% 1.08/1.66 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.08/1.66 c_Divides_Odiv__class_Odiv( X, Z, Y ) }.
% 1.08/1.66 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.08/1.66 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = Z }.
% 1.08/1.66 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.08/1.66 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) = Z }.
% 1.08/1.66 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.08/1.66 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.08/1.66 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 1.08/1.66 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.08/1.66 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 1.08/1.66 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 1.08/1.66 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.08/1.66 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, X ) =
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.08/1.66 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 1.08/1.66 c_Groups_Oone__class_Oone( X ) ) = Y }.
% 1.08/1.66 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.08/1.66 , c_Divides_Odiv__class_Odiv( X, Y, Y ) = c_Groups_Oone__class_Oone( X )
% 1.08/1.66 }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.08/1.66 tc_Int_Oint, Y, X ) ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ),
% 1.08/1.66 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.08/1.66 tc_Int_Oint, Y, X ) ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.08/1.66 tc_Int_Oint, Y, X ) ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ),
% 1.08/1.66 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_Int_Oint ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.08/1.66 tc_Int_Oint, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_Int_Oint ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.08/1.66 tc_Int_Oint, c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.08/1.66 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv
% 1.08/1.66 ( tc_Int_Oint, X, Y ) ) ) }.
% 1.08/1.66 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.08/1.66 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.08/1.66 }.
% 1.08/1.66 { ! c_Complex_Oii = c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 1.08/1.66 { ! c_Complex_Oii = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.08/1.66 { hAPP( c_Complex_ORe, c_Complex_Oii ) = c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_RealDef_Oreal ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 1.08/1.66 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Z ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.08/1.66 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ),
% 1.08/1.66 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 1.08/1.66 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.08/1.66 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ),
% 1.08/1.66 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ),
% 1.08/1.66 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_Int_Oint ) ), Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.08/1.66 ( tc_Int_Oint, Y ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.08/1.66 ( tc_Int_Oint, c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 1.08/1.66 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_Int_Oint ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.08/1.66 tc_Int_Oint, c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv
% 1.08/1.66 ( tc_Int_Oint, Y, X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.08/1.66 ( tc_Int_Oint, Y ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv
% 1.08/1.66 ( tc_Int_Oint, Y, X ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), Y ) ),
% 1.08/1.66 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.08/1.66 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_Int_Oint ) ), Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.08/1.66 ( tc_Int_Oint, Y ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.08/1.66 ( tc_Int_Oint, c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ),
% 1.08/1.66 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) ),
% 1.08/1.66 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ) }
% 1.08/1.66 .
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) ),
% 1.08/1.66 hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ), ! hBOOL( hAPP
% 1.08/1.66 ( c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.08/1.66 ( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.08/1.66 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.08/1.66 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 1.08/1.66 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), Y ) ) }
% 1.08/1.66 .
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), Y ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv
% 1.08/1.66 ( tc_Int_Oint, Y, X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.08/1.66 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv
% 1.08/1.66 ( tc_Int_Oint, Y, X ) ) ) }.
% 1.08/1.66 { ! c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha11( X, Y ) }.
% 1.08/1.66 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.08/1.66 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.08/1.66 { ! alpha11( X, Y ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.08/1.66 { ! alpha11( X, Y ), alpha25( X, Y ), alpha30( X, Y ) }.
% 1.08/1.66 { ! alpha25( X, Y ), alpha11( X, Y ) }.
% 1.08/1.66 { ! alpha30( X, Y ), alpha11( X, Y ) }.
% 1.08/1.66 { ! alpha30( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.08/1.66 tc_Int_Oint, Y ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.08/1.66 { ! alpha30( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.08/1.66 tc_Int_Oint, X ), Y ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), Y ) ), alpha30( X, Y ) }
% 1.08/1.66 .
% 1.08/1.66 { ! alpha25( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.08/1.66 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ) }.
% 1.08/1.66 { ! alpha25( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.08/1.66 tc_Int_Oint, Y ), X ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y ), X ) ), alpha25( X, Y ) }
% 1.08/1.66 .
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oone__class_Oone(
% 1.08/1.66 tc_Int_Oint ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.08/1.66 tc_Int_Oint, c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ), X ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ),
% 1.08/1.66 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 1.08/1.66 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.08/1.66 tc_Int_Oint, Z, Y ), X ) }.
% 1.08/1.66 { hAPP( c_Complex_OIm, c_Complex_Oii ) = c_Groups_Oone__class_Oone(
% 1.08/1.66 tc_RealDef_Oreal ) }.
% 1.08/1.66 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.08/1.66 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.08/1.66 ( X ), T ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y
% 1.08/1.66 ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ),
% 1.08/1.66 c_Divides_Odiv__class_Odiv( X, T, Y ) ) }.
% 1.08/1.66 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.08/1.66 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.08/1.66 ( X ), T ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y
% 1.08/1.66 ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ),
% 1.08/1.66 c_Divides_Odiv__class_Odiv( X, T, Y ) ) }.
% 1.08/1.66 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.08/1.66 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.08/1.66 ( X ), Z ), Y ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ),
% 1.08/1.66 c_Divides_Odiv__class_Odiv( X, Z, Y ) ), c_Groups_Oone__class_Oone( X ) )
% 1.08/1.66 }.
% 1.08/1.66 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.08/1.66 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.08/1.66 ( X ), Y ), Z ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ),
% 1.08/1.66 c_Divides_Odiv__class_Odiv( X, Z, Y ) ), c_Groups_Oone__class_Oone( X ) )
% 1.08/1.66 }.
% 1.08/1.66 { ! T = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP
% 1.08/1.66 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ), alpha43
% 1.08/1.66 ( X, Z ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), Z =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.08/1.66 tc_Int_Oint, T, Z ) = Y }.
% 1.08/1.66 { ! T = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP
% 1.08/1.66 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ), alpha43
% 1.08/1.66 ( X, Z ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, Z )
% 1.08/1.66 , X ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 1.08/1.66 ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), Z =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.08/1.66 tc_Int_Oint, T, Z ) = Y }.
% 1.08/1.66 { ! alpha43( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.08/1.66 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ) }.
% 1.08/1.66 { ! alpha43( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.08/1.66 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL
% 1.08/1.66 ( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), Y ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), alpha43( X, Y ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), Y ) ), alpha43( X, Y ) }
% 1.08/1.66 .
% 1.08/1.66 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 1.08/1.66 alpha12( X, Z ) }.
% 1.08/1.66 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 1.08/1.66 alpha26( X, Y, Z ) }.
% 1.08/1.66 { ! alpha12( X, Z ), ! alpha26( X, Y, Z ), hBOOL( hAPP( Z,
% 1.08/1.66 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ) }.
% 1.08/1.66 { ! alpha26( X, Y, Z ), alpha31( X, Y, Z ) }.
% 1.08/1.66 { ! alpha26( X, Y, Z ), alpha34( X, Y, Z ) }.
% 1.08/1.66 { ! alpha31( X, Y, Z ), ! alpha34( X, Y, Z ), alpha26( X, Y, Z ) }.
% 1.08/1.66 { ! alpha34( X, Y, Z ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.08/1.66 tc_Int_Oint, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), alpha37
% 1.08/1.66 ( X, Y, Z ) }.
% 1.08/1.66 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), alpha34( X, Y, Z ) }.
% 1.08/1.66 { ! alpha37( X, Y, Z ), alpha34( X, Y, Z ) }.
% 1.08/1.66 { ! alpha37( X, Y, Z ), ! alpha39( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( Z, skol55( T, U, Z ) ) ), alpha37( X, Y, Z ) }.
% 1.08/1.66 { alpha39( X, Y, skol55( X, Y, Z ) ), alpha37( X, Y, Z ) }.
% 1.08/1.66 { ! alpha39( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.08/1.66 tc_Int_Oint, X ), skol56( X, T, U ) ) ) }.
% 1.08/1.66 { ! alpha39( X, Y, Z ), alpha41( X, Y, Z, skol56( X, Y, Z ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, X ), T ) ), !
% 1.08/1.66 alpha41( X, Y, Z, T ), alpha39( X, Y, Z ) }.
% 1.08/1.66 { ! alpha41( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.08/1.66 tc_Int_Oint, T ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.08/1.66 { ! alpha41( X, Y, Z, T ), Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.08/1.66 tc_Int_Oint ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.08/1.66 X ), Z ) ), T ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! Y = hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ) ), T ), alpha41( X
% 1.08/1.66 , Y, Z, T ) }.
% 1.08/1.66 { ! alpha31( X, Y, Z ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.08/1.66 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), alpha35
% 1.08/1.66 ( X, Y, Z ) }.
% 1.08/1.66 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), alpha31( X, Y, Z ) }
% 1.08/1.66 .
% 1.08/1.66 { ! alpha35( X, Y, Z ), alpha31( X, Y, Z ) }.
% 1.08/1.66 { ! alpha35( X, Y, Z ), ! alpha38( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( Z, skol57( T, U, Z ) ) ), alpha35( X, Y, Z ) }.
% 1.08/1.66 { alpha38( X, Y, skol57( X, Y, Z ) ), alpha35( X, Y, Z ) }.
% 1.08/1.66 { ! alpha38( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.08/1.66 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), skol58( T, U,
% 1.08/1.66 W ) ) ) }.
% 1.08/1.66 { ! alpha38( X, Y, Z ), alpha40( X, Y, Z, skol58( X, Y, Z ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), T ) ), ! alpha40( X, Y, Z,
% 1.08/1.66 T ), alpha38( X, Y, Z ) }.
% 1.08/1.66 { ! alpha40( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.08/1.66 tc_Int_Oint, T ), X ) ) }.
% 1.08/1.66 { ! alpha40( X, Y, Z, T ), Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.08/1.66 tc_Int_Oint ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.08/1.66 X ), Z ) ), T ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint, T ), X ) ), !
% 1.08/1.66 Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ) ), T ), alpha40( X
% 1.08/1.66 , Y, Z, T ) }.
% 1.08/1.66 { ! alpha12( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.08/1.66 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.08/1.66 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha12( X, Y ) }.
% 1.08/1.66 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), alpha12
% 1.08/1.66 ( X, Y ) }.
% 1.08/1.66 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, Y, X ) ) ), hAPP(
% 1.08/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 1.08/1.66 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( c_Complex_ORe, Y )
% 1.08/1.66 , hAPP( c_Complex_ORe, X ) ) ) ), c_Groups_Oabs__class_Oabs(
% 1.08/1.66 tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP(
% 1.08/1.66 c_Complex_OIm, Y ), hAPP( c_Complex_OIm, X ) ) ) ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 1.08/1.66 , c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 1.08/1.66 tc_Int_Oint, X, Y ) }.
% 1.08/1.66 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ),
% 1.08/1.66 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint
% 1.08/1.66 ) }.
% 1.08/1.66 { ! class_Groups_Oordered__ab__group__add__abs( X ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 1.08/1.66 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ) )
% 1.08/1.66 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z )
% 1.08/1.66 ) ) ) }.
% 1.08/1.66 { ! class_Groups_Oordered__ab__group__add__abs( X ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 1.08/1.66 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ) )
% 1.08/1.66 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y )
% 1.08/1.66 ) ) ) }.
% 1.08/1.66 { ! class_Groups_Oordered__ab__group__add__abs( X ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 1.08/1.66 c_Groups_Ominus__class_Ominus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 1.08/1.66 c_Groups_Oabs__class_Oabs( X, Y ) ) ) ), c_Groups_Oabs__class_Oabs( X,
% 1.08/1.66 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) ) }.
% 1.08/1.66 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.08/1.66 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 1.08/1.66 = c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z )
% 1.08/1.66 ) }.
% 1.08/1.66 { ! class_Groups_Oordered__ab__group__add__abs( X ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 1.08/1.66 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 1.08/1.66 c_Groups_Oabs__class_Oabs( X, Y ) ) ) ) }.
% 1.08/1.66 { ! class_Groups_Oordered__ab__group__add__abs( X ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 1.08/1.66 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.08/1.66 ( X ), U ), T ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ) )
% 1.08/1.66 ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ),
% 1.08/1.66 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, U, Z ) )
% 1.08/1.66 ), c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Y
% 1.08/1.66 ) ) ) ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X,
% 1.08/1.66 c_Groups_Ominus__class_Ominus( X, T, Z ) ) ), Y ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.08/1.66 ) ), T ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X,
% 1.08/1.66 c_Groups_Ominus__class_Ominus( X, T, Z ) ) ), Y ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, T ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.08/1.66 ) ), T ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X, T ), hAPP(
% 1.08/1.66 hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X,
% 1.08/1.66 c_Groups_Ominus__class_Ominus( X, T, Z ) ) ), Y ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.08/1.66 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.08/1.66 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) = X }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.08/1.66 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.08/1.66 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, Z ) ),
% 1.08/1.66 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, Z ) ) ) }.
% 1.08/1.66 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.08/1.66 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ), Y ) ) }.
% 1.08/1.66 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 1.08/1.66 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 1.08/1.66 tc_Nat_Onat, Z, Y ), X ) }.
% 1.08/1.66 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 1.08/1.66 tc_Polynomial_Opoly( X ), T, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.08/1.66 tc_Polynomial_Opoly( X ) ), Z ), Y ) ) = c_Divides_Odiv__class_Odiv(
% 1.08/1.66 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 1.08/1.66 ( X ), T, Z ), Y ) }.
% 1.08/1.66 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.08/1.66 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.08/1.66 { Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.08/1.66 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 1.08/1.66 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 1.08/1.66 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.08/1.66 c_Groups_Oabs__class_Oabs( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X
% 1.08/1.66 ), c_Groups_Oabs__class_Oabs( X, Z ) ), c_Groups_Oabs__class_Oabs( X, Y
% 1.08/1.66 ) ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ),
% 1.08/1.66 c_Groups_Oabs__class_Oabs( X, Z ) ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 1.08/1.66 }.
% 1.08/1.66 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, Y ) ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.08/1.66 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 1.08/1.66 c_Groups_Oabs__class_Oabs( X, Y ) ) ), ! Y = c_Groups_Ozero__class_Ozero
% 1.08/1.66 ( X ) }.
% 1.08/1.66 { ! class_Groups_Oordered__ab__group__add__abs( X ), Y =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ),
% 1.08/1.66 c_Groups_Oabs__class_Oabs( X, Y ) ) ) }.
% 1.08/1.66 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.08/1.66 ), c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 1.08/1.66 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, Z ) ), Y
% 1.08/1.66 ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( X,
% 1.08/1.66 c_Groups_Oabs__class_Oabs( X, U ) ), T ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 1.08/1.66 c_Groups_Oabs__class_Oabs( X, U ) ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X,
% 1.08/1.66 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.08/1.66 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.08/1.66 c_Groups_Oabs__class_Oabs( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.08/1.66 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.08/1.66 c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.08/1.66 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.08/1.66 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.08/1.66 c_Groups_Oabs__class_Oabs( X, c_Groups_Oabs__class_Oabs( X, Y ) ) =
% 1.08/1.66 c_Groups_Oabs__class_Oabs( X, Y ) }.
% 1.08/1.66 { c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_RealDef_Oreal( tc_Nat_Onat
% 1.08/1.66 , X ) ) = c_RealDef_Oreal( tc_Nat_Onat, X ) }.
% 1.08/1.66 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Oabs__class_Oabs
% 1.08/1.66 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ) ) =
% 1.08/1.66 c_RealVector_Onorm__class_Onorm( X, Y ) }.
% 1.08/1.66 { c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, X ) =
% 1.08/1.66 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 1.08/1.66 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), c_Groups_Oabs__class_Oabs( X, Z ) ), Y
% 1.08/1.66 ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 1.08/1.66 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 1.08/1.66 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__idom( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 1.08/1.66 c_Groups_Oabs__class_Oabs( X, Y ) ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 1.08/1.66 { ! class_Groups_Oordered__ab__group__add__abs( X ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Oabs__class_Oabs( X,
% 1.08/1.66 Y ) ) ) }.
% 1.08/1.66 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ) )
% 1.08/1.66 , Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }
% 1.08/1.66 .
% 1.08/1.66 { ! class_Groups_Oordered__ab__group__add__abs( X ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, hAPP
% 1.08/1.66 ( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 1.08/1.66 c_Groups_Oabs__class_Oabs( X, Y ) ) ) ) }.
% 1.08/1.66 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.66 , Y ) ), c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 1.08/1.66 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Y ) )
% 1.08/1.66 , c_Groups_Ozero__class_Ozero( X ) ) ), Y = c_Groups_Ozero__class_Ozero(
% 1.08/1.66 X ) }.
% 1.08/1.66 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Y ) )
% 1.08/1.66 , c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.08/1.66 { ! class_Groups_Oordered__ab__group__add__abs( X ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.66 , c_Groups_Oabs__class_Oabs( X, Y ) ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__idom( X ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.66 , hAPP( hAPP( c_Power_Opower__class_Opower( X ),
% 1.08/1.66 c_Groups_Oabs__class_Oabs( X, Z ) ), Y ) ) ) }.
% 1.08/1.66 { ! class_Rings_Oordered__ring__abs( X ), alpha44( X, Z ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.66 , Y ) ), c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 1.08/1.66 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 1.08/1.66 { ! class_Rings_Oordered__ring__abs( X ), alpha44( X, Z ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.08/1.66 ) ) ), c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 1.08/1.66 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 1.08/1.66 { ! alpha44( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ) ), Y ) ) }.
% 1.08/1.66 { ! alpha44( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y
% 1.08/1.66 ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.08/1.66 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( X ) ), Y ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.08/1.66 ) ) ), alpha44( X, Y ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.08/1.66 , Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.08/1.66 c_Groups_Oabs__class_Oabs( X, Z ) ), Y ) = c_Groups_Oabs__class_Oabs( X,
% 1.08/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.08/1.66 { c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, c_Complex_Orcis( Y
% 1.08/1.66 , X ) ) = c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Y ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.08/1.66 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ) ),
% 1.08/1.66 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, X ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ),
% 1.08/1.66 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) = Y }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ),
% 1.08/1.66 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) = Y }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ),
% 1.08/1.66 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) =
% 1.08/1.66 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_Nat_Onat ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.08/1.66 tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ), Y ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ),
% 1.08/1.66 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Z ) ) ) ), Y =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP(
% 1.08/1.66 hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 1.08/1.66 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) ),
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), X ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), c_NthRoot_Oroot( X,
% 1.08/1.66 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ) ) =
% 1.08/1.66 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_NthRoot_Oroot( X, Y ) ) }
% 1.08/1.66 .
% 1.08/1.66 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_Transcendental_Ocos( X ) )
% 1.08/1.66 ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) }.
% 1.08/1.66 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_Transcendental_Osin( X ) )
% 1.08/1.66 ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) }.
% 1.08/1.66 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, hAPP( c_Complex_ORe, X ) ) )
% 1.08/1.66 , c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) }.
% 1.08/1.66 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, hAPP( c_Complex_OIm, X ) ) )
% 1.08/1.66 , c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.08/1.66 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.08/1.66 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.08/1.66 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.08/1.66 tc_Nat_Onat, Y, X ), X ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), X ) ),
% 1.08/1.66 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.08/1.66 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.08/1.66 tc_Nat_Onat, Y, X ), X ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 1.08/1.66 alpha13( X, Z ) }.
% 1.08/1.66 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 1.08/1.66 alpha27( X, Y, Z ) }.
% 1.08/1.66 { ! alpha13( X, Z ), ! alpha27( X, Y, Z ), hBOOL( hAPP( Z,
% 1.08/1.66 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ) }.
% 1.08/1.66 { ! alpha27( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.08/1.66 alpha32( X, Y, Z ) }.
% 1.08/1.66 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha27( X, Y, Z ) }.
% 1.08/1.66 { ! alpha32( X, Y, Z ), alpha27( X, Y, Z ) }.
% 1.08/1.66 { ! alpha32( X, Y, Z ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.08/1.66 tc_Nat_Onat, T ), X ) ), alpha36( X, Y, Z, T ) }.
% 1.08/1.66 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol59( X, T, U
% 1.08/1.66 ) ), X ) ), alpha32( X, Y, Z ) }.
% 1.08/1.66 { ! alpha36( X, Y, Z, skol59( X, Y, Z ) ), alpha32( X, Y, Z ) }.
% 1.08/1.66 { ! alpha36( X, Y, Z, T ), ! Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.08/1.66 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.08/1.66 X ), U ) ), T ), hBOOL( hAPP( Z, U ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( Z, skol60( U, W, Z, V0 ) ) ), alpha36( X, Y, Z, T ) }.
% 1.08/1.66 { Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol60( X, Y, Z, T ) )
% 1.08/1.66 ), T ), alpha36( X, Y, Z, T ) }.
% 1.08/1.66 { ! alpha13( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.08/1.66 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.08/1.66 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha13( X, Y ) }.
% 1.08/1.66 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha13
% 1.08/1.66 ( X, Y ) }.
% 1.08/1.66 { ! class_RealVector_Oreal__normed__vector( X ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.08/1.66 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.08/1.66 ( X, Y ) ) ) ), c_RealVector_Onorm__class_Onorm( X,
% 1.08/1.66 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) ) }.
% 1.08/1.66 { hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.08/1.66 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) ) ) ) }.
% 1.08/1.66 { ! c_Transcendental_Osin( X ) = c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_RealDef_Oreal ), c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 1.08/1.66 c_Transcendental_Ocos( X ) ) = c_Groups_Oone__class_Oone(
% 1.08/1.66 tc_RealDef_Oreal ) }.
% 1.08/1.66 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 1.08/1.66 alpha14( X, Z ), alpha28( X, Y, Z ) }.
% 1.08/1.66 { ! alpha14( X, Z ), hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 1.08/1.66 tc_Nat_Onat, Y, X ) ) ) }.
% 1.08/1.66 { ! alpha28( X, Y, Z ), hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 1.08/1.66 tc_Nat_Onat, Y, X ) ) ) }.
% 1.08/1.66 { ! alpha28( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.08/1.66 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 1.08/1.66 ), skol61( X, Y, T ) ) ), Y ) ) }.
% 1.08/1.66 { ! alpha28( X, Y, Z ), alpha33( X, Y, Z, skol61( X, Y, Z ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.08/1.66 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), T ) ), Y ) ), !
% 1.08/1.66 alpha33( X, Y, Z, T ), alpha28( X, Y, Z ) }.
% 1.08/1.66 { ! alpha33( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless(
% 1.08/1.66 tc_Nat_Onat, Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat
% 1.08/1.66 ), X ), c_Nat_OSuc( T ) ) ) ) }.
% 1.08/1.66 { ! alpha33( X, Y, Z, T ), hBOOL( hAPP( Z, T ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP(
% 1.08/1.66 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc( T )
% 1.08/1.66 ) ) ), ! hBOOL( hAPP( Z, T ) ), alpha33( X, Y, Z, T ) }.
% 1.08/1.66 { ! alpha14( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.08/1.66 { ! alpha14( X, Y ), hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_Nat_Onat ) ) ) }.
% 1.08/1.66 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( Y,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha14( X, Y ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ), Y ) ), ! hBOOL
% 1.08/1.66 ( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc( Z ) ) ) )
% 1.08/1.66 , Z = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! Z =
% 1.08/1.66 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ), Y ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! Z =
% 1.08/1.66 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc( Z ) ) ) )
% 1.08/1.66 }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Y ) ),
% 1.08/1.66 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.08/1.66 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.08/1.66 tc_Nat_Onat, Y, X ), X ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Nat__Transfer_Otsub( X, Y
% 1.08/1.66 ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 1.08/1.66 , c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 1.08/1.66 tc_Int_Oint, X, Y ) }.
% 1.08/1.66 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.08/1.66 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), U ), T ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( X ), c_Groups_Ominus__class_Ominus( X, U, Z
% 1.08/1.66 ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ) }.
% 1.08/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), Y ), X
% 1.08/1.66 ) = c_Complex_Ocomplex_OComplex( c_Groups_Ominus__class_Ominus(
% 1.08/1.66 tc_RealDef_Oreal, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.08/1.66 tc_RealDef_Oreal ), hAPP( c_Complex_ORe, Y ) ), hAPP( c_Complex_ORe, X )
% 1.08/1.66 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP(
% 1.08/1.66 c_Complex_OIm, Y ) ), hAPP( c_Complex_OIm, X ) ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( c_Complex_ORe, Y
% 1.08/1.66 ) ), hAPP( c_Complex_OIm, X ) ) ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( c_Complex_OIm, Y
% 1.08/1.66 ) ), hAPP( c_Complex_ORe, X ) ) ) ) }.
% 1.08/1.66 { ! c_Groups_Oabs__class_Oabs( tc_Int_Oint, hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) =
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 1.08/1.66 tc_Int_Oint, X ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.08/1.66 c_Groups_Oabs__class_Oabs( tc_Int_Oint, X ) ), c_Groups_Oone__class_Oone
% 1.08/1.66 ( tc_Int_Oint ) ) ), X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.08/1.66 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oabs__class_Oabs(
% 1.08/1.66 tc_Int_Oint, X ) ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) }.
% 1.08/1.66 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_Complex_Ocomplex ), Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 1.08/1.66 ) }.
% 1.08/1.66 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_Complex_Ocomplex ), X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 1.08/1.66 ) }.
% 1.08/1.66 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.08/1.66 c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_Complex_Ocomplex ) }.
% 1.08/1.66 { c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) =
% 1.08/1.66 c_Complex_Ocomplex_OComplex( c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_RealDef_Oreal ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.08/1.66 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex ),
% 1.08/1.66 c_Complex_Ocomplex_OComplex( T, Z ) ), c_Complex_Ocomplex_OComplex( Y, X
% 1.08/1.66 ) ) = c_Complex_Ocomplex_OComplex( hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), T ), Y ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Z ), X ) ) }.
% 1.08/1.66 { ! c_Complex_Ocomplex_OComplex( T, Z ) = c_Complex_Ocomplex_OComplex( Y, X
% 1.08/1.66 ), T = Y }.
% 1.08/1.66 { ! c_Complex_Ocomplex_OComplex( T, Z ) = c_Complex_Ocomplex_OComplex( Y, X
% 1.08/1.66 ), Z = X }.
% 1.08/1.66 { ! T = Y, ! Z = X, c_Complex_Ocomplex_OComplex( T, Z ) =
% 1.08/1.66 c_Complex_Ocomplex_OComplex( Y, X ) }.
% 1.08/1.66 { hAPP( c_Complex_OIm, c_Complex_Ocomplex_OComplex( Y, X ) ) = X }.
% 1.08/1.66 { hAPP( c_Complex_ORe, c_Complex_Ocomplex_OComplex( Y, X ) ) = Y }.
% 1.08/1.66 { c_Complex_Ocomplex_OComplex( hAPP( c_Complex_ORe, X ), hAPP(
% 1.08/1.66 c_Complex_OIm, X ) ) = X }.
% 1.08/1.66 { c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex,
% 1.08/1.66 c_Complex_Ocomplex_OComplex( T, Z ), c_Complex_Ocomplex_OComplex( Y, X )
% 1.08/1.66 ) = c_Complex_Ocomplex_OComplex( c_Groups_Ominus__class_Ominus(
% 1.08/1.66 tc_RealDef_Oreal, T, Y ), c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal
% 1.08/1.66 , Z, X ) ) }.
% 1.08/1.66 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 1.08/1.66 tc_Int_Oint, Y ) ), X ) ) ) }.
% 1.08/1.66 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Complex_Oii, Y =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.08/1.66 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Complex_Oii, X =
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.08/1.66 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ),
% 1.08/1.66 c_Complex_Ocomplex_OComplex( Y, X ) = c_Complex_Oii }.
% 1.08/1.66 { c_Complex_Oii = c_Complex_Ocomplex_OComplex( c_Groups_Ozero__class_Ozero
% 1.08/1.66 ( tc_RealDef_Oreal ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.08/1.66 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Oone__class_Oone(
% 1.08/1.66 tc_Complex_Ocomplex ), Y = c_Groups_Oone__class_Oone( tc_RealDef_Oreal )
% 1.08/1.66 }.
% 1.08/1.66 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Oone__class_Oone(
% 1.08/1.66 tc_Complex_Ocomplex ), X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 1.08/1.66 ) }.
% 1.08/1.66 { ! Y = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), ! X =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.08/1.66 c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Oone__class_Oone(
% 1.08/1.66 tc_Complex_Ocomplex ) }.
% 1.08/1.66 { c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) =
% 1.08/1.66 c_Complex_Ocomplex_OComplex( c_Groups_Oone__class_Oone( tc_RealDef_Oreal
% 1.08/1.66 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.08/1.66 { c_Complex_Ocis( X ) = c_Complex_Ocomplex_OComplex( c_Transcendental_Ocos
% 1.08/1.66 ( X ), c_Transcendental_Osin( X ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 1.08/1.66 tc_Int_Oint, Y ) ), X ) ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_Int_Oint ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.08/1.66 { Y = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_Int_Oint ) ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint )
% 1.08/1.66 , c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ) ) }.
% 1.08/1.66 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_Int_Oint ) ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint )
% 1.08/1.66 , c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ) ) }.
% 1.08/1.66 { c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.08/1.66 c_Complex_Ocomplex_OComplex( c_Transcendental_Ocos( X ),
% 1.08/1.66 c_Transcendental_Osin( X ) ) ) = c_Groups_Oone__class_Oone(
% 1.08/1.66 tc_RealDef_Oreal ) }.
% 1.08/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.08/1.66 c_Complex_Ocomplex_OComplex( T, Z ) ), c_Complex_Ocomplex_OComplex( Y, X
% 1.08/1.66 ) ) = c_Complex_Ocomplex_OComplex( c_Groups_Ominus__class_Ominus(
% 1.08/1.66 tc_RealDef_Oreal, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.08/1.66 tc_RealDef_Oreal ), T ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.08/1.66 tc_RealDef_Oreal ), Z ), X ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.08/1.66 tc_RealDef_Oreal ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.08/1.66 tc_RealDef_Oreal ), T ), X ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.08/1.66 ( tc_RealDef_Oreal ), Z ), Y ) ) ) }.
% 1.08/1.66 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex ), Y ), X )
% 1.08/1.66 = c_Complex_Ocomplex_OComplex( hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.08/1.66 tc_RealDef_Oreal ), hAPP( c_Complex_ORe, Y ) ), hAPP( c_Complex_ORe, X )
% 1.08/1.66 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP(
% 1.08/1.66 c_Complex_OIm, Y ) ), hAPP( c_Complex_OIm, X ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 1.08/1.66 ( tc_Int_Oint, Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint
% 1.08/1.66 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ),
% 1.08/1.66 c_Groups_Oabs__class_Oabs( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 1.08/1.66 tc_Int_Oint, Z, Y ) ) ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X
% 1.08/1.66 ) ) ), Y ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 1.08/1.66 tc_Int_Oint, c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, Z ) ) ),
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ) ) ) }.
% 1.08/1.66 { c_Complex_Ocomplex_Ocomplex__size( c_Complex_Ocomplex_OComplex( Y, X ) )
% 1.08/1.66 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ),
% 1.08/1.66 c_Transcendental_Ocos( c_Complex_Oarg( c_Complex_Ocomplex_OComplex(
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) ) ) =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.08/1.66 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.08/1.66 c_Transcendental_Ocos( c_Complex_Oarg( c_Complex_Ocomplex_OComplex(
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) ) ) =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ),
% 1.08/1.66 c_Transcendental_Ocos( c_Complex_Oarg( c_Complex_Ocomplex_OComplex(
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) ) ) =
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.08/1.66 { c_Nat_Osize__class_Osize( tc_Complex_Ocomplex,
% 1.08/1.66 c_Complex_Ocomplex_OComplex( Y, X ) ) = c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_Nat_Onat ) }.
% 1.08/1.66 { c_Complex_Ocomplex_Ocomplex__case( T, Z, c_Complex_Ocomplex_OComplex( Y,
% 1.08/1.66 X ) ) = hAPP( hAPP( Z, Y ), X ) }.
% 1.08/1.66 { c_Complex_Ocomplex_Ocomplex__rec( T, Z, c_Complex_Ocomplex_OComplex( Y, X
% 1.08/1.66 ) ) = hAPP( hAPP( Z, Y ), X ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.08/1.66 tc_Nat_Onat ) ), Y ) ), c_RComplete_Onatfloor(
% 1.08/1.66 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 1.08/1.66 tc_Nat_Onat, Y ) ) ) = c_Divides_Odiv__class_Odiv( tc_Nat_Onat,
% 1.08/1.66 c_RComplete_Onatfloor( X ), Y ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.08/1.66 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ) ), alpha15( X
% 1.08/1.66 , Y ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.08/1.66 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ) ), alpha29( X
% 1.08/1.66 , Y ) }.
% 1.08/1.66 { ! alpha15( X, Y ), ! alpha29( X, Y ), hBOOL( hAPP(
% 1.08/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.08/1.66 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ) ) }.
% 1.08/1.66 { ! alpha29( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.08/1.66 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y )
% 1.08/1.66 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X )
% 1.08/1.66 , c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), alpha29( X, Y )
% 1.08/1.66 }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ), alpha29( X, Y ) }.
% 1.08/1.66 { ! alpha15( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.08/1.66 tc_RealDef_Oreal, Y ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) )
% 1.08/1.66 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ), alpha15( X, Y ) }.
% 1.08/1.66 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), alpha15( X, Y )
% 1.08/1.66 }.
% 1.08/1.66 { ! class_Rings_Odivision__ring( X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), T ), c_Rings_Oinverse__class_Odivide
% 1.08/1.66 ( X, Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 1.08/1.66 { c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), hAPP( hAPP(
% 1.08/1.66 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ) =
% 1.08/1.66 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X, Y ) }.
% 1.08/1.66 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X, T
% 1.08/1.66 , Z ) ), Y ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.08/1.66 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.08/1.66 { ! class_Fields_Ofield__inverse__zero( X ), !
% 1.08/1.66 class_RealVector_Oreal__normed__field( X ),
% 1.08/1.66 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Odivide( X, Z
% 1.08/1.66 , Y ) ) = c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 1.08/1.66 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.08/1.66 ( X, Y ) ) }.
% 1.08/1.66 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 1.08/1.66 .
% 1.08/1.66 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.08/1.66 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.66 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 1.08/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.66 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 1.08/1.66 { class_Groups_Ocancel__comm__monoid__add( tc_Complex_Ocomplex ) }.
% 1.08/1.66 { class_Rings_Ocomm__ring( tc_Complex_Ocomplex ) }.
% 1.08/1.66 { class_Rings_Oidom( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Groups_Ocancel__comm__monoid__add( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Rings_Ocomm__ring( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 1.08/1.66 { class_Rings_Oidom( tc_Int_Oint ) }.
% 1.08/1.66 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 1.08/1.66 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 1.08/1.66 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 1.08/1.66 ) ) }.
% 1.08/1.66 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 1.08/1.66 .
% 1.08/1.66 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 1.08/1.66 { ! class_Groups_Ominus( X ), class_Groups_Ominus( tc_fun( Y, X ) ) }.
% 1.08/1.66 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.08/1.66 tc_Int_Oint ) }.
% 1.08/1.66 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.08/1.66 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 1.08/1.66 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 1.08/1.66 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 1.08/1.66 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 1.08/1.66 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 1.08/1.66 { class_Groups_Oordered__ab__group__add__abs( tc_Int_Oint ) }.
% 1.08/1.66 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 1.08/1.66 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 1.08/1.66 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.08/1.66 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 1.08/1.66 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 1.08/1.66 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 1.08/1.66 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 1.08/1.66 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 1.08/1.66 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 1.08/1.66 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 1.08/1.66 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 1.08/1.66 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 1.08/1.66 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 1.08/1.66 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 1.08/1.66 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 1.08/1.66 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 1.08/1.66 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 1.08/1.66 { class_Rings_Oordered__ring__abs( tc_Int_Oint ) }.
% 1.08/1.66 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 1.08/1.66 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 1.08/1.66 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 1.08/1.66 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 1.08/1.66 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 1.08/1.66 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 1.08/1.66 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 1.08/1.66 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 1.08/1.66 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 1.08/1.66 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 1.08/1.66 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 1.08/1.66 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 1.08/1.66 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 1.08/1.66 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 1.08/1.66 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 1.08/1.66 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 1.08/1.66 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 1.08/1.66 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 1.08/1.66 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 1.08/1.66 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 1.08/1.66 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 1.08/1.66 { class_Orderings_Oord( tc_Int_Oint ) }.
% 1.08/1.66 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 1.08/1.66 { class_Groups_Ominus( tc_Int_Oint ) }.
% 1.08/1.66 { class_Power_Opower( tc_Int_Oint ) }.
% 1.08/1.66 { class_Groups_Ozero( tc_Int_Oint ) }.
% 1.08/1.66 { class_Rings_Oring( tc_Int_Oint ) }.
% 1.08/1.66 { class_Groups_Oone( tc_Int_Oint ) }.
% 1.08/1.66 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.08/1.66 tc_Nat_Onat ) }.
% 1.08/1.66 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.08/1.66 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 1.08/1.66 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 1.08/1.66 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 1.08/1.66 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.08/1.66 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 1.08/1.66 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.08/1.66 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 1.08/1.66 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 1.08/1.66 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 1.08/1.66 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 1.08/1.66 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 1.08/1.66 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 1.08/1.66 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 1.08/1.66 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 1.08/1.66 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 1.08/1.66 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 1.08/1.66 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 1.08/1.66 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 1.08/1.66 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 1.08/1.66 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 1.08/1.66 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 1.08/1.66 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 1.08/1.66 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 1.08/1.66 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 1.08/1.66 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 1.08/1.66 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 1.08/1.66 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 1.08/1.66 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 1.08/1.66 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 1.08/1.66 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 1.08/1.66 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 1.08/1.66 { class_Groups_Ominus( tc_Nat_Onat ) }.
% 1.08/1.66 { class_Power_Opower( tc_Nat_Onat ) }.
% 1.08/1.66 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 1.08/1.66 { class_Groups_Oone( tc_Nat_Onat ) }.
% 1.08/1.66 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 1.08/1.66 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 1.08/1.66 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 1.08/1.66 { class_Groups_Ominus( tc_HOL_Obool ) }.
% 1.08/1.66 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.08/1.66 tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_RealDef_Oreal ) }
% 1.08/1.66 .
% 1.08/1.66 { class_Rings_Olinordered__comm__semiring__strict( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Rings_Olinordered__semiring__1__strict( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_RealVector_Oreal__normed__div__algebra( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Rings_Olinordered__semiring__strict( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_RealVector_Oreal__normed__algebra__1( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Groups_Oordered__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Groups_Oordered__ab__group__add__abs( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_RealVector_Oreal__normed__algebra( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Groups_Oordered__comm__monoid__add( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Groups_Olinordered__ab__group__add( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Groups_Ocancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Rings_Oring__1__no__zero__divisors( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Rings_Oordered__cancel__semiring( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_RealVector_Oreal__normed__vector( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Rings_Olinordered__ring__strict( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_RealVector_Oreal__normed__field( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Rings_Oring__no__zero__divisors( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Rings_Oordered__comm__semiring( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Rings_Olinordered__semiring__1( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Groups_Oordered__ab__group__add( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Groups_Ocancel__semigroup__add( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Rings_Olinordered__semiring( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Fields_Ofield__inverse__zero( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Rings_Olinordered__semidom( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Groups_Oab__semigroup__mult( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Groups_Ocomm__monoid__mult( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Groups_Oab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Rings_Oordered__semiring( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Rings_Oordered__ring__abs( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Rings_Ono__zero__divisors( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Groups_Ocomm__monoid__add( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Rings_Olinordered__ring( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Rings_Olinordered__idom( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Rings_Ocomm__semiring__1( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Rings_Ocomm__semiring__0( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Rings_Odivision__ring( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Rings_Ocomm__semiring( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Groups_Oab__group__add( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Rings_Ozero__neq__one( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Rings_Oordered__ring( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Orderings_Opreorder( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Orderings_Olinorder( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Groups_Omonoid__mult( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Rings_Ocomm__ring__1( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Groups_Omonoid__add( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Rings_Osemiring__0( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Groups_Ogroup__add( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Rings_Omult__zero( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Orderings_Oorder( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Rings_Osemiring( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Orderings_Oord( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Rings_Oring__1( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Groups_Ominus( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Fields_Ofield( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Power_Opower( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Groups_Ozero( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Rings_Oring( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Groups_Oone( tc_RealDef_Oreal ) }.
% 1.08/1.66 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.08/1.66 tc_Complex_Ocomplex ) }.
% 1.08/1.66 { class_RealVector_Oreal__normed__div__algebra( tc_Complex_Ocomplex ) }.
% 1.08/1.66 { class_RealVector_Oreal__normed__algebra__1( tc_Complex_Ocomplex ) }.
% 1.08/1.66 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 1.08/1.66 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.08/1.66 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.08/1.66 { class_RealVector_Oreal__normed__vector( tc_Complex_Ocomplex ) }.
% 1.08/1.66 { class_RealVector_Oreal__normed__field( tc_Complex_Ocomplex ) }.
% 1.08/1.66 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.08/1.66 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.08/1.66 { class_Fields_Ofield__inverse__zero( tc_Complex_Ocomplex ) }.
% 1.08/1.66 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 1.08/1.66 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 1.08/1.66 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.08/1.66 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.08/1.66 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 1.08/1.66 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 1.08/1.66 { class_Rings_Ocomm__semiring__0( tc_Complex_Ocomplex ) }.
% 1.08/1.66 { class_Rings_Odivision__ring( tc_Complex_Ocomplex ) }.
% 1.08/1.66 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 1.08/1.66 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 1.08/1.66 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 1.08/1.66 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 1.08/1.66 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 1.08/1.66 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 1.08/1.66 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 1.08/1.66 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 1.08/1.66 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 1.08/1.66 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 1.08/1.66 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 1.08/1.66 { class_Groups_Ominus( tc_Complex_Ocomplex ) }.
% 1.08/1.66 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 1.08/1.66 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 1.08/1.66 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 1.08/1.66 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 1.08/1.66 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 1.08/1.66 { ! class_Rings_Oidom( X ),
% 1.08/1.66 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.08/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__idom( X ),
% 1.08/1.66 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 1.08/1.66 ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__idom( X ),
% 1.08/1.66 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 1.08/1.66 X ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__idom( X ),
% 1.08/1.66 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 1.08/1.66 ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__idom( X ),
% 1.08/1.66 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 1.08/1.66 }.
% 1.08/1.66 { ! class_Rings_Olinordered__idom( X ),
% 1.08/1.66 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__idom( X ),
% 1.08/1.66 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__idom( X ),
% 1.08/1.66 class_Groups_Oordered__ab__group__add__abs( tc_Polynomial_Opoly( X ) ) }
% 1.08/1.66 .
% 1.08/1.66 { ! class_Rings_Olinordered__idom( X ),
% 1.08/1.66 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__idom( X ),
% 1.08/1.66 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.66 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.08/1.66 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.66 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 1.08/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__idom( X ),
% 1.08/1.66 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__idom( X ),
% 1.08/1.66 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.66 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 1.08/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__idom( X ),
% 1.08/1.66 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__idom( X ),
% 1.08/1.66 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__idom( X ),
% 1.08/1.66 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.66 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.08/1.66 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 1.08/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 1.08/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.66 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 1.08/1.66 ( tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.66 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 1.08/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.66 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 1.08/1.66 ( tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 1.08/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring__abs(
% 1.08/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.66 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 1.08/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.66 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 1.08/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 1.08/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.66 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 1.08/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.66 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 1.08/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.67 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 1.08/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.67 { ! class_Fields_Ofield( X ), class_Divides_Osemiring__div(
% 1.08/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.67 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 1.08/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.67 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 1.08/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.67 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 1.08/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.67 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 1.08/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.67 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 1.08/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.67 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 1.08/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.67 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 1.08/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.67 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 1.08/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.67 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 1.08/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.67 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 1.08/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.67 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 1.08/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.67 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 1.08/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.67 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 1.08/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.67 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 1.08/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.67 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 1.08/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.67 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 1.08/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.67 { ! class_Groups_Oab__group__add( X ), class_Groups_Ominus(
% 1.08/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.67 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 1.08/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.67 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 1.08/1.67 }.
% 1.08/1.67 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 1.08/1.67 ) ) }.
% 1.08/1.67 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 1.08/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.08/1.67 { hAPP( c_COMBK( T, Z, Y ), X ) = Y }.
% 1.08/1.67 { hAPP( c_COMBB( W, U, T, Z, Y ), X ) = hAPP( Z, hAPP( Y, X ) ) }.
% 1.08/1.67 { hAPP( c_COMBC( W, U, T, Z, Y ), X ) = hAPP( hAPP( Z, X ), Y ) }.
% 1.08/1.67 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.08/1.67 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), v_r ) ) }.
% 1.08/1.67
% 1.08/1.67 *** allocated 15000 integers for clauses
% 1.08/1.67 *** allocated 22500 integers for clauses
% 1.08/1.67 *** allocated 33750 integers for clauses
% 1.08/1.67 *** allocated 50625 integers for clauses
% 1.08/1.67 *** allocated 75937 integers for clauses
% 1.08/1.67 percentage equality = 0.239488, percentage horn = 0.921865
% 1.08/1.67 This is a problem with some equality
% 1.08/1.67
% 1.08/1.67
% 1.08/1.67
% 1.08/1.67 Options Used:
% 1.08/1.67
% 1.08/1.67 useres = 1
% 1.08/1.67 useparamod = 1
% 1.08/1.67 useeqrefl = 1
% 1.08/1.67 useeqfact = 1
% 1.08/1.67 usefactor = 1
% 1.08/1.67 usesimpsplitting = 0
% 1.08/1.67 usesimpdemod = 5
% 1.08/1.67 usesimpres = 3
% 1.08/1.67
% 1.08/1.67 resimpinuse = 1000
% 1.08/1.67 resimpclauses = 20000
% 1.08/1.67 substype = eqrewr
% 1.08/1.67 backwardsubs = 1
% 1.08/1.67 selectoldest = 5
% 1.08/1.67
% 1.08/1.67 litorderings [0] = split
% 1.08/1.67 litorderings [1] = extend the termordering, first sorting on arguments
% 1.08/1.67
% 1.08/1.67 termordering = kbo
% 1.08/1.67
% 1.08/1.67 litapriori = 0
% 1.08/1.67 termapriori = 1
% 1.08/1.67 litaposteriori = 0
% 1.08/1.67 termaposteriori = 0
% 1.08/1.67 demodaposteriori = 0
% 1.08/1.67 ordereqreflfact = 0
% 1.08/1.67
% 1.08/1.67 litselect = negord
% 1.08/1.67
% 1.08/1.67 maxweight = 15
% 1.08/1.67 maxdepth = 30000
% 1.08/1.67 maxlength = 115
% 1.08/1.67 maxnrvars = 195
% 1.08/1.67 excuselevel = 1
% 1.08/1.67 increasemaxweight = 1
% 1.08/1.67
% 1.08/1.67 maxselected = 10000000
% 1.08/1.67 maxnrclauses = 10000000
% 1.08/1.67
% 1.08/1.67 showgenerated = 0
% 1.08/1.67 showkept = 0
% 1.08/1.67 showselected = 0
% 1.08/1.67 showdeleted = 0
% 1.08/1.67 showresimp = 1
% 1.08/1.67 showstatus = 2000
% 1.08/1.67
% 1.08/1.67 prologoutput = 0
% 1.08/1.67 nrgoals = 5000000
% 1.08/1.67 totalproof = 1
% 1.08/1.67
% 1.08/1.67 Symbols occurring in the translation:
% 1.08/1.67
% 1.08/1.67 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.08/1.67 . [1, 2] (w:1, o:245, a:1, s:1, b:0),
% 1.08/1.67 ! [4, 1] (w:0, o:147, a:1, s:1, b:0),
% 1.08/1.67 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.08/1.67 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.08/1.67 hAPP [38, 2] (w:1, o:269, a:1, s:1, b:0),
% 1.08/1.67 v_ga____ [39, 0] (w:1, o:14, a:1, s:1, b:0),
% 1.08/1.67 c_SEQ_Osubseq [40, 1] (w:1, o:154, a:1, s:1, b:0),
% 1.08/1.67 class_Orderings_Opreorder [43, 1] (w:1, o:157, a:1, s:1, b:0),
% 1.08/1.67 c_Orderings_Oord__class_Oless__eq [44, 2] (w:1, o:273, a:1, s:1, b:0)
% 1.08/1.67 ,
% 1.08/1.67 hBOOL [45, 1] (w:1, o:158, a:1, s:1, b:0),
% 1.08/1.67 tc_RealDef_Oreal [47, 0] (w:1, o:35, a:1, s:1, b:0),
% 1.08/1.67 tc_Complex_Ocomplex [48, 0] (w:1, o:36, a:1, s:1, b:0),
% 1.08/1.67 v_s [49, 0] (w:1, o:38, a:1, s:1, b:0),
% 1.08/1.67 c_RealVector_Onorm__class_Onorm [50, 2] (w:1, o:274, a:1, s:1, b:0),
% 1.08/1.67
% 1.08/1.67 v_r [51, 0] (w:1, o:37, a:1, s:1, b:0),
% 1.08/1.67 tc_Nat_Onat [52, 0] (w:1, o:39, a:1, s:1, b:0),
% 1.08/1.67 c_Groups_Ozero__class_Ozero [53, 1] (w:1, o:159, a:1, s:1, b:0),
% 1.08/1.67 v_f____ [54, 0] (w:1, o:13, a:1, s:1, b:0),
% 1.08/1.67 class_Orderings_Oord [61, 1] (w:1, o:155, a:1, s:1, b:0),
% 1.08/1.67 tc_fun [62, 2] (w:1, o:315, a:1, s:1, b:0),
% 1.08/1.67 class_Orderings_Olinorder [64, 1] (w:1, o:160, a:1, s:1, b:0),
% 1.08/1.67 class_Orderings_Oorder [67, 1] (w:1, o:156, a:1, s:1, b:0),
% 1.08/1.67 class_RealVector_Oreal__normed__vector [71, 1] (w:1, o:161, a:1, s:1
% 1.08/1.67 , b:0),
% 1.08/1.67 class_Groups_Ozero [74, 1] (w:1, o:164, a:1, s:1, b:0),
% 1.08/1.67 c_RealDef_Oreal [75, 2] (w:1, o:316, a:1, s:1, b:0),
% 1.08/1.67 c_Groups_Otimes__class_Otimes [76, 1] (w:1, o:165, a:1, s:1, b:0),
% 1.08/1.67 class_RealVector_Oreal__normed__div__algebra [77, 1] (w:1, o:166, a:1
% 1.08/1.67 , s:1, b:0),
% 1.08/1.67 class_Groups_Oab__semigroup__mult [83, 1] (w:1, o:167, a:1, s:1, b:0)
% 1.08/1.67 ,
% 1.08/1.67 class_RealVector_Oreal__normed__algebra [84, 1] (w:1, o:168, a:1, s:1
% 1.08/1.67 , b:0),
% 1.08/1.67 class_Rings_Olinordered__ring [88, 1] (w:1, o:169, a:1, s:1, b:0),
% 1.08/1.67 class_Rings_Olinordered__ring__strict [89, 1] (w:1, o:170, a:1, s:1
% 1.08/1.67 , b:0),
% 1.08/1.67 class_Rings_Oordered__cancel__semiring [90, 1] (w:1, o:180, a:1, s:1
% 1.08/1.67 , b:0),
% 1.08/1.67 class_Rings_Oordered__ring [91, 1] (w:1, o:181, a:1, s:1, b:0),
% 1.08/1.67 class_Rings_Oordered__semiring [92, 1] (w:1, o:183, a:1, s:1, b:0),
% 1.08/1.67 class_Rings_Oordered__comm__semiring [93, 1] (w:1, o:184, a:1, s:1
% 1.08/1.67 , b:0),
% 1.08/1.67 class_Rings_Ono__zero__divisors [96, 1] (w:1, o:179, a:1, s:1, b:0),
% 1.08/1.67
% 1.08/1.67 class_Rings_Oring__no__zero__divisors [97, 1] (w:1, o:185, a:1, s:1
% 1.08/1.67 , b:0),
% 1.08/1.67 class_Rings_Omult__zero [98, 1] (w:1, o:178, a:1, s:1, b:0),
% 1.08/1.67 c_SEQ_Odecseq [101, 2] (w:1, o:317, a:1, s:1, b:0),
% 1.08/1.67 class_Rings_Ocomm__semiring__1 [103, 1] (w:1, o:189, a:1, s:1, b:0),
% 1.08/1.67
% 1.08/1.67 c_SEQ_Oincseq [107, 2] (w:1, o:318, a:1, s:1, b:0),
% 1.08/1.67 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [113, 2] (w:1, o:
% 1.08/1.67 319, a:1, s:1, b:0),
% 1.08/1.67 tc_Polynomial_Opoly [114, 1] (w:1, o:199, a:1, s:1, b:0),
% 1.08/1.67 c_RComplete_Onatfloor [115, 1] (w:1, o:152, a:1, s:1, b:0),
% 1.08/1.67 c_SEQ_Omonoseq [116, 2] (w:1, o:320, a:1, s:1, b:0),
% 1.08/1.67 c_RComplete_Onatceiling [117, 1] (w:1, o:153, a:1, s:1, b:0),
% 1.08/1.67 class_Lattices_Oab__semigroup__idem__mult [118, 1] (w:1, o:200, a:1
% 1.08/1.67 , s:1, b:0),
% 1.08/1.67 class_Rings_Ocomm__semiring__0 [120, 1] (w:1, o:188, a:1, s:1, b:0),
% 1.08/1.67
% 1.08/1.67 c_Complex_OIm [122, 0] (w:1, o:91, a:1, s:1, b:0),
% 1.08/1.67 c_COMBB [123, 5] (w:1, o:398, a:1, s:1, b:0),
% 1.08/1.67 c_Orderings_Oord__class_Oless [124, 2] (w:1, o:321, a:1, s:1, b:0),
% 1.08/1.67 c_Complex_ORe [127, 0] (w:1, o:105, a:1, s:1, b:0),
% 1.08/1.67 class_Rings_Olinordered__idom [128, 1] (w:1, o:171, a:1, s:1, b:0),
% 1.08/1.67 class_Rings_Olinordered__semiring__strict [131, 1] (w:1, o:172, a:1
% 1.08/1.67 , s:1, b:0),
% 1.08/1.67 class_Rings_Olinordered__comm__semiring__strict [132, 1] (w:1, o:173
% 1.08/1.67 , a:1, s:1, b:0),
% 1.08/1.67 class_Rings_Olinordered__semiring [134, 1] (w:1, o:174, a:1, s:1, b:0
% 1.08/1.67 ),
% 1.08/1.67 c_SEQ_OBseq [136, 2] (w:1, o:322, a:1, s:1, b:0),
% 1.08/1.67 c_Nat_OSuc [140, 1] (w:1, o:201, a:1, s:1, b:0),
% 1.08/1.67 c_Fun_Ocomp [143, 5] (w:1, o:399, a:1, s:1, b:0),
% 1.08/1.67 c_COMBK [155, 3] (w:1, o:343, a:1, s:1, b:0),
% 1.08/1.67 c_NthRoot_Oroot [157, 2] (w:1, o:270, a:1, s:1, b:0),
% 1.08/1.67 c_Groups_Oone__class_Oone [164, 1] (w:1, o:202, a:1, s:1, b:0),
% 1.08/1.67 c_Power_Opower__class_Opower [165, 1] (w:1, o:203, a:1, s:1, b:0),
% 1.08/1.67 class_RealVector_Oreal__normed__algebra__1 [166, 1] (w:1, o:204, a:1
% 1.08/1.67 , s:1, b:0),
% 1.08/1.67 class_Groups_Oone [167, 1] (w:1, o:205, a:1, s:1, b:0),
% 1.08/1.67 class_Rings_Ozero__neq__one [168, 1] (w:1, o:206, a:1, s:1, b:0),
% 1.08/1.67 class_Groups_Ocomm__monoid__mult [169, 1] (w:1, o:207, a:1, s:1, b:0)
% 1.08/1.67 ,
% 1.08/1.67 class_Groups_Omonoid__mult [170, 1] (w:1, o:209, a:1, s:1, b:0),
% 1.08/1.67 class_Rings_Olinordered__semidom [171, 1] (w:1, o:175, a:1, s:1, b:0)
% 1.08/1.67 ,
% 1.08/1.67 class_Rings_Oring__1__no__zero__divisors [172, 1] (w:1, o:210, a:1
% 1.08/1.67 , s:1, b:0),
% 1.08/1.67 class_Power_Opower [173, 1] (w:1, o:211, a:1, s:1, b:0),
% 1.08/1.67 class_Rings_Osemiring__0 [174, 1] (w:1, o:214, a:1, s:1, b:0),
% 1.08/1.67 c_Power_Opower_Opower [175, 3] (w:1, o:344, a:1, s:1, b:0),
% 1.08/1.67 c_Groups_Oplus__class_Oplus [177, 1] (w:1, o:215, a:1, s:1, b:0),
% 1.08/1.67 c_Transcendental_Oln [178, 1] (w:1, o:216, a:1, s:1, b:0),
% 1.08/1.67 class_Groups_Oab__semigroup__add [179, 1] (w:1, o:217, a:1, s:1, b:0)
% 1.08/1.67 ,
% 1.08/1.67 class_Groups_Ocancel__semigroup__add [180, 1] (w:1, o:218, a:1, s:1
% 1.08/1.67 , b:0),
% 1.08/1.67 class_Groups_Ocancel__ab__semigroup__add [181, 1] (w:1, o:219, a:1
% 1.08/1.67 , s:1, b:0),
% 1.08/1.67 class_Rings_Ocomm__semiring [182, 1] (w:1, o:220, a:1, s:1, b:0),
% 1.08/1.67 class_Rings_Osemiring [184, 1] (w:1, o:221, a:1, s:1, b:0),
% 1.08/1.67 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 1.08/1.67 189, 1] (w:1, o:225, a:1, s:1, b:0),
% 1.08/1.67 class_Groups_Oordered__ab__semigroup__add__imp__le [191, 1] (w:1, o:
% 1.08/1.67 226, a:1, s:1, b:0),
% 1.08/1.67 class_Groups_Oordered__cancel__ab__semigroup__add [192, 1] (w:1, o:
% 1.08/1.67 227, a:1, s:1, b:0),
% 1.08/1.67 class_Groups_Oordered__ab__semigroup__add [193, 1] (w:1, o:228, a:1
% 1.08/1.67 , s:1, b:0),
% 1.08/1.67 class_Groups_Ocomm__monoid__add [194, 1] (w:1, o:229, a:1, s:1, b:0)
% 1.08/1.67 ,
% 1.08/1.67 class_Groups_Omonoid__add [195, 1] (w:1, o:230, a:1, s:1, b:0),
% 1.08/1.67 class_Groups_Olinordered__ab__group__add [196, 1] (w:1, o:208, a:1
% 1.08/1.67 , s:1, b:0),
% 1.08/1.67 class_Groups_Oordered__comm__monoid__add [197, 1] (w:1, o:231, a:1
% 1.08/1.67 , s:1, b:0),
% 1.08/1.67 class_Rings_Olinordered__semiring__1 [202, 1] (w:1, o:176, a:1, s:1
% 1.08/1.67 , b:0),
% 1.08/1.67 class_Rings_Olinordered__semiring__1__strict [203, 1] (w:1, o:177, a:
% 1.08/1.67 1, s:1, b:0),
% 1.08/1.67 tc_Int_Oint [204, 0] (w:1, o:133, a:1, s:1, b:0),
% 1.08/1.67 c_COMBC [207, 5] (w:1, o:400, a:1, s:1, b:0),
% 1.08/1.67 c_Complex_Ocis [210, 1] (w:1, o:232, a:1, s:1, b:0),
% 1.08/1.67 c_Complex_Orcis [211, 2] (w:1, o:323, a:1, s:1, b:0),
% 1.08/1.67 c_Complex_Oexpi [212, 1] (w:1, o:233, a:1, s:1, b:0),
% 1.08/1.67 c_Transcendental_Ocos [213, 1] (w:1, o:234, a:1, s:1, b:0),
% 1.08/1.67 c_Transcendental_Osin [220, 1] (w:1, o:235, a:1, s:1, b:0),
% 1.08/1.67 c_Groups_Ominus__class_Ominus [221, 3] (w:1, o:345, a:1, s:1, b:0),
% 1.08/1.67 class_Groups_Oordered__ab__group__add [222, 1] (w:1, o:236, a:1, s:1
% 1.08/1.67 , b:0),
% 1.08/1.67 class_Groups_Ominus [227, 1] (w:1, o:237, a:1, s:1, b:0),
% 1.08/1.67 class_Groups_Oab__group__add [228, 1] (w:1, o:238, a:1, s:1, b:0),
% 1.08/1.67 class_Groups_Ogroup__add [229, 1] (w:1, o:239, a:1, s:1, b:0),
% 1.08/1.67 class_Rings_Oring [230, 1] (w:1, o:212, a:1, s:1, b:0),
% 1.08/1.67 class_Rings_Oring__1 [232, 1] (w:1, o:213, a:1, s:1, b:0),
% 1.08/1.67 class_Rings_Ocomm__ring__1 [235, 1] (w:1, o:186, a:1, s:1, b:0),
% 1.08/1.67 c_Complex_Oii [237, 0] (w:1, o:140, a:1, s:1, b:0),
% 1.08/1.67 c_Divides_Odiv__class_Odiv [238, 3] (w:1, o:348, a:1, s:1, b:0),
% 1.08/1.67 class_Divides_Osemiring__div [239, 1] (w:1, o:240, a:1, s:1, b:0),
% 1.08/1.67 c_Groups_Oabs__class_Oabs [243, 2] (w:1, o:324, a:1, s:1, b:0),
% 1.08/1.67 c_Nat__Transfer_Otsub [244, 2] (w:1, o:271, a:1, s:1, b:0),
% 1.08/1.67 class_Groups_Oordered__ab__group__add__abs [245, 1] (w:1, o:241, a:1
% 1.08/1.67 , s:1, b:0),
% 1.08/1.67 class_Fields_Ofield [247, 1] (w:1, o:162, a:1, s:1, b:0),
% 1.08/1.67 class_Rings_Oordered__ring__abs [248, 1] (w:1, o:182, a:1, s:1, b:0)
% 1.08/1.67 ,
% 1.08/1.67 c_Complex_Ocomplex_OComplex [251, 2] (w:1, o:325, a:1, s:1, b:0),
% 1.08/1.67 c_Complex_Ocomplex_Ocomplex__size [258, 1] (w:1, o:242, a:1, s:1, b:0
% 1.08/1.67 ),
% 1.08/1.67 c_Complex_Oarg [259, 1] (w:1, o:243, a:1, s:1, b:0),
% 1.08/1.67 c_Nat_Osize__class_Osize [260, 2] (w:1, o:272, a:1, s:1, b:0),
% 1.76/2.12 c_Complex_Ocomplex_Ocomplex__case [262, 3] (w:1, o:346, a:1, s:1, b:0
% 1.76/2.12 ),
% 1.76/2.12 c_Complex_Ocomplex_Ocomplex__rec [263, 3] (w:1, o:347, a:1, s:1, b:0)
% 1.76/2.12 ,
% 1.76/2.12 c_Rings_Oinverse__class_Odivide [264, 3] (w:1, o:349, a:1, s:1, b:0)
% 1.76/2.12 ,
% 1.76/2.12 class_Rings_Odivision__ring [265, 1] (w:1, o:222, a:1, s:1, b:0),
% 1.76/2.12 class_Fields_Ofield__inverse__zero [266, 1] (w:1, o:163, a:1, s:1, b:
% 1.76/2.12 0),
% 1.76/2.12 class_RealVector_Oreal__normed__field [267, 1] (w:1, o:223, a:1, s:1
% 1.76/2.12 , b:0),
% 1.76/2.12 class_Rings_Oidom [269, 1] (w:1, o:224, a:1, s:1, b:0),
% 1.76/2.12 class_Groups_Ocancel__comm__monoid__add [270, 1] (w:1, o:244, a:1, s:
% 1.76/2.12 1, b:0),
% 1.76/2.12 class_Rings_Ocomm__ring [271, 1] (w:1, o:187, a:1, s:1, b:0),
% 1.76/2.12 tc_HOL_Obool [273, 0] (w:1, o:132, a:1, s:1, b:0),
% 1.76/2.12 alpha1 [278, 3] (w:1, o:350, a:1, s:1, b:1),
% 1.76/2.12 alpha2 [279, 3] (w:1, o:354, a:1, s:1, b:1),
% 1.76/2.12 alpha3 [280, 2] (w:1, o:330, a:1, s:1, b:1),
% 1.76/2.12 alpha4 [281, 4] (w:1, o:389, a:1, s:1, b:1),
% 1.76/2.12 alpha5 [282, 4] (w:1, o:392, a:1, s:1, b:1),
% 1.76/2.12 alpha6 [283, 2] (w:1, o:331, a:1, s:1, b:1),
% 1.76/2.12 alpha7 [284, 2] (w:1, o:332, a:1, s:1, b:1),
% 1.76/2.12 alpha8 [285, 2] (w:1, o:333, a:1, s:1, b:1),
% 1.76/2.12 alpha9 [286, 3] (w:1, o:355, a:1, s:1, b:1),
% 1.76/2.12 alpha10 [287, 3] (w:1, o:351, a:1, s:1, b:1),
% 1.76/2.12 alpha11 [288, 2] (w:1, o:334, a:1, s:1, b:1),
% 1.76/2.12 alpha12 [289, 2] (w:1, o:335, a:1, s:1, b:1),
% 1.76/2.12 alpha13 [290, 2] (w:1, o:336, a:1, s:1, b:1),
% 1.76/2.12 alpha14 [291, 2] (w:1, o:337, a:1, s:1, b:1),
% 1.76/2.12 alpha15 [292, 2] (w:1, o:338, a:1, s:1, b:1),
% 1.76/2.12 alpha16 [293, 3] (w:1, o:352, a:1, s:1, b:1),
% 1.76/2.12 alpha17 [294, 3] (w:1, o:353, a:1, s:1, b:1),
% 1.76/2.12 alpha18 [295, 2] (w:1, o:339, a:1, s:1, b:1),
% 1.76/2.12 alpha19 [296, 4] (w:1, o:393, a:1, s:1, b:1),
% 1.76/2.12 alpha20 [297, 4] (w:1, o:394, a:1, s:1, b:1),
% 1.76/2.12 alpha21 [298, 2] (w:1, o:326, a:1, s:1, b:1),
% 1.76/2.12 alpha22 [299, 2] (w:1, o:327, a:1, s:1, b:1),
% 1.76/2.12 alpha23 [300, 3] (w:1, o:356, a:1, s:1, b:1),
% 1.76/2.12 alpha24 [301, 3] (w:1, o:357, a:1, s:1, b:1),
% 1.76/2.12 alpha25 [302, 2] (w:1, o:328, a:1, s:1, b:1),
% 1.76/2.12 alpha26 [303, 3] (w:1, o:358, a:1, s:1, b:1),
% 1.76/2.12 alpha27 [304, 3] (w:1, o:359, a:1, s:1, b:1),
% 1.76/2.12 alpha28 [305, 3] (w:1, o:360, a:1, s:1, b:1),
% 1.76/2.12 alpha29 [306, 2] (w:1, o:329, a:1, s:1, b:1),
% 1.76/2.12 alpha30 [307, 2] (w:1, o:340, a:1, s:1, b:1),
% 1.76/2.12 alpha31 [308, 3] (w:1, o:361, a:1, s:1, b:1),
% 1.76/2.12 alpha32 [309, 3] (w:1, o:362, a:1, s:1, b:1),
% 1.76/2.12 alpha33 [310, 4] (w:1, o:387, a:1, s:1, b:1),
% 1.76/2.12 alpha34 [311, 3] (w:1, o:363, a:1, s:1, b:1),
% 1.76/2.12 alpha35 [312, 3] (w:1, o:364, a:1, s:1, b:1),
% 1.76/2.12 alpha36 [313, 4] (w:1, o:388, a:1, s:1, b:1),
% 1.76/2.12 alpha37 [314, 3] (w:1, o:365, a:1, s:1, b:1),
% 1.76/2.12 alpha38 [315, 3] (w:1, o:366, a:1, s:1, b:1),
% 1.76/2.12 alpha39 [316, 3] (w:1, o:367, a:1, s:1, b:1),
% 1.76/2.12 alpha40 [317, 4] (w:1, o:390, a:1, s:1, b:1),
% 1.76/2.12 alpha41 [318, 4] (w:1, o:391, a:1, s:1, b:1),
% 1.76/2.12 alpha42 [319, 3] (w:1, o:368, a:1, s:1, b:1),
% 1.76/2.12 alpha43 [320, 2] (w:1, o:341, a:1, s:1, b:1),
% 1.76/2.12 alpha44 [321, 2] (w:1, o:342, a:1, s:1, b:1),
% 1.76/2.12 alpha45 [322, 3] (w:1, o:369, a:1, s:1, b:1),
% 1.76/2.12 skol1 [323, 2] (w:1, o:275, a:1, s:1, b:1),
% 1.76/2.12 skol2 [324, 3] (w:1, o:370, a:1, s:1, b:1),
% 1.76/2.12 skol3 [325, 2] (w:1, o:278, a:1, s:1, b:1),
% 1.76/2.12 skol4 [326, 1] (w:1, o:192, a:1, s:1, b:1),
% 1.76/2.12 skol5 [327, 2] (w:1, o:287, a:1, s:1, b:1),
% 1.76/2.12 skol6 [328, 2] (w:1, o:289, a:1, s:1, b:1),
% 1.76/2.12 skol7 [329, 2] (w:1, o:296, a:1, s:1, b:1),
% 1.76/2.12 skol8 [330, 1] (w:1, o:193, a:1, s:1, b:1),
% 1.76/2.12 skol9 [331, 2] (w:1, o:297, a:1, s:1, b:1),
% 1.76/2.12 skol10 [332, 2] (w:1, o:298, a:1, s:1, b:1),
% 1.76/2.12 skol11 [333, 2] (w:1, o:299, a:1, s:1, b:1),
% 1.76/2.12 skol12 [334, 2] (w:1, o:300, a:1, s:1, b:1),
% 1.76/2.12 skol13 [335, 2] (w:1, o:301, a:1, s:1, b:1),
% 1.76/2.12 skol14 [336, 2] (w:1, o:302, a:1, s:1, b:1),
% 1.76/2.12 skol15 [337, 1] (w:1, o:194, a:1, s:1, b:1),
% 1.76/2.12 skol16 [338, 0] (w:1, o:26, a:1, s:1, b:1),
% 1.76/2.12 skol17 [339, 2] (w:1, o:303, a:1, s:1, b:1),
% 1.76/2.12 skol18 [340, 2] (w:1, o:304, a:1, s:1, b:1),
% 20.65/21.07 skol19 [341, 1] (w:1, o:195, a:1, s:1, b:1),
% 20.65/21.07 skol20 [342, 2] (w:1, o:276, a:1, s:1, b:1),
% 20.65/21.07 skol21 [343, 0] (w:1, o:27, a:1, s:1, b:1),
% 20.65/21.07 skol22 [344, 0] (w:1, o:28, a:1, s:1, b:1),
% 20.65/21.07 skol23 [345, 0] (w:1, o:29, a:1, s:1, b:1),
% 20.65/21.07 skol24 [346, 0] (w:1, o:30, a:1, s:1, b:1),
% 20.65/21.07 skol25 [347, 0] (w:1, o:31, a:1, s:1, b:1),
% 20.65/21.07 skol26 [348, 0] (w:1, o:32, a:1, s:1, b:1),
% 20.65/21.07 skol27 [349, 2] (w:1, o:277, a:1, s:1, b:1),
% 20.65/21.07 skol28 [350, 3] (w:1, o:371, a:1, s:1, b:1),
% 20.65/21.07 skol29 [351, 4] (w:1, o:395, a:1, s:1, b:1),
% 20.65/21.07 skol30 [352, 3] (w:1, o:372, a:1, s:1, b:1),
% 20.65/21.07 skol31 [353, 3] (w:1, o:373, a:1, s:1, b:1),
% 20.65/21.07 skol32 [354, 2] (w:1, o:305, a:1, s:1, b:1),
% 20.65/21.07 skol33 [355, 0] (w:1, o:33, a:1, s:1, b:1),
% 20.65/21.07 skol34 [356, 2] (w:1, o:306, a:1, s:1, b:1),
% 20.65/21.07 skol35 [357, 1] (w:1, o:190, a:1, s:1, b:1),
% 20.65/21.07 skol36 [358, 2] (w:1, o:307, a:1, s:1, b:1),
% 20.65/21.07 skol37 [359, 1] (w:1, o:191, a:1, s:1, b:1),
% 20.65/21.07 skol38 [360, 2] (w:1, o:308, a:1, s:1, b:1),
% 20.65/21.07 skol39 [361, 2] (w:1, o:309, a:1, s:1, b:1),
% 20.65/21.07 skol40 [362, 0] (w:1, o:34, a:1, s:1, b:1),
% 20.65/21.07 skol41 [363, 1] (w:1, o:196, a:1, s:1, b:1),
% 20.65/21.07 skol42 [364, 2] (w:1, o:279, a:1, s:1, b:1),
% 20.65/21.07 skol43 [365, 2] (w:1, o:280, a:1, s:1, b:1),
% 20.65/21.07 skol44 [366, 2] (w:1, o:281, a:1, s:1, b:1),
% 20.65/21.07 skol45 [367, 2] (w:1, o:282, a:1, s:1, b:1),
% 20.65/21.07 skol46 [368, 2] (w:1, o:283, a:1, s:1, b:1),
% 20.65/21.07 skol47 [369, 2] (w:1, o:284, a:1, s:1, b:1),
% 20.65/21.07 skol48 [370, 2] (w:1, o:285, a:1, s:1, b:1),
% 20.65/21.07 skol49 [371, 2] (w:1, o:286, a:1, s:1, b:1),
% 20.65/21.07 skol50 [372, 2] (w:1, o:288, a:1, s:1, b:1),
% 20.65/21.07 skol51 [373, 3] (w:1, o:374, a:1, s:1, b:1),
% 20.65/21.07 skol52 [374, 3] (w:1, o:375, a:1, s:1, b:1),
% 20.65/21.07 skol53 [375, 1] (w:1, o:197, a:1, s:1, b:1),
% 20.65/21.07 skol54 [376, 4] (w:1, o:396, a:1, s:1, b:1),
% 20.65/21.07 skol55 [377, 3] (w:1, o:376, a:1, s:1, b:1),
% 20.65/21.07 skol56 [378, 3] (w:1, o:377, a:1, s:1, b:1),
% 20.65/21.07 skol57 [379, 3] (w:1, o:378, a:1, s:1, b:1),
% 20.65/21.07 skol58 [380, 3] (w:1, o:379, a:1, s:1, b:1),
% 20.65/21.07 skol59 [381, 3] (w:1, o:380, a:1, s:1, b:1),
% 20.65/21.07 skol60 [382, 4] (w:1, o:397, a:1, s:1, b:1),
% 20.65/21.07 skol61 [383, 3] (w:1, o:381, a:1, s:1, b:1),
% 20.65/21.07 skol62 [384, 2] (w:1, o:290, a:1, s:1, b:1),
% 20.65/21.07 skol63 [385, 2] (w:1, o:291, a:1, s:1, b:1),
% 20.65/21.07 skol64 [386, 2] (w:1, o:292, a:1, s:1, b:1),
% 20.65/21.07 skol65 [387, 2] (w:1, o:293, a:1, s:1, b:1),
% 20.65/21.07 skol66 [388, 2] (w:1, o:294, a:1, s:1, b:1),
% 20.65/21.07 skol67 [389, 2] (w:1, o:295, a:1, s:1, b:1),
% 20.65/21.07 skol68 [390, 1] (w:1, o:198, a:1, s:1, b:1),
% 20.65/21.07 skol69 [391, 3] (w:1, o:382, a:1, s:1, b:1),
% 20.65/21.07 skol70 [392, 2] (w:1, o:310, a:1, s:1, b:1),
% 20.65/21.07 skol71 [393, 2] (w:1, o:311, a:1, s:1, b:1),
% 20.65/21.07 skol72 [394, 2] (w:1, o:312, a:1, s:1, b:1),
% 20.65/21.07 skol73 [395, 3] (w:1, o:383, a:1, s:1, b:1),
% 20.65/21.07 skol74 [396, 3] (w:1, o:384, a:1, s:1, b:1),
% 20.65/21.07 skol75 [397, 3] (w:1, o:385, a:1, s:1, b:1),
% 20.65/21.07 skol76 [398, 3] (w:1, o:386, a:1, s:1, b:1),
% 20.65/21.07 skol77 [399, 2] (w:1, o:313, a:1, s:1, b:1),
% 20.65/21.07 skol78 [400, 2] (w:1, o:314, a:1, s:1, b:1).
% 20.65/21.07
% 20.65/21.07
% 20.65/21.07 Starting Search:
% 20.65/21.07
% 20.65/21.07 *** allocated 113905 integers for clauses
% 20.65/21.07 *** allocated 170857 integers for clauses
% 20.65/21.07 Resimplifying inuse:
% 20.65/21.07 Done
% 20.65/21.07
% 20.65/21.07
% 20.65/21.07 Intermediate Status:
% 20.65/21.07 Generated: 3038
% 20.65/21.07 Kept: 2001
% 20.65/21.07 Inuse: 48
% 20.65/21.07 Deleted: 0
% 20.65/21.07 Deletedinuse: 0
% 20.65/21.07
% 20.65/21.07 *** allocated 256285 integers for clauses
% 20.65/21.07 *** allocated 170857 integers for termspace/termends
% 20.65/21.07 Resimplifying inuse:
% 20.65/21.07 Done
% 20.65/21.07
% 20.65/21.07 Resimplifying inuse:
% 20.65/21.07 Done
% 20.65/21.07
% 20.65/21.07 *** allocated 384427 integers for clauses
% 20.65/21.07
% 20.65/21.07 Intermediate Status:
% 20.65/21.07 Generated: 8031
% 20.65/21.07 Kept: 4295
% 20.65/21.07 Inuse: 169
% 20.65/21.07 Deleted: 3
% 20.65/21.07 Deletedinuse: 1
% 20.65/21.07
% 20.65/21.07 *** allocated 256285 integers for termspace/termends
% 20.65/21.07 Resimplifying inuse:
% 20.65/21.07 Done
% 20.65/21.07
% 20.65/21.07 Resimplifying inuse:
% 20.65/21.07 Done
% 20.65/21.07
% 20.65/21.07
% 20.65/21.07 Intermediate Status:
% 20.65/21.07 Generated: 13763
% 20.65/21.07 Kept: 6446
% 20.65/21.07 Inuse: 233
% 20.65/21.07 Deleted: 4
% 20.65/21.07 Deletedinuse: 1
% 20.65/21.07
% 20.65/21.07 *** allocated 576640 integers for clauses
% 20.65/21.07 Resimplifying inuse:
% 20.65/21.07 Done
% 20.65/21.07
% 20.65/21.07 *** allocated 384427 integers for termspace/termends
% 20.65/21.07 Resimplifying inuse:
% 20.65/21.07 Done
% 20.65/21.07
% 20.65/21.07
% 20.65/21.07 Intermediate Status:
% 20.65/21.07 Generated: 22513
% 20.65/21.07 Kept: 8845
% 20.65/21.07 Inuse: 273
% 71.91/72.31 Deleted: 5
% 71.91/72.31 Deletedinuse: 2
% 71.91/72.31
% 71.91/72.31 Resimplifying inuse:
% 71.91/72.31 Done
% 71.91/72.31
% 71.91/72.31 *** allocated 864960 integers for clauses
% 71.91/72.31
% 71.91/72.31 Intermediate Status:
% 71.91/72.31 Generated: 32335
% 71.91/72.31 Kept: 11089
% 71.91/72.31 Inuse: 288
% 71.91/72.31 Deleted: 5
% 71.91/72.31 Deletedinuse: 2
% 71.91/72.31
% 71.91/72.31 Resimplifying inuse:
% 71.91/72.31 Done
% 71.91/72.31
% 71.91/72.31 Resimplifying inuse:
% 71.91/72.31 Done
% 71.91/72.31
% 71.91/72.31
% 71.91/72.31 Intermediate Status:
% 71.91/72.31 Generated: 37771
% 71.91/72.31 Kept: 13162
% 71.91/72.31 Inuse: 348
% 71.91/72.31 Deleted: 5
% 71.91/72.31 Deletedinuse: 2
% 71.91/72.31
% 71.91/72.31 Resimplifying inuse:
% 71.91/72.31 Done
% 71.91/72.31
% 71.91/72.31 *** allocated 576640 integers for termspace/termends
% 71.91/72.31 Resimplifying inuse:
% 71.91/72.31 Done
% 71.91/72.31
% 71.91/72.31
% 71.91/72.31 Intermediate Status:
% 71.91/72.31 Generated: 43310
% 71.91/72.31 Kept: 15172
% 71.91/72.31 Inuse: 400
% 71.91/72.31 Deleted: 7
% 71.91/72.31 Deletedinuse: 2
% 71.91/72.31
% 71.91/72.31 Resimplifying inuse:
% 71.91/72.31 Done
% 71.91/72.31
% 71.91/72.31 Resimplifying inuse:
% 71.91/72.31 Done
% 71.91/72.31
% 71.91/72.31
% 71.91/72.31 Intermediate Status:
% 71.91/72.31 Generated: 50167
% 71.91/72.31 Kept: 17264
% 71.91/72.31 Inuse: 426
% 71.91/72.31 Deleted: 7
% 71.91/72.31 Deletedinuse: 2
% 71.91/72.31
% 71.91/72.31 Resimplifying inuse:
% 71.91/72.31 Done
% 71.91/72.31
% 71.91/72.31 *** allocated 1297440 integers for clauses
% 71.91/72.31 Resimplifying inuse:
% 71.91/72.31 Done
% 71.91/72.31
% 71.91/72.31
% 71.91/72.31 Intermediate Status:
% 71.91/72.31 Generated: 58403
% 71.91/72.31 Kept: 19270
% 71.91/72.31 Inuse: 447
% 71.91/72.31 Deleted: 7
% 71.91/72.31 Deletedinuse: 2
% 71.91/72.31
% 71.91/72.31 *** allocated 864960 integers for termspace/termends
% 71.91/72.31 Resimplifying inuse:
% 71.91/72.31 Done
% 71.91/72.31
% 71.91/72.31 Resimplifying clauses:
% 71.91/72.31 Done
% 71.91/72.31
% 71.91/72.31
% 71.91/72.31 Intermediate Status:
% 71.91/72.31 Generated: 81336
% 71.91/72.31 Kept: 22707
% 71.91/72.31 Inuse: 466
% 71.91/72.31 Deleted: 274
% 71.91/72.31 Deletedinuse: 2
% 71.91/72.31
% 71.91/72.31 Resimplifying inuse:
% 71.91/72.31 Done
% 71.91/72.31
% 71.91/72.31 Resimplifying inuse:
% 71.91/72.31 Done
% 71.91/72.31
% 71.91/72.31
% 71.91/72.31 Intermediate Status:
% 71.91/72.31 Generated: 97067
% 71.91/72.31 Kept: 26183
% 71.91/72.31 Inuse: 501
% 71.91/72.31 Deleted: 274
% 71.91/72.31 Deletedinuse: 2
% 71.91/72.31
% 71.91/72.31 Resimplifying inuse:
% 71.91/72.31 Done
% 71.91/72.31
% 71.91/72.31 Resimplifying inuse:
% 71.91/72.31 Done
% 71.91/72.31
% 71.91/72.31
% 71.91/72.31 Intermediate Status:
% 71.91/72.31 Generated: 107855
% 71.91/72.31 Kept: 28193
% 71.91/72.31 Inuse: 515
% 71.91/72.31 Deleted: 274
% 71.91/72.31 Deletedinuse: 2
% 71.91/72.31
% 71.91/72.31 *** allocated 1946160 integers for clauses
% 71.91/72.31 *** allocated 1297440 integers for termspace/termends
% 71.91/72.31 Resimplifying inuse:
% 71.91/72.31 Done
% 71.91/72.31
% 71.91/72.31
% 71.91/72.31 Intermediate Status:
% 71.91/72.31 Generated: 121825
% 71.91/72.31 Kept: 30415
% 71.91/72.31 Inuse: 541
% 71.91/72.31 Deleted: 274
% 71.91/72.31 Deletedinuse: 2
% 71.91/72.31
% 71.91/72.31 Resimplifying inuse:
% 71.91/72.31 Done
% 71.91/72.31
% 71.91/72.31 Resimplifying inuse:
% 71.91/72.31 Done
% 71.91/72.31
% 71.91/72.31
% 71.91/72.31 Intermediate Status:
% 71.91/72.31 Generated: 128673
% 71.91/72.31 Kept: 32516
% 71.91/72.31 Inuse: 571
% 71.91/72.31 Deleted: 274
% 71.91/72.31 Deletedinuse: 2
% 71.91/72.31
% 71.91/72.31 Resimplifying inuse:
% 71.91/72.31 Done
% 71.91/72.31
% 71.91/72.31 Resimplifying inuse:
% 71.91/72.31 Done
% 71.91/72.31
% 71.91/72.31
% 71.91/72.31 Intermediate Status:
% 71.91/72.31 Generated: 135071
% 71.91/72.31 Kept: 34833
% 71.91/72.31 Inuse: 606
% 71.91/72.31 Deleted: 275
% 71.91/72.31 Deletedinuse: 3
% 71.91/72.31
% 71.91/72.31 Resimplifying inuse:
% 71.91/72.31 Done
% 71.91/72.31
% 71.91/72.31 Resimplifying inuse:
% 71.91/72.31 Done
% 71.91/72.31
% 71.91/72.31
% 71.91/72.31 Intermediate Status:
% 71.91/72.31 Generated: 140828
% 71.91/72.31 Kept: 37140
% 71.91/72.31 Inuse: 636
% 71.91/72.31 Deleted: 277
% 71.91/72.31 Deletedinuse: 5
% 71.91/72.31
% 71.91/72.31 Resimplifying inuse:
% 71.91/72.31 Done
% 71.91/72.31
% 71.91/72.31 Resimplifying inuse:
% 71.91/72.31 Done
% 71.91/72.31
% 71.91/72.31
% 71.91/72.31 Intermediate Status:
% 71.91/72.31 Generated: 151559
% 71.91/72.31 Kept: 40336
% 71.91/72.31 Inuse: 671
% 71.91/72.31 Deleted: 277
% 71.91/72.31 Deletedinuse: 5
% 71.91/72.31
% 71.91/72.31 Resimplifying inuse:
% 71.91/72.31 Done
% 71.91/72.31
% 71.91/72.31 *** allocated 1946160 integers for termspace/termends
% 71.91/72.31 Resimplifying clauses:
% 71.91/72.31 Done
% 71.91/72.31
% 71.91/72.31 Resimplifying inuse:
% 71.91/72.31 Done
% 71.91/72.31
% 71.91/72.31 *** allocated 2919240 integers for clauses
% 71.91/72.31
% 71.91/72.31 Intermediate Status:
% 71.91/72.31 Generated: 158135
% 71.91/72.31 Kept: 42396
% 71.91/72.31 Inuse: 711
% 71.91/72.31 Deleted: 458
% 71.91/72.31 Deletedinuse: 5
% 71.91/72.31
% 71.91/72.31 Resimplifying inuse:
% 71.91/72.31 Done
% 71.91/72.31
% 71.91/72.31 Resimplifying inuse:
% 71.91/72.31 Done
% 71.91/72.31
% 71.91/72.31
% 71.91/72.31 Intermediate Status:
% 71.91/72.31 Generated: 164420
% 71.91/72.31 Kept: 44415
% 71.91/72.31 Inuse: 745
% 71.91/72.31 Deleted: 458
% 71.91/72.31 Deletedinuse: 5
% 71.91/72.31
% 71.91/72.31 Resimplifying inuse:
% 71.91/72.31 Done
% 71.91/72.31
% 71.91/72.31 Resimplifying inuse:
% 71.91/72.31 Done
% 71.91/72.31
% 71.91/72.31
% 71.91/72.31 Intermediate Status:
% 71.91/72.31 Generated: 172808
% 71.91/72.31 Kept: 46431
% 71.91/72.31 Inuse: 786
% 71.91/72.31 Deleted: 458
% 71.91/72.31 Deletedinuse: 5
% 71.91/72.31
% 71.91/72.31 Resimplifying inuse:
% 71.91/72.31 Done
% 71.91/72.31
% 71.91/72.31 Resimplifying inuse:
% 71.91/72.31 Done
% 71.91/72.31
% 71.91/72.31
% 71.91/72.31 Intermediate Status:
% 71.91/72.31 Generated: 181771
% 71.91/72.31 Kept: 48560
% 71.91/72.31 Inuse: 821
% 71.91/72.31 Deleted: 459
% 71.91/72.31 Deletedinuse: 6
% 71.91/72.31
% 71.91/72.31 Resimplifying inuse:
% 71.91/72.31 Done
% 71.91/72.31
% 71.91/72.31 Resimplifying inuse:
% 71.91/72.31 Done
% 71.91/72.31
% 71.91/72.31
% 71.91/72.31 Intermediate Status:
% 71.91/72.31 Generated: 190343
% 71.91/72.31 Kept: 50828
% 71.91/72.31 Inuse: 856
% 71.91/72.31 Deleted: 459
% 71.91/72.31 Deletedinuse: 6
% 71.91/72.31
% 71.91/72.31 Resimplifying inuse:
% 71.91/72.31 Done
% 71.91/72.31
% 71.91/72.31
% 71.91/72.31 Intermediate Status:
% 71.91/72.31 Generated: 197267
% 71.91/72.31 Kept: 52862
% 71.91/72.31 Inuse: 876
% 71.91/72.31 Deleted: 459
% 71.91/72.31 Deletedinuse: 6
% 71.91/72.31
% 71.91/72.31 Resimplifying inuse:
% 71.91/72.31 Done
% 71.91/72.31
% 71.91/72.31 Resimplifying inuse:
% 71.91/72.31 Done
% 71.91/72.31
% 71.91/72.31
% 71.91/72.31 Intermediate Status:
% 71.91/72.31 Generated: 208395
% 71.91/72.31 Kept: 54862
% 71.91/72.31 Inuse: 892
% 71.91/72.31 Deleted: 459
% 71.91/72.31 Deletedinuse: 6
% 71.91/72.31
% 71.91/72.31 Resimplifying inuse:
% 71.91/72.31 Done
% 71.91/72.31
% 71.91/72.31
% 71.91/72.31 Intermediate Status:
% 71.91/72.31 Generated: 220391
% 71.91/72.31 Kept: 56881
% 71.91/72.31 Inuse: 914
% 71.91/72.31 Deleted: 459
% 71.91/72.31 Deletedinuse: 6
% 71.91/72.31
% 71.91/72.31 Resimplifying inuse:
% 71.91/72.31 Done
% 71.91/72.31
% 71.91/72.31 Resimplifying inuse:
% 71.91/72.31 Done
% 71.91/72.31
% 71.91/72.31
% 71.91/72.31 Intermediate Status:
% 71.91/72.31 Generated: 236796
% 71.91/72.31 Kept: 60573
% 71.91/72.31 Inuse: 953
% 71.91/72.31 Deleted: 459
% 71.91/72.31 Deletedinuse: 6
% 71.91/72.31
% 71.91/72.31 Resimplifying inuse:
% 232.96/233.43 Done
% 232.96/233.43
% 232.96/233.43 Resimplifying inuse:
% 232.96/233.43 Done
% 232.96/233.43
% 232.96/233.43 Resimplifying clauses:
% 232.96/233.43 Done
% 232.96/233.43
% 232.96/233.43
% 232.96/233.43 Intermediate Status:
% 232.96/233.43 Generated: 248733
% 232.96/233.43 Kept: 62619
% 232.96/233.43 Inuse: 971
% 232.96/233.43 Deleted: 1400
% 232.96/233.43 Deletedinuse: 8
% 232.96/233.43
% 232.96/233.43 *** allocated 4378860 integers for clauses
% 232.96/233.43 *** allocated 2919240 integers for termspace/termends
% 232.96/233.43
% 232.96/233.43 Intermediate Status:
% 232.96/233.43 Generated: 257721
% 232.96/233.43 Kept: 68108
% 232.96/233.43 Inuse: 981
% 232.96/233.43 Deleted: 1400
% 232.96/233.43 Deletedinuse: 8
% 232.96/233.43
% 232.96/233.43 Resimplifying inuse:
% 232.96/233.43 Done
% 232.96/233.43
% 232.96/233.43 Resimplifying inuse:
% 232.96/233.43 Done
% 232.96/233.43
% 232.96/233.43
% 232.96/233.43 Intermediate Status:
% 232.96/233.43 Generated: 264129
% 232.96/233.43 Kept: 70114
% 232.96/233.43 Inuse: 1026
% 232.96/233.43 Deleted: 1400
% 232.96/233.43 Deletedinuse: 8
% 232.96/233.43
% 232.96/233.43 Resimplifying inuse:
% 232.96/233.43 Done
% 232.96/233.43
% 232.96/233.43
% 232.96/233.43 Intermediate Status:
% 232.96/233.43 Generated: 275197
% 232.96/233.43 Kept: 73279
% 232.96/233.43 Inuse: 1036
% 232.96/233.43 Deleted: 1400
% 232.96/233.43 Deletedinuse: 8
% 232.96/233.43
% 232.96/233.43 Resimplifying inuse:
% 232.96/233.43 Done
% 232.96/233.43
% 232.96/233.43
% 232.96/233.43 Intermediate Status:
% 232.96/233.43 Generated: 288190
% 232.96/233.43 Kept: 76963
% 232.96/233.43 Inuse: 1056
% 232.96/233.43 Deleted: 1400
% 232.96/233.43 Deletedinuse: 8
% 232.96/233.43
% 232.96/233.43 Resimplifying inuse:
% 232.96/233.43 Done
% 232.96/233.43
% 232.96/233.43 Resimplifying inuse:
% 232.96/233.43 Done
% 232.96/233.43
% 232.96/233.43
% 232.96/233.43 Intermediate Status:
% 232.96/233.43 Generated: 298649
% 232.96/233.43 Kept: 81398
% 232.96/233.43 Inuse: 1086
% 232.96/233.43 Deleted: 1400
% 232.96/233.43 Deletedinuse: 8
% 232.96/233.43
% 232.96/233.43 Resimplifying inuse:
% 232.96/233.43 Done
% 232.96/233.43
% 232.96/233.43
% 232.96/233.43 Intermediate Status:
% 232.96/233.43 Generated: 312008
% 232.96/233.43 Kept: 85425
% 232.96/233.43 Inuse: 1106
% 232.96/233.43 Deleted: 1400
% 232.96/233.43 Deletedinuse: 8
% 232.96/233.43
% 232.96/233.43 Resimplifying inuse:
% 232.96/233.43 Done
% 232.96/233.43
% 232.96/233.43 Resimplifying clauses:
% 232.96/233.43 Done
% 232.96/233.43
% 232.96/233.43
% 232.96/233.43 Intermediate Status:
% 232.96/233.43 Generated: 324613
% 232.96/233.43 Kept: 89224
% 232.96/233.43 Inuse: 1121
% 232.96/233.43 Deleted: 1488
% 232.96/233.43 Deletedinuse: 8
% 232.96/233.43
% 232.96/233.43 Resimplifying inuse:
% 232.96/233.43 Done
% 232.96/233.43
% 232.96/233.43 Resimplifying inuse:
% 232.96/233.43 Done
% 232.96/233.43
% 232.96/233.43
% 232.96/233.43 Intermediate Status:
% 232.96/233.43 Generated: 330784
% 232.96/233.43 Kept: 91419
% 232.96/233.43 Inuse: 1151
% 232.96/233.43 Deleted: 1488
% 232.96/233.43 Deletedinuse: 8
% 232.96/233.43
% 232.96/233.43 Resimplifying inuse:
% 232.96/233.43 Done
% 232.96/233.43
% 232.96/233.43 Resimplifying inuse:
% 232.96/233.43 Done
% 232.96/233.43
% 232.96/233.43
% 232.96/233.43 Intermediate Status:
% 232.96/233.43 Generated: 337239
% 232.96/233.43 Kept: 93680
% 232.96/233.43 Inuse: 1191
% 232.96/233.43 Deleted: 1488
% 232.96/233.43 Deletedinuse: 8
% 232.96/233.43
% 232.96/233.43 Resimplifying inuse:
% 232.96/233.43 Done
% 232.96/233.43
% 232.96/233.43 Resimplifying inuse:
% 232.96/233.43 Done
% 232.96/233.43
% 232.96/233.43
% 232.96/233.43 Intermediate Status:
% 232.96/233.43 Generated: 342926
% 232.96/233.43 Kept: 95725
% 232.96/233.43 Inuse: 1226
% 232.96/233.43 Deleted: 1488
% 232.96/233.43 Deletedinuse: 8
% 232.96/233.43
% 232.96/233.43 Resimplifying inuse:
% 232.96/233.43 Done
% 232.96/233.43
% 232.96/233.43 Resimplifying inuse:
% 232.96/233.43 Done
% 232.96/233.43
% 232.96/233.43 *** allocated 4378860 integers for termspace/termends
% 232.96/233.43
% 232.96/233.43 Intermediate Status:
% 232.96/233.43 Generated: 349962
% 232.96/233.43 Kept: 98045
% 232.96/233.43 Inuse: 1251
% 232.96/233.43 Deleted: 1488
% 232.96/233.43 Deletedinuse: 8
% 232.96/233.43
% 232.96/233.43 Resimplifying inuse:
% 232.96/233.43 Done
% 232.96/233.43
% 232.96/233.43 Resimplifying inuse:
% 232.96/233.43 Done
% 232.96/233.43
% 232.96/233.43 *** allocated 6568290 integers for clauses
% 232.96/233.43
% 232.96/233.43 Intermediate Status:
% 232.96/233.43 Generated: 357119
% 232.96/233.43 Kept: 100465
% 232.96/233.43 Inuse: 1269
% 232.96/233.43 Deleted: 1490
% 232.96/233.43 Deletedinuse: 8
% 232.96/233.43
% 232.96/233.43 Resimplifying inuse:
% 232.96/233.43 Done
% 232.96/233.43
% 232.96/233.43 Resimplifying inuse:
% 232.96/233.43 Done
% 232.96/233.43
% 232.96/233.43
% 232.96/233.43 Intermediate Status:
% 232.96/233.43 Generated: 363658
% 232.96/233.43 Kept: 102605
% 232.96/233.43 Inuse: 1284
% 232.96/233.43 Deleted: 1490
% 232.96/233.43 Deletedinuse: 8
% 232.96/233.43
% 232.96/233.43 Resimplifying inuse:
% 232.96/233.43 Done
% 232.96/233.43
% 232.96/233.43
% 232.96/233.43 Intermediate Status:
% 232.96/233.43 Generated: 370862
% 232.96/233.43 Kept: 104932
% 232.96/233.43 Inuse: 1299
% 232.96/233.43 Deleted: 1490
% 232.96/233.43 Deletedinuse: 8
% 232.96/233.43
% 232.96/233.43 Resimplifying inuse:
% 232.96/233.43 Done
% 232.96/233.43
% 232.96/233.43 Resimplifying clauses:
% 232.96/233.43 Done
% 232.96/233.43
% 232.96/233.43 Resimplifying inuse:
% 232.96/233.43 Done
% 232.96/233.43
% 232.96/233.43
% 232.96/233.43 Intermediate Status:
% 232.96/233.43 Generated: 379652
% 232.96/233.43 Kept: 107191
% 232.96/233.43 Inuse: 1319
% 232.96/233.43 Deleted: 1726
% 232.96/233.43 Deletedinuse: 9
% 232.96/233.43
% 232.96/233.43 Resimplifying inuse:
% 232.96/233.43 Done
% 232.96/233.43
% 232.96/233.43 Resimplifying inuse:
% 232.96/233.43 Done
% 232.96/233.43
% 232.96/233.43
% 232.96/233.43 Intermediate Status:
% 232.96/233.43 Generated: 389335
% 232.96/233.43 Kept: 109563
% 232.96/233.43 Inuse: 1339
% 232.96/233.43 Deleted: 1727
% 232.96/233.43 Deletedinuse: 10
% 232.96/233.43
% 232.96/233.43 Resimplifying inuse:
% 232.96/233.43 Done
% 232.96/233.43
% 232.96/233.43 Resimplifying inuse:
% 232.96/233.43 Done
% 232.96/233.43
% 232.96/233.43
% 232.96/233.43 Intermediate Status:
% 232.96/233.43 Generated: 397843
% 232.96/233.43 Kept: 111711
% 232.96/233.43 Inuse: 1359
% 232.96/233.43 Deleted: 1727
% 232.96/233.43 Deletedinuse: 10
% 232.96/233.43
% 232.96/233.43 Resimplifying inuse:
% 232.96/233.43 Done
% 232.96/233.43
% 232.96/233.43 Resimplifying inuse:
% 232.96/233.43 Done
% 232.96/233.43
% 232.96/233.43
% 232.96/233.43 Intermediate Status:
% 232.96/233.43 Generated: 405224
% 232.96/233.43 Kept: 114173
% 232.96/233.43 Inuse: 1379
% 232.96/233.43 Deleted: 1727
% 232.96/233.43 Deletedinuse: 10
% 232.96/233.43
% 232.96/233.43 Resimplifying inuse:
% 232.96/233.43 Done
% 232.96/233.43
% 232.96/233.43 Resimplifying inuse:
% 232.96/233.43 Done
% 232.96/233.43
% 232.96/233.43
% 232.96/233.43 Intermediate Status:
% 232.96/233.43 Generated: 417886
% 232.96/233.43 Kept: 116977
% 232.96/233.43 Inuse: 1394
% 232.96/233.43 Deleted: 1727
% 232.96/233.43 Deletedinuse: 10
% 232.96/233.43
% 232.96/233.43 Resimplifying inuse:
% 232.96/233.43 Done
% 232.96/233.43
% 232.96/233.43 Resimplifying inuse:
% 232.96/233.43 Done
% 232.96/233.43
% 232.96/233.43
% 232.96/233.43 Intermediate Status:
% 232.96/233.43 Generated: 428211
% 232.96/233.43 Kept: 119155
% 232.96/233.43 Inuse: 1404
% 232.96/233.43 Deleted: 1727
% 232.96/233.43 Deletedinuse: 10
% 232.96/233.43
% 232.96/233.43 Resimplifying inuse:
% 232.96/233.43 Done
% 232.96/233.43
% 232.96/233.43 Resimplifying inuse:
% 232.96/233.43 Done
% 232.96/233.43
% 232.96/233.43
% 232.96/233.43 Intermediate Status:
% 232.96/233.43 Generated: 434872
% 232.96/233.43 Kept: 121408
% 232.96/233.43 Inuse: 1419
% 232.96/233.43 Deleted: 1727
% 232.96/233.43 Deletedinuse: 10
% 232.96/233.43
% 232.96/233.43 Resimplifying inuse:
% 232.96/233.43 Done
% 232.96/233.43
% 232.96/233.43
% 232.96/233.43 Intermediate Status:
% 232.96/233.43 Generated: 441221
% 232.96/233.43 Kept: 123556
% 232.96/233.43 Inuse: 1434
% 232.96/233.43 Deleted: 1727
% 232.96/233.43 Deletedinuse: 10
% 232.96/233.43
% 232.96/233.43 Resimplifying inuse:
% 232.96/233.43 Done
% 232.96/233.43
% 232.96/233.43
% 232.96/233.43 Intermediate Status:
% 232.96/233.43 Generated: 449051
% 232.96/233.43 Kept: Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------