TSTP Solution File: SWW220+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW220+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n024.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 23:21:20 EDT 2022
% Result : Timeout 300.04s 300.49s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SWW220+1 : TPTP v8.1.0. Released v5.2.0.
% 0.08/0.14 % Command : bliksem %s
% 0.14/0.36 % Computer : n024.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % DateTime : Sat Jun 4 07:18:50 EDT 2022
% 0.14/0.36 % CPUTime :
% 1.33/1.68 *** allocated 10000 integers for termspace/termends
% 1.33/1.68 *** allocated 10000 integers for clauses
% 1.33/1.68 *** allocated 10000 integers for justifications
% 1.33/1.68 *** allocated 15000 integers for termspace/termends
% 1.33/1.68 *** allocated 22500 integers for termspace/termends
% 1.33/1.68 *** allocated 33750 integers for termspace/termends
% 1.33/1.68 Bliksem 1.12
% 1.33/1.68
% 1.33/1.68
% 1.33/1.68 Automatic Strategy Selection
% 1.33/1.68
% 1.33/1.68 *** allocated 50625 integers for termspace/termends
% 1.33/1.68 *** allocated 75937 integers for termspace/termends
% 1.33/1.68 *** allocated 113905 integers for termspace/termends
% 1.33/1.68
% 1.33/1.68 Clauses:
% 1.33/1.68
% 1.33/1.68 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 1.33/1.68 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.33/1.68 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.33/1.68 c_RealVector_Onorm__class_Onorm( X, Y ) ), ! Y =
% 1.33/1.68 c_Groups_Ozero__class_Ozero( X ) }.
% 1.33/1.68 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 1.33/1.68 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless(
% 1.33/1.68 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.33/1.68 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 1.33/1.68 { c_SEQ_Osubseq( skol2 ) }.
% 1.33/1.68 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol78( X ) ), Y ) ),
% 1.33/1.68 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.68 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.33/1.68 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, v_g____( hAPP( skol2
% 1.33/1.68 , Y ) ), skol59 ) ), X ) }.
% 1.33/1.68 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.33/1.68 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.68 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 1.33/1.68 tc_RealDef_Oreal ) ) }.
% 1.33/1.68 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.33/1.68 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 1.33/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.33/1.68 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.33/1.68 c_RealVector_Onorm__class_Onorm( X, Y ) = c_Groups_Ozero__class_Ozero(
% 1.33/1.68 tc_RealDef_Oreal ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.33/1.68 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 1.33/1.68 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X, Y )
% 1.33/1.68 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.33/1.68 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.33/1.68 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.33/1.68 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 1.33/1.68 ( X ) ) }.
% 1.33/1.68 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.33/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.33/1.68 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.33/1.68 , Z, Y ) }.
% 1.33/1.68 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 1.33/1.68 , Y ) ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.33/1.68 { ! class_Groups_Oordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 1.33/1.68 , Y ) ), c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.33/1.68 { ! c_SEQ_Osubseq( X ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.68 tc_Nat_Onat, Y ), hAPP( X, Y ) ) ) }.
% 1.33/1.68 { ! class_Orderings_Opreorder( X ), hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, Y ), Y ) ) }.
% 1.33/1.68 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.33/1.68 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 1.33/1.68 Y ) ) = c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 1.33/1.68 ( X, Y, Z ) ) }.
% 1.33/1.68 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.33/1.68 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.33/1.68 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 1.33/1.68 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.33/1.68 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.33/1.68 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.33/1.68 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 1.33/1.68 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 1.33/1.68 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.33/1.68 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.33/1.68 ( X, Z, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, U ), T
% 1.33/1.68 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.33/1.68 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.33/1.68 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.33/1.68 ( X, Z, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), Y
% 1.33/1.68 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, U ), T ) ) }.
% 1.33/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), v_r ) ) }.
% 1.33/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.68 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_g____( X ) ) ),
% 1.33/1.68 v_r ) ) }.
% 1.33/1.68 { ! c_SEQ_Osubseq( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z
% 1.33/1.68 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( X, Y ), hAPP( X, Z
% 1.33/1.68 ) ) }.
% 1.33/1.68 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol3( X ), skol60( X ) ),
% 1.33/1.68 c_SEQ_Osubseq( X ) }.
% 1.33/1.68 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( X, skol3( X ) ), hAPP
% 1.33/1.68 ( X, skol60( X ) ) ), c_SEQ_Osubseq( X ) }.
% 1.33/1.68 { ! class_RealVector_Oreal__normed__vector( X ), hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.68 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.33/1.68 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.33/1.68 ( X, Y ) ) ), c_RealVector_Onorm__class_Onorm( X,
% 1.33/1.68 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) ) }.
% 1.33/1.68 { ! class_RealVector_Oreal__normed__vector( X ), hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.33/1.68 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) }.
% 1.33/1.68 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.68 c_RealVector_Onorm__class_Onorm( X, Y ) ), c_Groups_Ozero__class_Ozero(
% 1.33/1.68 tc_RealDef_Oreal ) ) ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.33/1.68 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 1.33/1.68 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.68 c_RealVector_Onorm__class_Onorm( X, Y ) ), c_Groups_Ozero__class_Ozero(
% 1.33/1.68 tc_RealDef_Oreal ) ) ) }.
% 1.33/1.68 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 1.33/1.68 c_Groups_Ozero__class_Ozero( X ) }.
% 1.33/1.68 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.33/1.68 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 1.33/1.68 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 1.33/1.68 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ), hBOOL(
% 1.33/1.68 hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ) ), hAPP( Y, U )
% 1.33/1.68 ) ) }.
% 1.33/1.68 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ), hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ) }.
% 1.33/1.68 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), Y = Z }.
% 1.33/1.68 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, Y ), T ) ), hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), T ) ) }.
% 1.33/1.68 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), Z = Y }.
% 1.33/1.68 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! Z = T, hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ) }.
% 1.33/1.68 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! Y = T, hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), T ) ) }.
% 1.33/1.68 { ! class_Orderings_Oorder( X ), ! Z = Y, ! hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ), hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ) }.
% 1.33/1.68 { ! class_Orderings_Oord( X ), ! Z = Y, ! hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, Y ), T ) ), hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), T ) ) }.
% 1.33/1.68 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), Y = Z }.
% 1.33/1.68 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! Y = Z, hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 1.33/1.68 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ), hBOOL(
% 1.33/1.68 hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ) ), hAPP( Y, U )
% 1.33/1.68 ) ) }.
% 1.33/1.68 { ! class_Orderings_Opreorder( X ), ! Z = Y, hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.33/1.68 { ! class_Orderings_Oorder( X ), ! Z = Y, hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.33/1.68 { ! class_Orderings_Oorder( X ), ! Z = Y, hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 1.33/1.68 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), Z = Y }.
% 1.33/1.68 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 1.33/1.68 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ), hBOOL(
% 1.33/1.68 hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ) ), hAPP( Y, U )
% 1.33/1.68 ) ) }.
% 1.33/1.68 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, skol4( X, Y, Z ) ) ), hAPP
% 1.33/1.68 ( Y, skol4( X, Y, Z ) ) ) ), hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ) }.
% 1.33/1.68 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.33/1.68 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.33/1.68 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.33/1.68 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.33/1.68 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.33/1.68 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.33/1.68 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.33/1.68 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.33/1.68 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 1.33/1.68 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.33/1.68 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.33/1.68 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.33/1.68 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 1.33/1.68 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.33/1.68 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 1.33/1.68 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 1.33/1.68 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 1.33/1.68 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.33/1.68 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.33/1.68 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.33/1.68 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.33/1.68 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.33/1.68 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.33/1.68 , ! Y = Z }.
% 1.33/1.68 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.33/1.68 , ! Z = Y }.
% 1.33/1.68 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.33/1.68 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.33/1.68 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.33/1.68 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.33/1.68 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.33/1.68 , ! Z = Y }.
% 1.33/1.68 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 1.33/1.68 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.33/1.68 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.33/1.68 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 1.33/1.68 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.33/1.68 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.33/1.68 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.33/1.68 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.33/1.68 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.33/1.68 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 1.33/1.68 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.33/1.68 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.33/1.68 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 1.33/1.68 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.33/1.68 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 1.33/1.68 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.33/1.68 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.33/1.68 Y ), ! Z = Y }.
% 1.33/1.68 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.33/1.68 Z ), ! Z = Y }.
% 1.33/1.68 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.33/1.68 Y ) }.
% 1.33/1.68 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.33/1.68 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 1.33/1.68 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.33/1.68 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 1.33/1.68 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), !
% 1.33/1.68 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 1.33/1.68 X, T, Y ) }.
% 1.33/1.68 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), !
% 1.33/1.68 c_Orderings_Oord__class_Oless( X, Y, T ), c_Orderings_Oord__class_Oless(
% 1.33/1.68 X, Z, T ) }.
% 1.33/1.68 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.33/1.68 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ),
% 1.33/1.68 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.33/1.68 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.33/1.68 Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ), T ) ),
% 1.33/1.68 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.33/1.68 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), Y = Z,
% 1.33/1.68 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.33/1.68 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), Z = Y,
% 1.33/1.68 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.33/1.68 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ),
% 1.33/1.68 c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.33/1.68 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ),
% 1.33/1.68 c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.33/1.68 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! Z = Y, !
% 1.33/1.68 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.33/1.68 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.33/1.68 Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.33/1.68 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), !
% 1.33/1.68 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.33/1.68 { ! class_Orderings_Oorder( X ), Z = Y, ! hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ),
% 1.33/1.68 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.33/1.68 { ! class_Orderings_Oorder( X ), Z = Y, ! hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ),
% 1.33/1.68 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.33/1.68 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.33/1.68 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), Z =
% 1.33/1.68 Y }.
% 1.33/1.68 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.33/1.68 ), ! Z = Y, hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), Y )
% 1.33/1.68 ) }.
% 1.33/1.68 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ),
% 1.33/1.68 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.33/1.68 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.33/1.68 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 1.33/1.68 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ),
% 1.33/1.68 c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.33/1.68 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.33/1.68 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.33/1.68 { ! class_Orderings_Oorder( X ), ! Z = Y, hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.33/1.68 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.33/1.68 Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.33/1.68 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.33/1.68 Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 1.33/1.68 { ! class_Orderings_Opreorder( X ), ! hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ),
% 1.33/1.68 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.33/1.68 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.33/1.68 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.33/1.68 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.33/1.68 , ! Z = Y }.
% 1.33/1.68 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), Z = Y,
% 1.33/1.68 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.33/1.68 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ),
% 1.33/1.68 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.33/1.68 { ! class_Orderings_Olinorder( X ), hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ),
% 1.33/1.68 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.33/1.68 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.33/1.68 Z ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.33/1.68 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.33/1.68 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ) }.
% 1.33/1.68 { ! class_Orderings_Olinorder( X ), ! hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, Y ), Z ) ), !
% 1.33/1.68 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.33/1.68 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.33/1.68 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.33/1.68 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 1.33/1.68 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.33/1.68 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 1.33/1.68 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.33/1.68 ) }.
% 1.33/1.68 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.33/1.68 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.33/1.68 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 1.33/1.68 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.33/1.68 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 1.33/1.68 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.33/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.33/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ) }.
% 1.33/1.68 { ! class_Orderings_Oorder( X ), ! c_SEQ_Odecseq( X, Y ), ! hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), T ) ), hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ) ), hAPP( Y, Z ) ) ) }
% 1.33/1.68 .
% 1.33/1.68 { ! class_Orderings_Oorder( X ), hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol5( X, Y ) ), skol61(
% 1.33/1.68 X, Y ) ) ), c_SEQ_Odecseq( X, Y ) }.
% 1.33/1.68 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, skol61( X, Y ) ) ), hAPP(
% 1.33/1.68 Y, skol5( X, Y ) ) ) ), c_SEQ_Odecseq( X, Y ) }.
% 1.33/1.68 { ! class_Orderings_Oorder( X ), ! c_SEQ_Oincseq( X, Y ), ! hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), T ) ), hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, Z ) ), hAPP( Y, T ) ) ) }
% 1.33/1.68 .
% 1.33/1.68 { ! class_Orderings_Oorder( X ), hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol6( X, Y ) ), skol62(
% 1.33/1.68 X, Y ) ) ), c_SEQ_Oincseq( X, Y ) }.
% 1.33/1.68 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, skol6( X, Y ) ) ), hAPP( Y
% 1.33/1.68 , skol62( X, Y ) ) ) ), c_SEQ_Oincseq( X, Y ) }.
% 1.33/1.68 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.33/1.68 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol7( Z, T ) ) }.
% 1.33/1.68 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.33/1.68 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.68 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ) ), skol7( X, Y ) ) ) }
% 1.33/1.68 .
% 1.33/1.68 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.33/1.68 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.68 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), ! hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.68 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol63( X, Y, Z ) ) ) ), Z )
% 1.33/1.68 ), c_SEQ_OBseq( X, Y ) }.
% 1.33/1.68 { ! class_Orderings_Oorder( X ), ! c_SEQ_Omonoseq( X, Y ), alpha1( X, Y ),
% 1.33/1.68 alpha22( X, Y ) }.
% 1.33/1.68 { ! class_Orderings_Oorder( X ), ! alpha1( X, Y ), c_SEQ_Omonoseq( X, Y ) }
% 1.33/1.68 .
% 1.33/1.68 { ! class_Orderings_Oorder( X ), ! alpha22( X, Y ), c_SEQ_Omonoseq( X, Y )
% 1.33/1.68 }.
% 1.33/1.68 { ! alpha22( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.68 tc_Nat_Onat, Z ), T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.68 X, hAPP( Y, T ) ), hAPP( Y, Z ) ) ) }.
% 1.33/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol8( X, Y
% 1.33/1.68 ) ), skol64( X, Y ) ) ), alpha22( X, Y ) }.
% 1.33/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, skol64( X,
% 1.33/1.68 Y ) ) ), hAPP( Y, skol8( X, Y ) ) ) ), alpha22( X, Y ) }.
% 1.33/1.68 { ! alpha1( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.68 tc_Nat_Onat, Z ), T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.68 X, hAPP( Y, Z ) ), hAPP( Y, T ) ) ) }.
% 1.33/1.68 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol9( X, Y
% 1.33/1.68 ) ), skol65( X, Y ) ) ), alpha1( X, Y ) }.
% 1.33/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, skol9( X, Y
% 1.33/1.68 ) ) ), hAPP( Y, skol65( X, Y ) ) ) ), alpha1( X, Y ) }.
% 1.33/1.68 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.33/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 1.33/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.68 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.33/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.33/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.68 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.33/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.33/1.68 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ),
% 1.33/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.33/1.68 ( tc_Nat_Onat, Y, Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z )
% 1.33/1.68 ) }.
% 1.33/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.68 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 1.33/1.68 ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.33/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 1.33/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 1.33/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 1.33/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.68 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 1.33/1.68 ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 1.33/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.33/1.68 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.33/1.68 ) }.
% 1.33/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.68 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 1.33/1.68 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.33/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 1.33/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) ), hBOOL( hAPP(
% 1.33/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Z ) ) }.
% 1.33/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.68 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 1.33/1.68 ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Z
% 1.33/1.68 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.33/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 1.33/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) ) }.
% 1.33/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.68 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 1.33/1.68 ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.33/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 1.33/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) =
% 1.33/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 1.33/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.68 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 1.33/1.68 ), ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.33/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 1.33/1.68 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.68 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 1.33/1.68 ), ! X = Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.33/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 1.33/1.68 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.33/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.33/1.68 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.33/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.33/1.68 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 1.33/1.68 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.33/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.33/1.68 tc_Nat_Onat ), X ) }.
% 1.33/1.68 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.33/1.68 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 1.33/1.68 .
% 1.33/1.68 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.33/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.33/1.68 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.33/1.68 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 1.33/1.68 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.33/1.68 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.33/1.68 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.33/1.68 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 1.33/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.33/1.68 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 1.33/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.33/1.68 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 1.33/1.68 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.33/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.33/1.68 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 1.33/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 1.33/1.68 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 1.33/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.33/1.68 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 1.33/1.68 X ), Z, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_fun( T, X
% 1.33/1.69 ), Z ), Y ) ) }.
% 1.33/1.69 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 1.33/1.69 X ), Z, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_fun( T
% 1.33/1.69 , X ), Y ), Z ) ) }.
% 1.33/1.69 { ! class_Orderings_Oord( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z ), Y ) ), hBOOL(
% 1.33/1.69 hAPP( c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y ), Z ) ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 1.33/1.69 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.33/1.69 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.33/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 1.33/1.69 { ! class_Orderings_Oorder( X ), ! c_SEQ_Odecseq( X, Y ), c_SEQ_Omonoseq( X
% 1.33/1.69 , Y ) }.
% 1.33/1.69 { ! class_Orderings_Oorder( X ), ! c_SEQ_Oincseq( X, Y ), c_SEQ_Omonoseq( X
% 1.33/1.69 , Y ) }.
% 1.33/1.69 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.33/1.69 ( tc_Nat_Onat, Y, X ), Y ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.33/1.69 ( tc_Nat_Onat, Y, Z ), X ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.33/1.69 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.33/1.69 ) }.
% 1.33/1.69 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.33/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.33/1.69 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.33/1.69 tc_Nat_Onat ), X ) }.
% 1.33/1.69 { alpha59( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 1.33/1.69 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.33/1.69 { alpha59( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 1.33/1.69 ( X, Y ), Z ) ) }.
% 1.33/1.69 { ! alpha59( X, Y, Z ), alpha63( X, Y, Z ), Z = Y }.
% 1.33/1.69 { ! alpha59( X, Y, Z ), alpha63( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 1.33/1.69 ) ) }.
% 1.33/1.69 { ! alpha63( X, Y, Z ), alpha59( X, Y, Z ) }.
% 1.33/1.69 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha59( X, Y, Z ) }.
% 1.33/1.69 { ! alpha63( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 1.33/1.69 }.
% 1.33/1.69 { ! alpha63( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 1.33/1.69 X, Y ), Z ) ), alpha63( X, Y, Z ) }.
% 1.33/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), X ) ) }
% 1.33/1.69 .
% 1.33/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ),
% 1.33/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Y ) ) }
% 1.33/1.69 .
% 1.33/1.69 { ! Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y )
% 1.33/1.69 , X ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.69 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Z )
% 1.33/1.69 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), Z )
% 1.33/1.69 ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.69 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Y )
% 1.33/1.69 ), Y = X }.
% 1.33/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ),
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.33/1.69 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ),
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.69 , Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.69 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 1.33/1.69 { ! Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y )
% 1.33/1.69 , X ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.69 , Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 1.33/1.69 { ! Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y )
% 1.33/1.69 , X ) ) }.
% 1.33/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.33/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ), Y ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.69 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.33/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) ),
% 1.33/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.69 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.33/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ) ),
% 1.33/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.69 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 1.33/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 1.33/1.69 X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.69 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) ),
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.69 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) ),
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ), X ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ), X ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), ! Y = X }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 1.33/1.69 X ) ), Y = X, c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 1.33/1.69 X ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), Y = X }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ), X ) ) }.
% 1.33/1.69 { ! Y = X, hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal
% 1.33/1.69 , Y ), X ) ) }.
% 1.33/1.69 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol10( Z, T ) ) }.
% 1.33/1.69 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.33/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ) ), skol10( X, Y ) ) )
% 1.33/1.69 }.
% 1.33/1.69 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( Z, skol11( X, Y, Z ) ) ) ), Y )
% 1.33/1.69 ), c_SEQ_OBseq( X, Z ) }.
% 1.33/1.69 { ! class_RealVector_Oreal__normed__vector( X ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), skol12( U, W, V0, T
% 1.33/1.69 ) ) ), c_SEQ_OBseq( X, Y ) }.
% 1.33/1.69 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol12( X, Y, Z, T ) ) ) ),
% 1.33/1.69 Z ) ), c_SEQ_OBseq( X, Y ) }.
% 1.33/1.69 { ! class_Groups_Ozero( X ), !
% 1.33/1.69 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.69 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.33/1.69 tc_Polynomial_Opoly( X ) ),
% 1.33/1.69 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.33/1.69 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol13( X, Y, Z ) ) ) ), Z )
% 1.33/1.69 ), c_SEQ_OBseq( X, Y ) }.
% 1.33/1.69 { ! class_Orderings_Oorder( X ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol14( X, Y ) ), skol66
% 1.33/1.69 ( X, Y ) ) ), c_SEQ_Omonoseq( X, Y ) }.
% 1.33/1.69 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, skol66( X, Y ) ) ), hAPP(
% 1.33/1.69 Y, skol14( X, Y ) ) ) ), c_SEQ_Omonoseq( X, Y ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 1.33/1.69 X ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal
% 1.33/1.69 , X ), Y ) ), Y = X }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 1.33/1.69 X ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal
% 1.33/1.69 , X ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.69 tc_RealDef_Oreal, Y ), Z ) ) }.
% 1.33/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ), X
% 1.33/1.69 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X
% 1.33/1.69 ), Y ) ) }.
% 1.33/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ), X
% 1.33/1.69 ) ) }.
% 1.33/1.69 { ! class_Orderings_Oorder( X ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol15( X, Y ) ), skol67
% 1.33/1.69 ( X, Y ) ) ), c_SEQ_Omonoseq( X, Y ) }.
% 1.33/1.69 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, skol15( X, Y ) ) ), hAPP(
% 1.33/1.69 Y, skol67( X, Y ) ) ) ), c_SEQ_Omonoseq( X, Y ) }.
% 1.33/1.69 { ! c_HOL_Oequal__class_Oequal( tc_RealDef_Oreal, Y, X ),
% 1.33/1.69 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.33/1.69 { ! c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.33/1.69 c_HOL_Oequal__class_Oequal( tc_RealDef_Oreal, Y, X ) }.
% 1.33/1.69 { ! class_RealVector_Oreal__normed__vector( X ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.69 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 1.33/1.69 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.33/1.69 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.33/1.69 ( X, Y ) ) ) ), c_RealVector_Onorm__class_Onorm( X,
% 1.33/1.69 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 1.33/1.69 c_RealDef_Opositive( c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X,
% 1.33/1.69 Y ) ) }.
% 1.33/1.69 { ! c_RealDef_Opositive( c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X
% 1.33/1.69 , Y ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( c_RealDef_Oreal(
% 1.33/1.69 tc_Nat_Onat ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( c_RealDef_Oreal(
% 1.33/1.69 tc_Nat_Onat ), X ) ) }.
% 1.33/1.69 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.33/1.69 hAPP( X, Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.69 tc_Nat_Onat, skol16( Z, Y ) ), Y ) ) }.
% 1.33/1.69 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.33/1.69 hAPP( X, Y ) ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, skol16(
% 1.33/1.69 X, Y ) ), ! hBOOL( hAPP( X, Z ) ) }.
% 1.33/1.69 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.33/1.69 hAPP( X, Y ) ), hBOOL( hAPP( X, skol16( X, Y ) ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.33/1.69 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( X ), Y ) ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.33/1.69 tc_Nat_Onat ), Y ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.33/1.69 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.33/1.69 ( c_Nat_Osemiring__1__class_Oof__nat( X ), Y ) ) }.
% 1.33/1.69 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.33/1.69 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 1.33/1.69 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.33/1.69 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.33/1.69 ( X, Z, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.33/1.69 tc_Nat_Onat ), T ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.33/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), hAPP( c_RealDef_Oreal
% 1.33/1.69 ( tc_Nat_Onat ), X ) ) ) }.
% 1.33/1.69 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( X ) }.
% 1.33/1.69 { c_RealDef_Oreal( tc_Nat_Onat ) = c_Nat_Osemiring__1__class_Oof__nat(
% 1.33/1.69 tc_RealDef_Oreal ) }.
% 1.33/1.69 { c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, hAPP( c_RealDef_Oreal(
% 1.33/1.69 tc_Nat_Onat ), X ) ) = hAPP( c_RealDef_Oreal( tc_Nat_Onat ), X ) }.
% 1.33/1.69 { hAPP( c_RealDef_Oreal( tc_Nat_Onat ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), hAPP( c_RealDef_Oreal(
% 1.33/1.69 tc_Nat_Onat ), Y ) ), X ) }.
% 1.33/1.69 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), hAPP(
% 1.33/1.69 c_RealDef_Oreal( tc_Nat_Onat ), Y ) ), X ) = hAPP( c_RealDef_Oreal(
% 1.33/1.69 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 1.33/1.69 ), X ) ) }.
% 1.33/1.69 { ! hAPP( c_RealDef_Oreal( tc_Nat_Onat ), Y ) = hAPP( c_RealDef_Oreal(
% 1.33/1.69 tc_Nat_Onat ), X ), Y = X }.
% 1.33/1.69 { ! Y = X, hAPP( c_RealDef_Oreal( tc_Nat_Onat ), Y ) = hAPP(
% 1.33/1.69 c_RealDef_Oreal( tc_Nat_Onat ), X ) }.
% 1.33/1.69 { c_RealDef_Oreal( tc_Nat_Onat ) = c_Nat_Osemiring__1__class_Oof__nat(
% 1.33/1.69 tc_RealDef_Oreal ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__idom( X ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.69 , hAPP( hAPP( c_Power_Opower__class_Opower( X ),
% 1.33/1.69 c_Groups_Oabs__class_Oabs( X, Z ) ), Y ) ) ) }.
% 1.33/1.69 { c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, X ) =
% 1.33/1.69 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) }.
% 1.33/1.69 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.33/1.69 c_Groups_Oabs__class_Oabs( X, c_Groups_Oabs__class_Oabs( X, Y ) ) =
% 1.33/1.69 c_Groups_Oabs__class_Oabs( X, Y ) }.
% 1.33/1.69 { ! class_Rings_Osemiring__1( X ), hAPP( c_Nat_Osemiring__1__class_Oof__nat
% 1.33/1.69 ( X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y )
% 1.33/1.69 ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( X ), Z ) ), Y ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 1.33/1.69 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), c_Groups_Oabs__class_Oabs( X, Z ) ), Y
% 1.33/1.69 ) }.
% 1.33/1.69 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 1.33/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.33/1.69 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) }.
% 1.33/1.69 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 1.33/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( X ), Y ) ) = hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_RealDef_Oreal ), Y ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 1.33/1.69 ( c_Nat_Osemiring__1__class_Oof__nat( X ), Y ) ) = hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( X ), Y ) }.
% 1.33/1.69 { ! class_Nat_Osemiring__char__0( X ), ! hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( X ), Z ) = hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( X ), Y ), Z = Y }.
% 1.33/1.69 { ! class_Nat_Osemiring__char__0( X ), ! Z = Y, hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( X ), Z ) = hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( X ), Y ) }.
% 1.33/1.69 { ! class_RealVector_Oreal__normed__algebra__1( X ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), Z ), Y ) ) ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.33/1.69 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) ) ) }.
% 1.33/1.69 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.33/1.69 c_Groups_Oabs__class_Oabs( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) }.
% 1.33/1.69 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.33/1.69 c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) }.
% 1.33/1.69 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) }.
% 1.33/1.69 { ! class_Groups_Oordered__ab__group__add__abs( X ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Oabs__class_Oabs( X,
% 1.33/1.69 Y ) ) ) }.
% 1.33/1.69 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ) )
% 1.33/1.69 , Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }
% 1.33/1.69 .
% 1.33/1.69 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.33/1.69 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 1.33/1.69 = c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z )
% 1.33/1.69 ) }.
% 1.33/1.69 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Oabs__class_Oabs
% 1.33/1.69 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ) ) =
% 1.33/1.69 c_RealVector_Onorm__class_Onorm( X, Y ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.69 , Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.69 , Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), Z ), T ) ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), Y ), T ) ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.33/1.69 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 1.33/1.69 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.33/1.69 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.33/1.69 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.33/1.69 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.33/1.69 .
% 1.33/1.69 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.33/1.69 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.33/1.69 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.33/1.69 tc_Nat_Onat ) }.
% 1.33/1.69 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.33/1.69 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.33/1.69 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 1.33/1.69 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.33/1.69 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.33/1.69 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.33/1.69 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 1.33/1.69 ), X ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 1.33/1.69 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 1.33/1.69 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.33/1.69 { ! class_Groups_Oordered__ab__group__add__abs( X ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.69 , c_Groups_Oabs__class_Oabs( X, Y ) ) ) }.
% 1.33/1.69 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Y ) )
% 1.33/1.69 , c_Groups_Ozero__class_Ozero( X ) ) ), Y = c_Groups_Ozero__class_Ozero(
% 1.33/1.69 X ) }.
% 1.33/1.69 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Y ) )
% 1.33/1.69 , c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.33/1.69 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.69 , Y ) ), c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 1.33/1.69 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, Y ),
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.33/1.69 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.33/1.69 c_Groups_Oabs__class_Oabs( X, Y ) ), ! Y = c_Groups_Ozero__class_Ozero( X
% 1.33/1.69 ) }.
% 1.33/1.69 { ! class_Groups_Oordered__ab__group__add__abs( X ), Y =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 1.33/1.69 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.33/1.69 c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 1.33/1.69 { ! class_Groups_Oordered__ab__group__add__abs( X ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 1.33/1.69 c_Groups_Ominus__class_Ominus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 1.33/1.69 c_Groups_Oabs__class_Oabs( X, Y ) ) ) ), c_Groups_Oabs__class_Oabs( X,
% 1.33/1.69 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) ) }.
% 1.33/1.69 { ! class_Groups_Oordered__ab__group__add__abs( X ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 1.33/1.69 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ) )
% 1.33/1.69 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y )
% 1.33/1.69 ) ) ) }.
% 1.33/1.69 { ! class_Groups_Oordered__ab__group__add__abs( X ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 1.33/1.69 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ) )
% 1.33/1.69 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z )
% 1.33/1.69 ) ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semidom( X ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.69 , hAPP( c_Nat_Osemiring__1__class_Oof__nat( X ), Y ) ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semidom( X ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.69 , hAPP( c_Nat_Osemiring__1__class_Oof__nat( X ), Y ) ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.33/1.69 ( X, hAPP( c_Nat_Osemiring__1__class_Oof__nat( X ), Y ),
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.33/1.69 { ! class_Rings_Osemiring__1( X ), hAPP( c_Nat_Osemiring__1__class_Oof__nat
% 1.33/1.69 ( X ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.33/1.69 ( X, hAPP( c_Nat_Osemiring__1__class_Oof__nat( X ), Z ), hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( X ), Y ) ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.33/1.69 ( tc_Nat_Onat, Z, Y ), c_Orderings_Oord__class_Oless( X, hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( X ), Z ), hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( X ), Y ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.33/1.69 ( tc_Nat_Onat, Z, Y ), c_Orderings_Oord__class_Oless( X, hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( X ), Z ), hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( X ), Y ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.33/1.69 ( X, hAPP( c_Nat_Osemiring__1__class_Oof__nat( X ), Z ), hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( X ), Y ) ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.33/1.69 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 1.33/1.69 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.69 , Y ) ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( X ), Z ) ), hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( X ), Y ) ) ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( X ), Z ) ), hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( X ), Y ) ) ) }.
% 1.33/1.69 { ! hAPP( c_RealDef_Oreal( tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_RealDef_Oreal ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.33/1.69 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_RealDef_Oreal(
% 1.33/1.69 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.33/1.69 { hAPP( c_RealDef_Oreal( tc_Nat_Onat ), c_Groups_Ozero__class_Ozero(
% 1.33/1.69 tc_Nat_Onat ) ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( c_RealDef_Oreal
% 1.33/1.69 ( tc_Nat_Onat ), X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }
% 1.33/1.69 .
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( c_RealDef_Oreal
% 1.33/1.69 ( tc_Nat_Onat ), Y ), hAPP( c_RealDef_Oreal( tc_Nat_Onat ), X ) ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( c_RealDef_Oreal(
% 1.33/1.69 tc_Nat_Onat ), Y ), hAPP( c_RealDef_Oreal( tc_Nat_Onat ), X ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP
% 1.33/1.69 ( c_RealDef_Oreal( tc_Nat_Onat ), Y ) ), hAPP( c_RealDef_Oreal(
% 1.33/1.69 tc_Nat_Onat ), X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.69 tc_Nat_Onat, Y ), X ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.69 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP
% 1.33/1.69 ( c_RealDef_Oreal( tc_Nat_Onat ), Y ) ), hAPP( c_RealDef_Oreal(
% 1.33/1.69 tc_Nat_Onat ), X ) ) ) }.
% 1.33/1.69 { ! c_RealDef_Opositive( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) )
% 1.33/1.69 }.
% 1.33/1.69 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), Y ), Z ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.69 , T ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) ), Y ) ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.33/1.69 tc_Nat_Onat ), Z ), T = Y }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP
% 1.33/1.69 ( c_RealDef_Oreal( tc_Nat_Onat ), X ) ), c_Groups_Ozero__class_Ozero(
% 1.33/1.69 tc_RealDef_Oreal ) ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 1.33/1.69 .
% 1.33/1.69 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 1.33/1.69 c_RealDef_Oreal( tc_Nat_Onat ), X ) ), c_Groups_Ozero__class_Ozero(
% 1.33/1.69 tc_RealDef_Oreal ) ) ) }.
% 1.33/1.69 { ! class_Rings_Oring__1( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ), hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( X ), c_Groups_Ominus__class_Ominus(
% 1.33/1.69 tc_Nat_Onat, Y, Z ) ) = c_Groups_Ominus__class_Ominus( X, hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( X ), Y ), hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( X ), Z ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.69 , hAPP( c_RealDef_Oreal( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus(
% 1.33/1.69 tc_Nat_Onat, X, Y ) ) = c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.33/1.69 hAPP( c_RealDef_Oreal( tc_Nat_Onat ), X ), hAPP( c_RealDef_Oreal(
% 1.33/1.69 tc_Nat_Onat ), Y ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( Z, hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint )
% 1.33/1.69 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) ), alpha2( X, Y
% 1.33/1.69 , Z ) }.
% 1.33/1.69 { ! hBOOL( hAPP( Z, hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint )
% 1.33/1.69 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) ), alpha23( X, Y
% 1.33/1.69 , Z ) }.
% 1.33/1.69 { ! alpha2( X, Y, Z ), ! alpha23( X, Y, Z ), hBOOL( hAPP( Z, hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ),
% 1.33/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) ) }.
% 1.33/1.69 { ! alpha23( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 1.33/1.69 ), hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.33/1.69 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha23( X, Y, Z ) }
% 1.33/1.69 .
% 1.33/1.69 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), alpha23
% 1.33/1.69 ( X, Y, Z ) }.
% 1.33/1.69 { ! alpha2( X, Y, Z ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.69 tc_Nat_Onat, X ), Y ) ), hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus(
% 1.33/1.69 tc_Int_Oint, hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y )
% 1.33/1.69 , hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) ) ) }.
% 1.33/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), Y ) ),
% 1.33/1.69 alpha2( X, Y, Z ) }.
% 1.33/1.69 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ), hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) ) ), alpha2( X,
% 1.33/1.69 Y, Z ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.69 , c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ), hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) ) = hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ),
% 1.33/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Int_Oint ), hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint )
% 1.33/1.69 , X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.33/1.69 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.33/1.69 tc_Nat_Onat ), Y ) }.
% 1.33/1.69 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.33/1.69 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 1.33/1.69 ), X ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.33/1.69 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol17( X, Y, Z ) ) ) ), Z )
% 1.33/1.69 ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), hAPP( c_RealDef_Oreal
% 1.33/1.69 ( tc_Nat_Onat ), c_Nat_OSuc( skol68( X, Y ) ) ) ) }.
% 1.33/1.69 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol79( X, Y, Z ) ) ), hAPP
% 1.33/1.69 ( c_RealDef_Oreal( tc_Nat_Onat ), c_Nat_OSuc( Z ) ) ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol81( T, U ) ) }.
% 1.33/1.69 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol79( X, Y, Z ) ) ), hAPP
% 1.33/1.69 ( c_RealDef_Oreal( tc_Nat_Onat ), c_Nat_OSuc( Z ) ) ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ) ), skol81( X, Y ) ) )
% 1.33/1.69 }.
% 1.33/1.69 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol18( X, Y, Z ) ) ) ), Z )
% 1.33/1.69 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ) ), hAPP(
% 1.33/1.69 c_RealDef_Oreal( tc_Nat_Onat ), c_Nat_OSuc( skol69( X, Y ) ) ) ) ) }.
% 1.33/1.69 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol80( X, Y, Z ) ) ) ),
% 1.33/1.69 hAPP( c_RealDef_Oreal( tc_Nat_Onat ), c_Nat_OSuc( Z ) ) ) ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol82( T, U ) ) }.
% 1.33/1.69 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol80( X, Y, Z ) ) ) ),
% 1.33/1.69 hAPP( c_RealDef_Oreal( tc_Nat_Onat ), c_Nat_OSuc( Z ) ) ) ), hBOOL( hAPP
% 1.33/1.69 ( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ) ), skol82( X, Y ) ) )
% 1.33/1.69 }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol19( T, U, W ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.69 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 1.33/1.69 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, T ) ), skol19( X, Y,
% 1.33/1.69 Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.69 Y ), T ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.69 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 1.33/1.69 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, T ) ), skol19( X, Y,
% 1.33/1.69 Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.69 T ), Z ) ) }.
% 1.33/1.69 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), hAPP( c_RealDef_Oreal
% 1.33/1.69 ( tc_Nat_Onat ), c_Nat_OSuc( skol20( X, Y ) ) ) ) }.
% 1.33/1.69 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol70( X, Y, Z ) ) ), hAPP
% 1.33/1.69 ( c_RealDef_Oreal( tc_Nat_Onat ), c_Nat_OSuc( Z ) ) ), c_SEQ_OBseq( X, Y
% 1.33/1.69 ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.33/1.69 X ) ) }.
% 1.33/1.69 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 1.33/1.69 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.33/1.69 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ),
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.33/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) ) }.
% 1.33/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 1.33/1.69 tc_Int_Oint, Y ) ), X ) ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint )
% 1.33/1.69 , c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ), ! Y =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.33/1.69 { Y = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.33/1.69 tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 1.33/1.69 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ) }.
% 1.33/1.69 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.33/1.69 tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 1.33/1.69 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 1.33/1.69 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.33/1.69 { ! hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) = hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ), Y = X }.
% 1.33/1.69 { ! Y = X, hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) =
% 1.33/1.69 hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) }.
% 1.33/1.69 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) ), X ) = hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.33/1.69 { hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) ), X ) }.
% 1.33/1.69 { c_Groups_Oabs__class_Oabs( tc_Int_Oint, hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) = hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) }.
% 1.33/1.69 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 1.33/1.69 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 1.33/1.69 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 1.33/1.69 { ! c_Nat_OSuc( X ) = X }.
% 1.33/1.69 { ! X = c_Nat_OSuc( X ) }.
% 1.33/1.69 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 1.33/1.69 , Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.33/1.69 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.33/1.69 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.33/1.69 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.33/1.69 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.33/1.69 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.33/1.69 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.33/1.69 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 1.33/1.69 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.33/1.69 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.33/1.69 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 1.33/1.69 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 1.33/1.69 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.33/1.69 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 1.33/1.69 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 1.33/1.69 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.33/1.69 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 1.33/1.69 .
% 1.33/1.69 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 1.33/1.69 .
% 1.33/1.69 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 1.33/1.69 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.33/1.69 X ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.33/1.69 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 1.33/1.69 }.
% 1.33/1.69 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 1.33/1.69 ( Y ) ), X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.69 tc_Nat_Onat, Y ), X ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ),
% 1.33/1.69 c_Nat_OSuc( X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.69 tc_Nat_Onat, Y ), X ) ), Y = c_Nat_OSuc( X ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.69 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ),
% 1.33/1.69 c_Nat_OSuc( X ) ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 1.33/1.69 ( Y ) ), c_Nat_OSuc( X ) ) ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.69 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 1.33/1.69 ( Y ) ), c_Nat_OSuc( X ) ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ),
% 1.33/1.69 c_Nat_OSuc( X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.69 tc_Nat_Onat, Y ), X ) ), Y = c_Nat_OSuc( X ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.69 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ),
% 1.33/1.69 c_Nat_OSuc( X ) ) ) }.
% 1.33/1.69 { ! Y = c_Nat_OSuc( X ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.69 tc_Nat_Onat, Y ), c_Nat_OSuc( X ) ) ) }.
% 1.33/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ),
% 1.33/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.33/1.69 X ) ), Y ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 1.33/1.69 ( X ) ), Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.69 tc_Nat_Onat, Y ), X ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 1.33/1.69 ( X ) ), X ) ) }.
% 1.33/1.69 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.33/1.69 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 1.33/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.33/1.69 ( tc_Nat_Onat, Z, Y ), X ) }.
% 1.33/1.69 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.33/1.69 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.33/1.69 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.33/1.69 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha3( X, Y ) }.
% 1.33/1.69 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.33/1.69 { ! alpha3( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.33/1.69 c_Nat_OSuc( X ) ) }.
% 1.33/1.69 { ! alpha3( X, Y ), Y = c_Nat_OSuc( skol21( Z, Y ) ) }.
% 1.33/1.69 { ! alpha3( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol21( X,
% 1.33/1.69 Y ), X ) }.
% 1.33/1.69 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 1.33/1.69 ), alpha3( X, Y ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.33/1.69 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol22( X ) ) }.
% 1.33/1.69 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 1.33/1.69 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ) ), X ) )
% 1.33/1.69 }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 1.33/1.69 ( Y ) ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), hBOOL
% 1.33/1.69 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.69 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 1.33/1.69 ( Y ) ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ) ), X ) )
% 1.33/1.69 }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.69 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ) ), X ) )
% 1.33/1.69 }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.69 , ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X =
% 1.33/1.69 Y }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.69 , ! X = Y, c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y )
% 1.33/1.69 ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 1.33/1.69 ( Y ) ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.33/1.69 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.33/1.69 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.69 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 1.33/1.69 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.33/1.69 { ! class_Orderings_Oorder( X ), ! c_SEQ_Omonoseq( X, Y ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, Z ) ), hAPP( Y, c_Nat_OSuc
% 1.33/1.69 ( Z ) ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( Y,
% 1.33/1.69 c_Nat_OSuc( T ) ) ), hAPP( Y, T ) ) ) }.
% 1.33/1.69 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, skol23( X, Y ) ) ), hAPP(
% 1.33/1.69 Y, c_Nat_OSuc( skol23( X, Y ) ) ) ) ), c_SEQ_Omonoseq( X, Y ) }.
% 1.33/1.69 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, c_Nat_OSuc( skol71( X, Y )
% 1.33/1.69 ) ) ), hAPP( Y, skol71( X, Y ) ) ) ), c_SEQ_Omonoseq( X, Y ) }.
% 1.33/1.69 { ! c_SEQ_Osubseq( X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( X
% 1.33/1.69 , Y ), hAPP( X, c_Nat_OSuc( Y ) ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( X, skol24( X ) ),
% 1.33/1.69 hAPP( X, c_Nat_OSuc( skol24( X ) ) ) ), c_SEQ_Osubseq( X ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ) ), ! hBOOL(
% 1.33/1.69 hAPP( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.33/1.69 X ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), Y )
% 1.33/1.69 ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), ! hBOOL( hAPP
% 1.33/1.69 ( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.33/1.69 ), Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) ), Y ) ), Z = Y }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.33/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 1.33/1.69 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 1.33/1.69 ) ) = X }.
% 1.33/1.69 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( c_RealDef_Oreal(
% 1.33/1.69 tc_Nat_Onat ), c_Nat_OSuc( X ) ) ) }.
% 1.33/1.69 { hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ),
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.33/1.69 { ! hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.33/1.69 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ),
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), X =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.33/1.69 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ),
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ), hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ), hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) ), hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.69 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) ), hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) ) }.
% 1.33/1.69 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.33/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ) ), hAPP(
% 1.33/1.69 c_RealDef_Oreal( tc_Nat_Onat ), c_Nat_OSuc( skol25( X, Y ) ) ) ) ) }.
% 1.33/1.69 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol72( X, Y, Z ) ) ) ),
% 1.33/1.69 hAPP( c_RealDef_Oreal( tc_Nat_Onat ), c_Nat_OSuc( Z ) ) ) ), c_SEQ_OBseq
% 1.33/1.69 ( X, Y ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ), hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ), hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) }.
% 1.33/1.69 { c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ),
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.33/1.69 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) ), X ) = hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) ), hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.69 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) ), hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) ) }.
% 1.33/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! hBOOL( hAPP( X, Y
% 1.33/1.69 ) ), hBOOL( hAPP( X, hAPP( c_Nat_Osemiring__1__class_Oof__nat(
% 1.33/1.69 tc_Int_Oint ), skol26( X ) ) ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( X, hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint )
% 1.33/1.69 , Y ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), skol73( Z ) ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( X, hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint )
% 1.33/1.69 , Y ) ) ), hBOOL( hAPP( X, skol73( X ) ) ) }.
% 1.33/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), X ) ) }
% 1.33/1.69 .
% 1.33/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ),
% 1.33/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), Y ) ) }
% 1.33/1.69 .
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 1.33/1.69 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), Z )
% 1.33/1.69 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), Z )
% 1.33/1.69 ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 1.33/1.69 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), Y )
% 1.33/1.69 ), Y = X }.
% 1.33/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Int_Oint ) ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) ) }.
% 1.33/1.69 { ! hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) = hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ), Y = X }.
% 1.33/1.69 { ! Y = X, hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) =
% 1.33/1.69 hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) }.
% 1.33/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), skol27( Y ) ) ), hBOOL(
% 1.33/1.69 hAPP( X, hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Z ) ) )
% 1.33/1.69 }.
% 1.33/1.69 { ! hBOOL( hAPP( X, skol27( X ) ) ), hBOOL( hAPP( X, hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( X, hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint )
% 1.33/1.69 , skol74( X ) ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.69 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL(
% 1.33/1.69 hAPP( X, Y ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 1.33/1.69 , c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 1.33/1.69 tc_Int_Oint, X, Y ) }.
% 1.33/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ),
% 1.33/1.69 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint
% 1.33/1.69 ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), skol28( Y ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Int_Oint ), X ), X = hAPP( c_Nat_Osemiring__1__class_Oof__nat(
% 1.33/1.69 tc_Int_Oint ), skol28( X ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol29( T, U, W ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.69 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 1.33/1.69 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, T ) ), skol29( X, Y,
% 1.33/1.69 Z ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, T ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.69 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 1.33/1.69 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, T ) ), skol29( X, Y,
% 1.33/1.69 Z ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, T, Z ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.33/1.69 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ), Y ) = hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ),
% 1.33/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 1.33/1.69 , c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 1.33/1.69 tc_Int_Oint, X, Y ) }.
% 1.33/1.69 { c_Nat__Transfer_Otsub( hAPP( c_Nat_Osemiring__1__class_Oof__nat(
% 1.33/1.69 tc_Int_Oint ), Y ), hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint
% 1.33/1.69 ), X ) ) = hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ),
% 1.33/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 1.33/1.69 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.33/1.69 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.33/1.69 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.33/1.69 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.33/1.69 }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv
% 1.33/1.69 ( tc_Int_Oint, X, Y ) ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.33/1.69 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.33/1.69 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.33/1.69 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.33/1.69 tc_Int_Oint ), Y ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.33/1.69 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.33/1.69 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.33/1.69 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.33/1.69 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 1.33/1.69 , ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ),
% 1.33/1.69 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 1.33/1.69 , ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ),
% 1.33/1.69 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ),
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.33/1.69 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.33/1.69 tc_Int_Oint ), Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.69 tc_Int_Oint, Y ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.69 tc_Int_Oint, c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 1.33/1.69 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ),
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.33/1.69 tc_Int_Oint ), Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.69 tc_Int_Oint, c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv
% 1.33/1.69 ( tc_Int_Oint, Y, X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.33/1.69 ( tc_Int_Oint, Y ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ),
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv
% 1.33/1.69 ( tc_Int_Oint, Y, X ) ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ),
% 1.33/1.69 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.33/1.69 tc_Int_Oint ), Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.69 tc_Int_Oint, Y ), Z ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.69 tc_Int_Oint, c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ),
% 1.33/1.69 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.33/1.69 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ), hBOOL(
% 1.33/1.69 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.33/1.69 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.33/1.69 tc_Int_Oint ), Y ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.33/1.69 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.33/1.69 tc_Int_Oint, X, Y ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.33/1.69 tc_Int_Oint, Y, X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.69 tc_Int_Oint, X ), Y ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.69 tc_Int_Oint, X ), Y ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.33/1.69 tc_Int_Oint, Y, X ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.69 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.33/1.69 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.69 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL(
% 1.33/1.69 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Odiv
% 1.33/1.69 ( tc_Int_Oint, Y, X ) ) ) }.
% 1.33/1.69 { ! c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha4( X, Y ) }.
% 1.33/1.69 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.33/1.69 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.33/1.69 { ! alpha4( X, Y ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.33/1.69 { ! alpha4( X, Y ), alpha24( X, Y ), alpha42( X, Y ) }.
% 1.33/1.69 { ! alpha24( X, Y ), alpha4( X, Y ) }.
% 1.33/1.69 { ! alpha42( X, Y ), alpha4( X, Y ) }.
% 1.33/1.69 { ! alpha42( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.69 tc_Int_Oint, Y ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.33/1.69 { ! alpha42( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ),
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ), alpha42( X, Y ) }.
% 1.33/1.69 { ! alpha24( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.69 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ) }.
% 1.33/1.69 { ! alpha24( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), alpha24( X, Y ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Nat__Transfer_Otsub( X, Y
% 1.33/1.69 ) ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Int_Onat, X ), Y ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Int_Onat, X ), Y ) }
% 1.33/1.69 .
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.69 tc_Nat_Onat, X ), Y ) ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X )
% 1.33/1.69 = c_Nat_OSuc( c_Divides_Odiv__class_Odiv( tc_Nat_Onat,
% 1.33/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), X ) ) }.
% 1.33/1.69 { ! class_Orderings_Oorder( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, skol30( X, Y ) ) ), hAPP(
% 1.33/1.69 Y, c_Nat_OSuc( skol30( X, Y ) ) ) ) ), c_SEQ_Oincseq( X, Y ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ),
% 1.33/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( c_Int_Onat, X ), hAPP(
% 1.33/1.69 c_Int_Onat, Y ) ) = hAPP( c_Int_Onat, c_Nat__Transfer_Otsub( X, Y ) ) }.
% 1.33/1.69 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.33/1.69 tc_Polynomial_Opoly( X ) ),
% 1.33/1.69 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.33/1.69 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.33/1.69 tc_Polynomial_Opoly( X ) ),
% 1.33/1.69 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) = c_Nat_OSuc(
% 1.33/1.69 c_Polynomial_Odegree( X, Y ) ) }.
% 1.33/1.69 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 1.33/1.69 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( T, X, Y,
% 1.33/1.69 Z, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.33/1.69 { ! class_Fields_Ofield( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 1.33/1.69 , c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) ),
% 1.33/1.69 c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), Z, Y ) =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.33/1.69 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ), Y ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.69 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.33/1.69 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, Z ) ),
% 1.33/1.69 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, Z ) ) ) }.
% 1.33/1.69 { hAPP( c_Int_Onat, hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint )
% 1.33/1.69 , X ) ) = X }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hAPP( c_Int_Onat,
% 1.33/1.69 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) =
% 1.33/1.69 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( c_Int_Onat, X ), hAPP(
% 1.33/1.69 c_Int_Onat, Y ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ),
% 1.33/1.69 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( c_Int_Onat, X ), hAPP(
% 1.33/1.69 c_Int_Onat, Y ) ) = hAPP( c_Int_Onat, c_Divides_Odiv__class_Odiv(
% 1.33/1.69 tc_Int_Oint, X, Y ) ) }.
% 1.33/1.69 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) = X }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.33/1.69 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.33/1.69 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.33/1.69 { c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = hAPP( c_Int_Onat,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.33/1.69 { hAPP( c_Int_Onat, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! hAPP( c_Int_Onat,
% 1.33/1.69 X ) = hAPP( c_Int_Onat, Y ), X = Y }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! X = Y, hAPP(
% 1.33/1.69 c_Int_Onat, X ) = hAPP( c_Int_Onat, Y ) }.
% 1.33/1.69 { ! hBOOL( hAPP( X, skol31( X ) ) ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP( X, hAPP
% 1.33/1.69 ( c_Int_Onat, Y ) ) ) }.
% 1.33/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), skol75( Y ) ) ), hBOOL(
% 1.33/1.69 hAPP( X, Z ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( X, hAPP( c_Int_Onat, skol75( X ) ) ) ), hBOOL( hAPP( X, Y
% 1.33/1.69 ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.69 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), skol32( Z ) )
% 1.33/1.69 ) }.
% 1.33/1.69 { ! hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, hAPP( c_Int_Onat, skol32( X ) )
% 1.33/1.69 ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! hBOOL( hAPP( X,
% 1.33/1.69 hAPP( c_Int_Onat, Y ) ) ), hBOOL( hAPP( X, skol76( X ) ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! hAPP( c_Int_Onat,
% 1.33/1.69 X ) = hAPP( c_Int_Onat, Y ), X = Y }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! X = Y, hAPP(
% 1.33/1.69 c_Int_Onat, X ) = hAPP( c_Int_Onat, Y ) }.
% 1.33/1.69 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ), hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) = hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ),
% 1.33/1.69 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) }.
% 1.33/1.69 { hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ),
% 1.33/1.69 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) =
% 1.33/1.69 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ), hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) }.
% 1.33/1.69 { ! class_Groups_Oab__group__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.33/1.69 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 1.33/1.69 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 1.33/1.69 X, c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, T ) ), Y )
% 1.33/1.69 }.
% 1.33/1.69 { ! class_Groups_Oab__group__add( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 1.33/1.69 Z ) ), Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.69 tc_Nat_Onat, c_Polynomial_Odegree( X, T ) ), Y ) ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 1.33/1.69 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, T ) ) ), Y )
% 1.33/1.69 ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.69 tc_Nat_Onat, X ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.69 tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ) ),
% 1.33/1.69 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, X ) ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ),
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hAPP( c_Int_Onat, X ) =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.33/1.69 { ! hAPP( c_Int_Onat, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.33/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ),
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ),
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), hAPP( c_Int_Onat, X ) =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 1.33/1.69 ( c_Int_Onat, Y ), hAPP( c_Int_Onat, X ) ), c_Orderings_Oord__class_Oless
% 1.33/1.69 ( tc_Int_Oint, Y, X ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X
% 1.33/1.69 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Int_Onat, Y ),
% 1.33/1.69 hAPP( c_Int_Onat, X ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Int_Onat, Y ), hAPP
% 1.33/1.69 ( c_Int_Onat, X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Int_Onat, Y ), hAPP
% 1.33/1.69 ( c_Int_Onat, X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 1.33/1.69 .
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X
% 1.33/1.69 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Int_Onat, Y ),
% 1.33/1.69 hAPP( c_Int_Onat, X ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( c_Int_Onat, X ) ),
% 1.33/1.69 hAPP( c_Int_Onat, Y ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.33/1.69 ( tc_Int_Oint, X ), Y ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), Y ) ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( c_Int_Onat, X ) ),
% 1.33/1.69 hAPP( c_Int_Onat, Y ) ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), hAPP( c_Int_Onat, X )
% 1.33/1.69 ) = X }.
% 1.33/1.69 { ! hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) = X, Y =
% 1.33/1.69 hAPP( c_Int_Onat, X ) }.
% 1.33/1.69 { ! hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) = X, hBOOL
% 1.33/1.69 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ) }.
% 1.33/1.69 { ! Y = hAPP( c_Int_Onat, X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) = X }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), hAPP( c_Int_Onat, X )
% 1.33/1.69 ) = X }.
% 1.33/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), hAPP( c_Int_Onat, X )
% 1.33/1.69 ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( c_Int_Onat, X ) )
% 1.33/1.69 , c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ), X ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ), X ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( c_Int_Onat, X ) ) }
% 1.33/1.69 .
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 1.33/1.69 ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 1.33/1.69 , c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.33/1.69 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.33/1.69 tc_Nat_Onat, Y, X ), X ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 1.33/1.69 , c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.33/1.69 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.33/1.69 tc_Nat_Onat, Y, X ), X ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Nat_Onat ), hAPP( c_Int_Onat, X ) ), c_Orderings_Oord__class_Oless(
% 1.33/1.69 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Int_Onat, X ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Int_Onat, X ), hAPP(
% 1.33/1.69 c_Int_Onat, Y ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Int_Onat, X ), hAPP(
% 1.33/1.69 c_Int_Onat, Y ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Int_Onat, X ), hAPP(
% 1.33/1.69 c_Int_Onat, Y ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( c_Int_Onat, X ), hAPP(
% 1.33/1.69 c_Int_Onat, Y ) ) }.
% 1.33/1.69 { alpha60( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.69 tc_Nat_Onat, hAPP( c_Int_Onat, Y ) ), hAPP( c_Int_Onat, X ) ) ), hBOOL(
% 1.33/1.69 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ) }.
% 1.33/1.69 { alpha60( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.69 tc_Int_Oint, Y ), X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.69 tc_Nat_Onat, hAPP( c_Int_Onat, Y ) ), hAPP( c_Int_Onat, X ) ) ) }.
% 1.33/1.69 { ! alpha60( X, Y ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 1.33/1.69 { ! alpha60( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.69 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ) }.
% 1.33/1.69 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.33/1.69 tc_Int_Oint ), Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.69 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), alpha60
% 1.33/1.69 ( X, Y ) }.
% 1.33/1.69 { ! hAPP( c_Int_Onat, Y ) = X, alpha5( X, Y ) }.
% 1.33/1.69 { ! hAPP( c_Int_Onat, Y ) = X, alpha25( X, Y ) }.
% 1.33/1.69 { ! alpha5( X, Y ), ! alpha25( X, Y ), hAPP( c_Int_Onat, Y ) = X }.
% 1.33/1.69 { ! alpha25( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.69 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), X =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), alpha25( X, Y ) }.
% 1.33/1.69 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha25( X, Y ) }.
% 1.33/1.69 { ! alpha5( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.69 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), Y =
% 1.33/1.69 hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) }.
% 1.33/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), alpha5( X, Y ) }.
% 1.33/1.69 { ! Y = hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ),
% 1.33/1.69 alpha5( X, Y ) }.
% 1.33/1.69 { ! Y = hAPP( c_Int_Onat, X ), alpha6( X, Y ) }.
% 1.33/1.69 { ! Y = hAPP( c_Int_Onat, X ), alpha26( X, Y ) }.
% 1.33/1.69 { ! alpha6( X, Y ), ! alpha26( X, Y ), Y = hAPP( c_Int_Onat, X ) }.
% 1.33/1.69 { ! alpha26( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.69 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), Y =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), alpha26( X, Y ) }.
% 1.33/1.69 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha26( X, Y ) }.
% 1.33/1.69 { ! alpha6( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.69 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), X =
% 1.33/1.69 hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) }.
% 1.33/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), alpha6( X, Y ) }.
% 1.33/1.69 { ! X = hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ),
% 1.33/1.69 alpha6( X, Y ) }.
% 1.33/1.69 { ! hBOOL( hAPP( Y, hAPP( c_Int_Onat, X ) ) ), alpha7( X, Y ) }.
% 1.33/1.69 { ! hBOOL( hAPP( Y, hAPP( c_Int_Onat, X ) ) ), alpha27( X, Y ) }.
% 1.33/1.69 { ! alpha7( X, Y ), ! alpha27( X, Y ), hBOOL( hAPP( Y, hAPP( c_Int_Onat, X
% 1.33/1.69 ) ) ) }.
% 1.33/1.69 { ! alpha27( X, Y ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hBOOL( hAPP( Y,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.33/1.69 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha27( X, Y ) }.
% 1.33/1.69 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha27
% 1.33/1.69 ( X, Y ) }.
% 1.33/1.69 { ! alpha7( X, Y ), ! X = hAPP( c_Nat_Osemiring__1__class_Oof__nat(
% 1.33/1.69 tc_Int_Oint ), Z ), hBOOL( hAPP( Y, Z ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( Y, skol33( Z, Y ) ) ), alpha7( X, Y ) }.
% 1.33/1.69 { X = hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), skol33( X, Y
% 1.33/1.69 ) ), alpha7( X, Y ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ), Y ) ), hAPP(
% 1.33/1.69 c_Int_Onat, c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 1.33/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( c_Int_Onat, Y ), hAPP(
% 1.33/1.69 c_Int_Onat, X ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( tc_Nat_Onat ), hAPP( c_Int_Onat, X ) ), Y )
% 1.33/1.69 = hAPP( c_Int_Onat, hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.33/1.69 tc_Int_Oint ), X ), Y ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hAPP( c_Int_Onat,
% 1.33/1.69 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) =
% 1.33/1.69 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), hAPP( c_Int_Onat
% 1.33/1.69 , X ) ), Y ) }.
% 1.33/1.69 { c_Nat__Transfer_Otransfer__morphism( tc_Int_Oint, tc_Nat_Onat, c_Int_Onat
% 1.33/1.69 , c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.33/1.69 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.33/1.69 tc_Polynomial_Opoly( X ) ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Oorder( X, Z
% 1.33/1.69 , Y ) ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.33/1.69 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osynthetic__div( X
% 1.33/1.69 , Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.33/1.69 c_Polynomial_Odegree( X, Z ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.33/1.69 }.
% 1.33/1.69 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Odegree( X, Z ) =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Polynomial_Osynthetic__div
% 1.33/1.69 ( X, Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( c_Int_Onat, X ) ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oone__class_Oone(
% 1.33/1.69 tc_Int_Oint ), X ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oone__class_Oone(
% 1.33/1.69 tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.33/1.69 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 1.33/1.69 c_Int_Onat, X ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 1.33/1.69 alpha8( X, Z ), alpha28( X, Y, Z ) }.
% 1.33/1.69 { ! alpha8( X, Z ), hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat
% 1.33/1.69 , Y, X ) ) ) }.
% 1.33/1.69 { ! alpha28( X, Y, Z ), hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 1.33/1.69 tc_Nat_Onat, Y, X ) ) ) }.
% 1.33/1.69 { ! alpha28( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.69 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 1.33/1.69 ), skol34( X, Y, T ) ) ), Y ) ) }.
% 1.33/1.69 { ! alpha28( X, Y, Z ), alpha43( X, Y, Z, skol34( X, Y, Z ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.33/1.69 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), T ) ), Y ) ), !
% 1.33/1.69 alpha43( X, Y, Z, T ), alpha28( X, Y, Z ) }.
% 1.33/1.69 { ! alpha43( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.33/1.69 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc
% 1.33/1.69 ( T ) ) ) }.
% 1.33/1.69 { ! alpha43( X, Y, Z, T ), hBOOL( hAPP( Z, T ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc( T ) ) ), !
% 1.33/1.69 hBOOL( hAPP( Z, T ) ), alpha43( X, Y, Z, T ) }.
% 1.33/1.69 { ! alpha8( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.33/1.69 { ! alpha8( X, Y ), hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero(
% 1.33/1.69 tc_Nat_Onat ) ) ) }.
% 1.33/1.69 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( Y,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha8( X, Y ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.33/1.69 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.33/1.69 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.33/1.69 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.33/1.69 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.33/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 1.33/1.69 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.33/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 1.33/1.69 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.33/1.69 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.33/1.69 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.33/1.69 = Y }.
% 1.33/1.69 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.33/1.69 = Y }.
% 1.33/1.69 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 1.33/1.69 c_Groups_Oone__class_Oone( X ) }.
% 1.33/1.69 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 1.33/1.69 c_Groups_Oone__class_Oone( X ) = Y }.
% 1.33/1.69 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.33/1.69 = Y }.
% 1.33/1.69 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.33/1.69 = Y }.
% 1.33/1.69 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 1.33/1.69 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oone__class_Oone( X ) ) =
% 1.33/1.69 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.33/1.69 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 1.33/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.33/1.69 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 1.33/1.69 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 1.33/1.69 { ! class_Rings_Osemiring__1( X ), hAPP( c_Nat_Osemiring__1__class_Oof__nat
% 1.33/1.69 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y )
% 1.33/1.69 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( X ), Z ) ), hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( X ), Y ) ) }.
% 1.33/1.69 { ! class_Rings_Osemiring__1( X ), hAPP( c_Nat_Osemiring__1__class_Oof__nat
% 1.33/1.69 ( X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) =
% 1.33/1.69 c_Groups_Oone__class_Oone( X ) }.
% 1.33/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.69 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.69 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ) ) }.
% 1.33/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.69 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.33/1.69 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 1.33/1.69 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) ) }.
% 1.33/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.33/1.69 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.33/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.33/1.69 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.33/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.33/1.69 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.33/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.33/1.69 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.33/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 1.33/1.69 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.33/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 1.33/1.69 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.33/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 1.33/1.69 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.33/1.69 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 1.33/1.69 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.33/1.69 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.33/1.69 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.33/1.69 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.33/1.69 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 1.33/1.69 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.33/1.69 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.33/1.69 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 1.33/1.69 .
% 1.33/1.69 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.33/1.69 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.33/1.69 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 1.33/1.69 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.33/1.69 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.33/1.69 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.33/1.69 .
% 1.33/1.69 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.33/1.69 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.33/1.69 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.33/1.69 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.33/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.33/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.33/1.69 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.33/1.69 = c_Groups_Oone__class_Oone( X ) }.
% 1.33/1.69 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 1.33/1.69 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 1.33/1.69 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.33/1.69 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 1.33/1.69 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.33/1.69 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.33/1.69 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.69 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), Z )
% 1.33/1.69 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.33/1.69 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ) ), hAPP(
% 1.33/1.69 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.69 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.33/1.69 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.69 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.33/1.69 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ) ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) ) }.
% 1.33/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), hAPP(
% 1.33/1.69 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) ) }.
% 1.33/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X ), hAPP(
% 1.33/1.69 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 1.33/1.69 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 1.33/1.69 c_Groups_Oone__class_Oone( X ) ) = Y }.
% 1.33/1.69 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 1.33/1.69 ( tc_Int_Oint ) }.
% 1.33/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.33/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.33/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.33/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.33/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 1.33/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.33/1.69 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 1.33/1.69 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 1.33/1.69 tc_Nat_Onat, Z, Y ), X ) }.
% 1.33/1.69 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.33/1.69 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.33/1.69 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ) ), Y
% 1.33/1.69 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.33/1.69 c_Groups_Oone__class_Oone( X ) ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.33/1.69 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 1.33/1.69 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.33/1.69 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 1.33/1.69 { ! class_Divides_Osemiring__div( X ), ! T = c_Groups_Ozero__class_Ozero( X
% 1.33/1.69 ), c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) }.
% 1.33/1.69 { ! class_Divides_Osemiring__div( X ), T = c_Groups_Ozero__class_Ozero( X )
% 1.33/1.69 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.33/1.69 c_Divides_Odiv__class_Odiv( X, Z, Y ) }.
% 1.33/1.69 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.33/1.69 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = Z }.
% 1.33/1.69 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.33/1.69 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) = Z }.
% 1.33/1.69 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.33/1.69 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.33/1.69 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 1.33/1.69 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.33/1.69 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 1.33/1.69 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 1.33/1.69 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 1.33/1.69 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.33/1.69 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.33/1.69 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.33/1.69 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.33/1.69 , c_Divides_Odiv__class_Odiv( X, Y, Y ) = c_Groups_Oone__class_Oone( X )
% 1.33/1.69 }.
% 1.33/1.69 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.33/1.69 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.33/1.69 c_Groups_Oone__class_Oone( X ) }.
% 1.33/1.69 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.33/1.69 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 1.33/1.69 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.33/1.69 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.33/1.69 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 1.33/1.69 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.33/1.69 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.33/1.69 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.33/1.69 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.33/1.69 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 1.33/1.69 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.33/1.69 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.33/1.69 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 1.33/1.69 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.33/1.69 tc_Nat_Onat ), Y ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 1.33/1.69 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.33/1.69 tc_Nat_Onat ), Z ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 1.33/1.69 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.33/1.69 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.33/1.69 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.33/1.69 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.33/1.69 Y ), X ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.33/1.69 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.33/1.69 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.33/1.69 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.33/1.69 ), X ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.33/1.69 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ) )
% 1.33/1.69 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 1.33/1.69 ) ), X ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.69 tc_Nat_Onat, Y ), X ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.69 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.33/1.69 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ) )
% 1.33/1.69 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 1.33/1.69 ) ), X ) ) ) }.
% 1.33/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oone__class_Oone(
% 1.33/1.69 tc_Int_Oint ) ) ) }.
% 1.33/1.69 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.33/1.69 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.33/1.69 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 1.33/1.69 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), Z )
% 1.33/1.69 , Y ) ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.33/1.69 c_Polynomial_Odegree( X, Z ) ), Y ) ) ) }.
% 1.33/1.69 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.69 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.33/1.69 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, X ) =
% 1.33/1.69 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.33/1.69 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.33/1.69 ) = c_Groups_Oone__class_Oone( X ) }.
% 1.33/1.69 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.33/1.69 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.33/1.69 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.33/1.69 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.33/1.69 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.33/1.69 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 1.33/1.69 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.33/1.69 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.33/1.69 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.33/1.69 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.33/1.69 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.33/1.69 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.33/1.69 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.33/1.69 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.33/1.69 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ), ! hBOOL( hAPP
% 1.33/1.69 ( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ) )
% 1.33/1.69 , T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), T ), Y ) ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 1.33/1.69 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), Y ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 1.33/1.69 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc
% 1.33/1.69 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), Y ) ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.33/1.69 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.33/1.69 tc_Nat_Onat ), Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.69 tc_Nat_Onat, Y ), X ) ) }.
% 1.33/1.69 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.33/1.69 tc_Nat_Onat ), Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.69 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z
% 1.33/1.69 ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z )
% 1.33/1.69 , X ) ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.69 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.33/1.69 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.33/1.69 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.33/1.69 tc_Nat_Onat ), Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.69 tc_Nat_Onat, Z ), X ) ) }.
% 1.33/1.69 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.33/1.69 tc_Nat_Onat ), Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.69 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z
% 1.33/1.69 ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X )
% 1.33/1.69 , Y ) ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), X ) )
% 1.33/1.69 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP
% 1.33/1.69 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 1.33/1.69 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) = Y }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 1.33/1.69 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) = Y }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.33/1.69 tc_Int_Oint ), X ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Int_Oint ), X ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.69 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) ) }.
% 1.33/1.69 { hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), c_Nat_OSuc(
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) =
% 1.33/1.69 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.33/1.69 { hAPP( c_Int_Onat, c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = c_Nat_OSuc
% 1.33/1.69 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.33/1.69 c_Groups_Oone__class_Oone( tc_Int_Oint ), Y ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.33/1.69 tc_Int_Oint, X, Y ), X ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ),
% 1.33/1.69 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 1.33/1.69 ( tc_Int_Oint ) ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 1.33/1.69 }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ),
% 1.33/1.69 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 1.33/1.69 ( tc_Int_Oint ) ) ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oabs__class_Oabs(
% 1.33/1.69 tc_Int_Oint, X ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.33/1.69 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oabs__class_Oabs(
% 1.33/1.69 tc_Int_Oint, X ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.69 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ),
% 1.33/1.69 c_Groups_Oone__class_Oone( X ) ) ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ), Y ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.33/1.69 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 1.33/1.69 c_Groups_Oone__class_Oone( X ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.33/1.69 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 1.33/1.69 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.33/1.69 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ), ! hBOOL( hAPP
% 1.33/1.69 ( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.33/1.69 ), T ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ),
% 1.33/1.69 c_Groups_Oone__class_Oone( X ) ) ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), T ), Z ) ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.33/1.69 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), Z ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.33/1.69 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), Z ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.33/1.69 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), Z ) ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.33/1.69 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.33/1.69 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 1.33/1.69 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.69 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 1.33/1.69 ), Z ) ), Y ) ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP(
% 1.33/1.69 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc( Z )
% 1.33/1.69 ) ), Z = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Nat_Onat ), X ), ! Z = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X
% 1.33/1.69 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP(
% 1.33/1.69 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ), Y ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Nat_Onat ), X ), ! Z = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X
% 1.33/1.69 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc( Z ) ) ) }
% 1.33/1.69 .
% 1.33/1.69 { ! class_Groups_Omonoid__mult( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), Y ) ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), T ), c_Groups_Ominus__class_Ominus(
% 1.33/1.69 tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) ) = hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), T ), c_Groups_Ominus__class_Ominus(
% 1.33/1.69 tc_Nat_Onat, Y, Z ) ) ), T ) }.
% 1.33/1.69 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 1.33/1.69 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 1.33/1.69 c_Groups_Oone__class_Oone( X ) }.
% 1.33/1.69 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.33/1.69 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 1.33/1.69 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 1.33/1.69 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) =
% 1.33/1.69 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.69 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 1.33/1.69 ), Z ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X )
% 1.33/1.69 , Y ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 1.33/1.69 ), Y ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.69 tc_Nat_Onat, Z ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.69 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 1.33/1.69 ), Z ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X )
% 1.33/1.69 , Y ) ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.69 , Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.33/1.69 c_Groups_Oabs__class_Oabs( X, Z ) ), Y ) = c_Groups_Oabs__class_Oabs( X,
% 1.33/1.69 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.33/1.69 { hAPP( c_RealDef_Oreal( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 1.33/1.69 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.33/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP
% 1.33/1.69 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) ), X ) =
% 1.33/1.69 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), hAPP
% 1.33/1.69 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.33/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) =
% 1.33/1.69 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y )
% 1.33/1.69 }.
% 1.33/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.33/1.69 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) = X }.
% 1.33/1.69 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP( hAPP
% 1.33/1.69 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ), Z = Y }.
% 1.33/1.69 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 1.33/1.69 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP(
% 1.33/1.69 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) }.
% 1.33/1.69 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP( hAPP
% 1.33/1.69 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), Z = Y }.
% 1.33/1.69 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 1.33/1.69 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP(
% 1.33/1.69 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) }.
% 1.33/1.69 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.33/1.69 tc_Nat_Onat ) ) = Y }.
% 1.33/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.33/1.69 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 1.33/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 1.33/1.69 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 1.33/1.69 { ! c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) =
% 1.33/1.69 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.33/1.69 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.69 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.33/1.69 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 1.33/1.69 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 1.33/1.69 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.33/1.69 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 1.33/1.69 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.33/1.69 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.33/1.69 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 1.33/1.69 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.33/1.69 , Y ), X ) }.
% 1.33/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.33/1.69 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.33/1.69 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.33/1.69 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 1.33/1.69 tc_Nat_Onat ) }.
% 1.33/1.69 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.33/1.69 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 1.33/1.69 tc_Nat_Onat ) }.
% 1.33/1.69 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.33/1.69 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.33/1.69 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.33/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.33/1.69 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 1.33/1.69 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.33/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.33/1.69 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 1.33/1.69 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.33/1.69 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 1.33/1.69 tc_Polynomial_Opoly( X ), T, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.33/1.69 tc_Polynomial_Opoly( X ) ), Z ), Y ) ) = c_Divides_Odiv__class_Odiv(
% 1.33/1.69 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 1.33/1.69 ( X ), T, Z ), Y ) }.
% 1.33/1.69 { ! c_RealDef_Opositive( X ), ! c_RealDef_Opositive( Y ),
% 1.33/1.69 c_RealDef_Opositive( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.33/1.69 tc_RealDef_Oreal ), X ), Y ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.33/1.69 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 1.33/1.69 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 1.33/1.69 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.33/1.69 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.33/1.69 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 1.33/1.69 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.33/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) ), hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) = hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.33/1.69 { hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) ), hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) }.
% 1.33/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) ), hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) = hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.33/1.69 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X,
% 1.33/1.69 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.33/1.69 { hAPP( c_RealDef_Oreal( tc_Nat_Onat ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( c_RealDef_Oreal
% 1.33/1.69 ( tc_Nat_Onat ), Y ) ), hAPP( c_RealDef_Oreal( tc_Nat_Onat ), X ) ) }.
% 1.33/1.69 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 1.33/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.33/1.69 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 1.33/1.69 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 1.33/1.69 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.33/1.69 { ! c_Groups_Oabs__class_Oabs( tc_Int_Oint, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) =
% 1.33/1.69 c_Groups_Oone__class_Oone( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 1.33/1.69 tc_Int_Oint, X ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.33/1.69 { hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ),
% 1.33/1.69 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone(
% 1.33/1.69 tc_Int_Oint ) }.
% 1.33/1.69 { c_Groups_Oone__class_Oone( tc_Int_Oint ) = hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ),
% 1.33/1.69 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.33/1.69 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( c_Int_Onat,
% 1.33/1.69 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) ), hAPP( hAPP
% 1.33/1.69 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) ), hBOOL
% 1.33/1.69 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z ), Y ) ) }
% 1.33/1.69 .
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z ), Y ) ), hBOOL(
% 1.33/1.69 hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) ), hAPP( hAPP
% 1.33/1.69 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) ), hAPP( hAPP
% 1.33/1.69 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ), hBOOL
% 1.33/1.69 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z ), Y ) ) }
% 1.33/1.69 .
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z ), Y ) ), hBOOL(
% 1.33/1.69 hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) ), hAPP( hAPP
% 1.33/1.69 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.33/1.69 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 1.33/1.69 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.33/1.69 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 1.33/1.69 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 1.33/1.69 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 1.33/1.69 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.33/1.69 X, Y, Z ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, hAPP(
% 1.33/1.69 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 1.33/1.69 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.33/1.69 tc_Int_Oint, Z, Y ), X ) }.
% 1.33/1.69 { hAPP( c_RealDef_Oreal( tc_Nat_Onat ), c_Nat_OSuc(
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) =
% 1.33/1.69 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 1.33/1.69 tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 1.33/1.69 tc_Nat_Onat, Y, X ), Y ) }.
% 1.33/1.69 { hAPP( c_Int_Onat, c_Groups_Oabs__class_Oabs( tc_Int_Oint, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) ) = hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( c_Int_Onat,
% 1.33/1.69 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ) ), hAPP( c_Int_Onat,
% 1.33/1.69 c_Groups_Oabs__class_Oabs( tc_Int_Oint, X ) ) ) }.
% 1.33/1.69 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Odegree( X,
% 1.33/1.69 c_Polynomial_Osynthetic__div( X, Z, Y ) ) = c_Groups_Ominus__class_Ominus
% 1.33/1.69 ( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Groups_Oone__class_Oone(
% 1.33/1.69 tc_Nat_Onat ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.33/1.69 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 1.33/1.69 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Z ) ), Y ), hAPP( hAPP
% 1.33/1.69 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP(
% 1.33/1.69 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Z ) ), X ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), hAPP( c_Int_Onat,
% 1.33/1.69 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) =
% 1.33/1.69 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP(
% 1.33/1.69 c_Int_Onat, X ) ), hAPP( c_Int_Onat, Y ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( c_Int_Onat, X ) ),
% 1.33/1.69 hAPP( c_Int_Onat, Y ) ) = hAPP( c_Int_Onat, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 1.33/1.69 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 1.33/1.69 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = X }.
% 1.33/1.69 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 1.33/1.69 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.33/1.69 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 1.33/1.69 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 1.33/1.69 ( tc_Nat_Onat ) ) ) ) }.
% 1.33/1.69 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 1.33/1.69 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 1.33/1.69 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 1.33/1.69 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 1.33/1.69 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 1.33/1.69 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.33/1.69 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) }.
% 1.33/1.69 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.33/1.69 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) }.
% 1.33/1.69 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.33/1.69 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.33/1.69 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) }.
% 1.33/1.69 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) }.
% 1.33/1.69 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.33/1.69 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) }.
% 1.33/1.69 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.33/1.69 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.33/1.69 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) }.
% 1.33/1.69 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 1.33/1.69 c_Groups_Oone__class_Oone( X ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 1.33/1.69 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 1.33/1.69 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__idom( X ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 1.33/1.69 c_Groups_Oabs__class_Oabs( X, Y ) ) = hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X,
% 1.33/1.69 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.33/1.69 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.33/1.69 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.33/1.69 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.33/1.69 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.33/1.69 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.33/1.69 .
% 1.33/1.69 { ! class_Rings_Olinordered__ring( X ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.69 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.69 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ), alpha9( X
% 1.33/1.69 , Y, Z ), alpha29( X, Y, Z ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha9( X, Y, Z ), hBOOL
% 1.33/1.69 ( hAPP( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( X ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha29( X, Y, Z ), hBOOL
% 1.33/1.69 ( hAPP( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( X ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.33/1.69 { ! alpha29( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.33/1.69 Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.33/1.69 { ! alpha29( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.33/1.69 Y ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.33/1.69 ) ) ), alpha29( X, Y, Z ) }.
% 1.33/1.69 { ! alpha9( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) ), Z ) ) }.
% 1.33/1.69 { ! alpha9( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) ), Y ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.69 , Y ) ), alpha9( X, Y, Z ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) ) ), alpha10( X, Y, Z ), alpha30( X, Y,
% 1.33/1.69 Z ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha10( X, Y, Z ), hBOOL
% 1.33/1.69 ( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha30( X, Y, Z ), hBOOL
% 1.33/1.69 ( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.33/1.69 { ! alpha30( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.33/1.69 Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.33/1.69 { ! alpha30( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) ), Y ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.69 , Y ) ), alpha30( X, Y, Z ) }.
% 1.33/1.69 { ! alpha10( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) ), Z ) ) }.
% 1.33/1.69 { ! alpha10( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.33/1.69 Y ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.33/1.69 ) ) ), alpha10( X, Y, Z ) }.
% 1.33/1.69 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.69 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.69 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.33/1.69 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.69 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.33/1.69 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.69 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.33/1.69 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.33/1.69 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.33/1.69 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.33/1.69 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.69 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.33/1.69 { ! class_Rings_Oordered__semiring( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.69 , T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 1.33/1.69 { ! class_Rings_Oordered__semiring( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.69 , T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 1.33/1.69 { ! class_Rings_Oordered__comm__semiring( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.69 , T ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 1.33/1.69 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, T ), c_Groups_Ozero__class_Ozero( X
% 1.33/1.69 ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) ) }.
% 1.33/1.69 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, T ), c_Groups_Ozero__class_Ozero( X
% 1.33/1.69 ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) ) }.
% 1.33/1.69 { ! class_Rings_Oordered__semiring( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.69 , Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) ), U ) ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 1.33/1.69 { ! class_Rings_Oordered__semiring( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.69 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) ), U ) ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 1.33/1.69 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.69 , Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) ), Y ) ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.69 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.33/1.69 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, Z ), c_Groups_Ozero__class_Ozero( X
% 1.33/1.69 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ),
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.69 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.33/1.69 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.69 , Z ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y ),
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.33/1.69 { ! class_Rings_Oordered__cancel__semiring( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, Z ), c_Groups_Ozero__class_Ozero( X
% 1.33/1.69 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) ), Y ) ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 1.33/1.69 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha11( X, Y, Z, T ),
% 1.33/1.69 alpha31( X, Y, Z, T ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha11( X, Y, Z, T ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha31( X, Y, Z, T ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.33/1.69 { ! alpha31( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.33/1.69 { ! alpha31( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.69 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha31( X, Y, Z, T ) }.
% 1.33/1.69 { ! alpha11( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.33/1.69 { ! alpha11( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.33/1.69 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha11( X, Y, Z, T ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha12( X, Y, Z, T ),
% 1.33/1.69 alpha32( X, Y, Z, T ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha12( X, Y, Z, T ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha32( X, Y, Z, T ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.33/1.69 { ! alpha32( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.33/1.69 { ! alpha32( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.69 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha32( X, Y, Z, T ) }.
% 1.33/1.69 { ! alpha12( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 1.33/1.69 { ! alpha12( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 1.33/1.69 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha12( X, Y, Z, T ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.33/1.69 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.33/1.69 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 1.33/1.69 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.33/1.69 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.33/1.69 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.33/1.69 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.33/1.69 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.33/1.69 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.69 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( X ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.33/1.69 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.69 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( X ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.33/1.69 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.33/1.69 .
% 1.33/1.69 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.33/1.69 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 1.33/1.69 .
% 1.33/1.69 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.33/1.69 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.33/1.69 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 1.33/1.69 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.33/1.69 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.33/1.69 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.33/1.69 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( X ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.33/1.69 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.69 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.33/1.69 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.33/1.69 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.33/1.69 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 1.33/1.69 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.33/1.69 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.33/1.69 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.33/1.69 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.33/1.69 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.33/1.69 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.33/1.69 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.33/1.69 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.33/1.69 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.33/1.69 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.33/1.69 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.33/1.69 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 1.33/1.69 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semidom( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ) ),
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semidom( X ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.69 , c_Groups_Oone__class_Oone( X ) ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.33/1.69 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 1.33/1.69 .
% 1.33/1.69 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.33/1.69 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.33/1.69 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.33/1.69 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 1.33/1.69 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.33/1.69 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), ! c_Orderings_Oord__class_Oless
% 1.33/1.69 ( X, c_Groups_Oabs__class_Oabs( X, U ), T ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 1.33/1.69 c_Groups_Oabs__class_Oabs( X, U ) ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.33/1.69 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.33/1.69 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.33/1.69 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.33/1.69 tc_Nat_Onat ), X ), Y ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 1.33/1.69 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 1.33/1.69 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.33/1.69 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 1.33/1.69 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.33/1.69 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.33/1.69 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.33/1.69 { Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.33/1.69 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 1.33/1.69 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.33/1.69 ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.33/1.69 ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ), hBOOL(
% 1.33/1.69 hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.33/1.69 ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, Z ), T ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.33/1.69 ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), T ) ), hBOOL(
% 1.33/1.69 hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.33/1.69 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ), Y ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.69 , U ) ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.33/1.69 ( X, U, T ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.69 , U ) ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, Z, Y ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.69 , Z ) ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero
% 1.33/1.69 ( X ), U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 1.33/1.69 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.69 , U ) ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 1.33/1.69 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.33/1.69 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.69 , Z ) ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.69 , Z ) ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 1.33/1.69 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.33/1.69 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.69 , T ) ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.69 , T ) ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.33/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__semiring__strict( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.33/1.69 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.69 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, Z ), c_Groups_Oone__class_Oone( X )
% 1.33/1.69 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) ) }.
% 1.33/1.69 { ! class_Rings_Olinordered__idom( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.69 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, Z ), c_Groups_Oone__class_Oone( X )
% 1.33/1.69 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) ) }.
% 1.33/1.69 { ! class_Rings_Oordered__ring__abs( X ), alpha61( X, Z ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.69 , Y ) ), c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 1.33/1.69 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 1.33/1.69 { ! class_Rings_Oordered__ring__abs( X ), alpha61( X, Z ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.33/1.69 ) ) ), c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 1.33/1.69 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 1.33/1.69 { ! alpha61( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) ), Y ) ) }.
% 1.33/1.69 { ! alpha61( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Y
% 1.33/1.69 ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.33/1.69 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) ), Y ) ), hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.33/1.69 ) ) ), alpha61( X, Y ) }.
% 1.33/1.69 { ! class_RealVector_Oreal__normed__vector( X ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.69 c_RealVector_Onorm__class_Onorm( X, Z ) ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ),
% 1.33/1.69 c_RealVector_Onorm__class_Onorm( X, T ) ) ) ), Z =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( X ) }.
% 1.33/1.69 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ),
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ), ! hBOOL( hAPP(
% 1.33/1.69 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.69 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ) ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ),
% 1.33/1.69 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Z ) ) ) ), Y =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.33/1.69 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ), X =
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.33/1.69 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 1.33/1.69 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.69 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 1.33/1.69 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.33/1.69 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 1.33/1.69 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.33/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 1.33/1.69 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.33/1.69 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 1.33/1.69 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 1.33/1.69 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 1.33/1.69 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.33/1.69 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 1.33/1.69 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.33/1.69 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 1.33/1.69 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.33/1.69 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 1.33/1.69 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.33/1.69 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.33/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.33/1.70 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.33/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.33/1.70 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.33/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.33/1.70 = Y }.
% 1.33/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.33/1.70 = Y }.
% 1.33/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.33/1.70 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.33/1.70 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.33/1.70 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.33/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.33/1.70 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.33/1.70 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.33/1.70 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 1.33/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.33/1.70 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.33/1.70 tc_Nat_Onat ) ) = Y }.
% 1.33/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.33/1.70 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.33/1.70 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 1.33/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.33/1.70 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.33/1.70 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 1.33/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.33/1.70 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.33/1.70 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.33/1.70 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 1.33/1.70 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ) ) }.
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( c_RealDef_Oreal
% 1.33/1.70 ( tc_Nat_Onat ), skol35( X, Y ) ) ), X ) ), Y ) ) }.
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ),
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( c_RealDef_Oreal
% 1.33/1.70 ( tc_Nat_Onat ), c_Nat_OSuc( skol35( X, Y ) ) ) ), X ) ) }.
% 1.33/1.70 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol36( Z, T ) ) }.
% 1.33/1.70 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.70 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.33/1.70 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol36( X, Y ) ) ) ) }.
% 1.33/1.70 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 1.33/1.70 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 1.33/1.70 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 1.33/1.70 ) ) }.
% 1.33/1.70 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol37( Y ) ) }.
% 1.33/1.70 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.70 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.33/1.70 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 1.33/1.70 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol37( X ) ) ) ) }.
% 1.33/1.70 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol38( Z, T ) ) }.
% 1.33/1.70 { ! class_RealVector_Oreal__normed__algebra( X ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.70 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.33/1.70 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol38( X, Y ) ) ) ) }.
% 1.33/1.70 { ! class_Rings_Ocomm__semiring__0( X ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 1.33/1.70 c_Polynomial_Opcompose( X, Z, Y ) ) ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Polynomial_Odegree( X, Z
% 1.33/1.70 ) ), c_Polynomial_Odegree( X, Y ) ) ) ) }.
% 1.33/1.70 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.33/1.70 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol39( Z, Y ) ) ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), T ) ), ! hBOOL( hAPP( Y, U
% 1.33/1.70 ) ), hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus( tc_Int_Oint, U, hAPP
% 1.33/1.70 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.33/1.70 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus(
% 1.33/1.70 tc_Int_Oint, skol39( X, Y ), X ) ) ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), ! hBOOL( hAPP( Y, T
% 1.33/1.70 ) ), hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus( tc_Int_Oint, T, hAPP
% 1.33/1.70 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) ) }.
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.33/1.70 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Z,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Groups_Oplus__class_Oplus
% 1.33/1.70 ( tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint,
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, Z ) ),
% 1.33/1.70 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ) ) }.
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.33/1.70 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Groups_Oplus__class_Oplus
% 1.33/1.70 ( tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint,
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ),
% 1.33/1.70 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ), Y ) }.
% 1.33/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.33/1.70 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.33/1.70 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.33/1.70 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.33/1.70 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.33/1.70 ) }.
% 1.33/1.70 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.33/1.70 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.33/1.70 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.33/1.70 ), ! U = T }.
% 1.33/1.70 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.33/1.70 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.33/1.70 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.33/1.70 ), ! Z = Y }.
% 1.33/1.70 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.33/1.70 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.33/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.33/1.70 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.33/1.70 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.33/1.70 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 1.33/1.70 ) ), Z ) }.
% 1.33/1.70 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 1.33/1.70 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.33/1.70 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 1.33/1.70 ) ), T ), Y ) }.
% 1.33/1.70 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.33/1.70 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.33/1.70 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.33/1.70 ), U = Z, T = Y }.
% 1.33/1.70 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.33/1.70 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.33/1.70 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.33/1.70 ) }.
% 1.33/1.70 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.33/1.70 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.33/1.70 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.33/1.70 ) }.
% 1.33/1.70 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.33/1.70 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.33/1.70 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.33/1.70 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.33/1.70 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.33/1.70 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.33/1.70 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.33/1.70 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.33/1.70 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.33/1.70 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.33/1.70 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 1.33/1.70 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 1.33/1.70 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 1.33/1.70 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 1.33/1.70 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.33/1.70 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 1.33/1.70 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 1.33/1.70 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 1.33/1.70 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.33/1.70 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.33/1.70 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.33/1.70 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 1.33/1.70 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 1.33/1.70 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 1.33/1.70 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.33/1.70 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.33/1.70 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 1.33/1.70 c_Groups_Ozero__class_Ozero( X ) }.
% 1.33/1.70 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.33/1.70 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 1.33/1.70 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.33/1.70 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.33/1.70 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.33/1.70 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.33/1.70 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.33/1.70 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.33/1.70 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.33/1.70 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.33/1.70 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.33/1.70 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.33/1.70 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.33/1.70 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.33/1.70 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.33/1.70 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.33/1.70 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.33/1.70 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 1.33/1.70 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.33/1.70 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.33/1.70 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.33/1.70 ( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T
% 1.33/1.70 , Z ) ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.33/1.70 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.33/1.70 ( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z
% 1.33/1.70 , T ) ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.33/1.70 { ! class_Groups_Oordered__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.33/1.70 U ) ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) ) }.
% 1.33/1.70 { ! class_Groups_Oordered__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.33/1.70 Z ) ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) ) }.
% 1.33/1.70 { ! class_Groups_Oordered__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.33/1.70 T ) ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) ) }.
% 1.33/1.70 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.33/1.70 ( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T
% 1.33/1.70 , Z ) ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ) }.
% 1.33/1.70 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.33/1.70 ( c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.33/1.70 Z ) ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) ) }.
% 1.33/1.70 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.33/1.70 ( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T
% 1.33/1.70 , Z ) ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ) }.
% 1.33/1.70 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), ! hBOOL( hAPP
% 1.33/1.70 ( c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.33/1.70 Z ) ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) ) }.
% 1.33/1.70 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.33/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.33/1.70 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 1.33/1.70 ( X, Z, Y ) }.
% 1.33/1.70 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.33/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 1.33/1.70 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 1.33/1.70 ( X, Z, Y ) }.
% 1.33/1.70 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.33/1.70 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.33/1.70 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 1.33/1.70 , T ) ) }.
% 1.33/1.70 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.33/1.70 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.33/1.70 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.33/1.70 , T, Y ) ) }.
% 1.33/1.70 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.33/1.70 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.33/1.70 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 1.33/1.70 , Y, T ) ) }.
% 1.33/1.70 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.33/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.33/1.70 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 1.33/1.70 ( X, Z, Y ) }.
% 1.33/1.70 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.33/1.70 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.33/1.70 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.33/1.70 , T, Y ) ) }.
% 1.33/1.70 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.33/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.33/1.70 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 1.33/1.70 ( X, T, Y ) }.
% 1.33/1.70 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.33/1.70 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 1.33/1.70 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.33/1.70 , Y, Z ) ) }.
% 1.33/1.70 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 1.33/1.70 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus(
% 1.33/1.70 X, U, Z ), c_Groups_Ominus__class_Ominus( X, T, Y ) ) }.
% 1.33/1.70 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 1.33/1.70 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.33/1.70 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 1.33/1.70 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 1.33/1.70 ( tc_Int_Oint ) ) = X }.
% 1.33/1.70 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.33/1.70 tc_Int_Oint ), X ) = X }.
% 1.33/1.70 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.33/1.70 c_Groups_Oabs__class_Oabs( X, c_Groups_Oplus__class_Oplus( X,
% 1.33/1.70 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ) )
% 1.33/1.70 = c_Groups_Oplus__class_Oplus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 1.33/1.70 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 1.33/1.70 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) ) }.
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.33/1.70 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 1.33/1.70 .
% 1.33/1.70 { ! class_RealVector_Oreal__normed__vector( X ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.70 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 1.33/1.70 ) ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.33/1.70 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.33/1.70 ( X, Y ) ) ) ) }.
% 1.33/1.70 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.70 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.70 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.70 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, U
% 1.33/1.70 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, T ) ) }.
% 1.33/1.70 { ! class_Rings_Osemiring__1( X ), hAPP( c_Nat_Osemiring__1__class_Oof__nat
% 1.33/1.70 ( X ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ) =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, hAPP( c_Nat_Osemiring__1__class_Oof__nat
% 1.33/1.70 ( X ), Z ), hAPP( c_Nat_Osemiring__1__class_Oof__nat( X ), Y ) ) }.
% 1.33/1.70 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 1.33/1.70 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 1.33/1.70 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 1.33/1.70 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.33/1.70 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 1.33/1.70 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.33/1.70 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.33/1.70 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.33/1.70 T, Y ), Z = Y }.
% 1.33/1.70 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.33/1.70 T, Y ) }.
% 1.33/1.70 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.33/1.70 Y, Z ), T = Y }.
% 1.33/1.70 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.33/1.70 Y, Z ) }.
% 1.33/1.70 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.33/1.70 T, Y ), Z = Y }.
% 1.33/1.70 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.33/1.70 T, Y ), Z = Y }.
% 1.33/1.70 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 1.33/1.70 Y, T ), Z = Y }.
% 1.33/1.70 { ! class_RealVector_Oreal__normed__vector( X ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.70 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 1.33/1.70 , Y ) ) ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.33/1.70 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, U,
% 1.33/1.70 Z ) ), c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 1.33/1.70 ( X, T, Y ) ) ) ) ) }.
% 1.33/1.70 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.70 , c_Groups_Oplus__class_Oplus( X, Y, Y ) ) ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.70 , Y ) ) }.
% 1.33/1.70 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.70 , Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Oplus__class_Oplus( X, Y, Y
% 1.33/1.70 ) ) ) }.
% 1.33/1.70 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 1.33/1.70 Y ) ), c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.33/1.70 ) ) ) }.
% 1.33/1.70 { ! class_Groups_Olinordered__ab__group__add( X ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.33/1.70 ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Groups_Ozero__class_Ozero( X
% 1.33/1.70 ) ) ) }.
% 1.33/1.70 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.70 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.70 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) ) }.
% 1.33/1.70 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.70 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! c_Groups_Oplus__class_Oplus
% 1.33/1.70 ( X, Y, Z ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.33/1.70 c_Groups_Ozero__class_Ozero( X ) }.
% 1.33/1.70 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.70 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! c_Groups_Oplus__class_Oplus
% 1.33/1.70 ( X, Y, Z ) = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.33/1.70 c_Groups_Ozero__class_Ozero( X ) }.
% 1.33/1.70 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.70 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), ! Y =
% 1.33/1.70 c_Groups_Ozero__class_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X )
% 1.33/1.70 , c_Groups_Oplus__class_Oplus( X, Y, Z ) = c_Groups_Ozero__class_Ozero( X
% 1.33/1.70 ) }.
% 1.33/1.70 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.70 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), Z ) )
% 1.33/1.70 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) ) }.
% 1.33/1.70 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.70 , Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), Z ) )
% 1.33/1.70 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ) }.
% 1.33/1.70 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.33/1.70 ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 1.33/1.70 c_Groups_Ozero__class_Ozero( X ) ) ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 1.33/1.70 Z ) ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.33/1.70 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.33/1.70 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.33/1.70 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 1.33/1.70 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.33/1.70 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.33/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 1.33/1.70 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.33/1.70 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.33/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.33/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 1.33/1.70 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.33/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.33/1.70 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 1.33/1.70 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.33/1.70 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.33/1.70 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.33/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.33/1.70 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.33/1.70 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.33/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.33/1.70 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.33/1.70 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.33/1.70 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.33/1.70 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.33/1.70 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.70 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.33/1.70 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.33/1.70 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.33/1.70 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 1.33/1.70 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 1.33/1.70 ) ) }.
% 1.33/1.70 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.33/1.70 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.33/1.70 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 1.33/1.70 ) ) }.
% 1.33/1.70 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.33/1.70 c_Orderings_Oord__class_Oless( X, Z, Y ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, U ), T ) ),
% 1.33/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 1.33/1.70 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.33/1.70 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), !
% 1.33/1.70 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 1.33/1.70 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 1.33/1.70 , Y, T ) ) }.
% 1.33/1.70 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.33/1.70 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.33/1.70 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 1.33/1.70 ) }.
% 1.33/1.70 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.33/1.70 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.33/1.70 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 1.33/1.70 ) }.
% 1.33/1.70 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.33/1.70 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.33/1.70 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 1.33/1.70 c_Groups_Ozero__class_Ozero( X ) }.
% 1.33/1.70 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.33/1.70 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.33/1.70 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.33/1.70 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 1.33/1.70 ) }.
% 1.33/1.70 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.33/1.70 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.33/1.70 Z ) ), U ), T ) = Y }.
% 1.33/1.70 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.33/1.70 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.33/1.70 ( X ), Z ), U ), Y ) }.
% 1.33/1.70 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.33/1.70 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.33/1.70 W ) ), U ), Y ) }.
% 1.33/1.70 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.33/1.70 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.33/1.70 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.33/1.70 ( X ), Z ), U ), Y ) }.
% 1.33/1.70 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.33/1.70 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 1.33/1.70 Z ) ), Y ) ) }.
% 1.33/1.70 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.33/1.70 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.33/1.70 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.33/1.70 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 1.33/1.70 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 1.33/1.70 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 1.33/1.70 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.33/1.70 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 1.33/1.70 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.33/1.70 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 1.33/1.70 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 1.33/1.70 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.33/1.70 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 1.33/1.70 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.33/1.70 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 1.33/1.70 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 1.33/1.70 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.33/1.70 { ! class_Groups_Oordered__ab__group__add__abs( X ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ), c_Groups_Oplus__class_Oplus(
% 1.33/1.70 X, c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 1.33/1.70 ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oplus__class_Oplus
% 1.33/1.70 ( tc_Int_Oint, X, Y ) ) ) }.
% 1.33/1.70 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.33/1.70 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T ), Z ) ),
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.33/1.70 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 1.33/1.70 .
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.33/1.70 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 1.33/1.70 = X }.
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.33/1.70 tc_Int_Oint ) ) ) }.
% 1.33/1.70 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.33/1.70 tc_Int_Oint ) ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 1.33/1.70 , X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP(
% 1.33/1.70 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), skol40( X, Y ) ) ) }.
% 1.33/1.70 { ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP(
% 1.33/1.70 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Z ) ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) ) }.
% 1.33/1.70 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.33/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.33/1.70 ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( X ) ), Z ) ), c_Orderings_Oord__class_Oless
% 1.33/1.70 ( X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.33/1.70 , Z ) ) }.
% 1.33/1.70 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.70 , Y ) ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero
% 1.33/1.70 ( X ), Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero
% 1.33/1.70 ( X ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.33/1.70 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.33/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.33/1.70 ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), Z ) ),
% 1.33/1.70 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.33/1.70 ) ) }.
% 1.33/1.70 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.70 , Y ) ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.33/1.70 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.33/1.70 ) ) }.
% 1.33/1.70 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.33/1.70 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.33/1.70 ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 1.33/1.70 c_Groups_Ozero__class_Ozero( X ) ) ), c_Orderings_Oord__class_Oless( X,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X )
% 1.33/1.70 ) }.
% 1.33/1.70 { ! class_Groups_Oordered__comm__monoid__add( X ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.33/1.70 ) ) ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X )
% 1.33/1.70 ) }.
% 1.33/1.70 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.33/1.70 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ),
% 1.33/1.70 c_Groups_Ozero__class_Ozero( X ) ) ), Z = c_Groups_Ozero__class_Ozero( X
% 1.33/1.70 ) }.
% 1.33/1.70 { ! class_Rings_Olinordered__ring__strict( X ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.33/1.70 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ),
% 1.33/1.70 c_Groups_Ozero__class_Ozero( X ) ) ), Y = c_Groups_Ozero__class_Ozero( X
% 1.33/1.70 ) }.
% 1.33/1.70 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.33/1.70 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.33/1.70 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.33/1.70 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.33/1.70 ) ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.33/1.70 { ! class_Rings_Olinordered__ring( X ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.70 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) ) }.
% 1.33/1.70 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.33/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.33/1.70 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.33/1.70 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 1.33/1.70 c_Groups_Ozero__class_Ozero( X ) }.
% 1.33/1.70 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 1.33/1.70 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.33/1.70 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.33/1.70 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 1.33/1.70 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.33/1.70 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.33/1.70 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 1.33/1.70 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.33/1.70 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.33/1.70 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.33/1.70 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.33/1.70 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 1.33/1.70 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.33/1.70 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.33/1.70 ( X ), Z ), U ), Y ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.33/1.70 ( X, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.33/1.70 Z ) ), U ), T ) ), Y ) ) }.
% 1.33/1.70 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.33/1.70 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.33/1.70 c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ) ), Y ) ), hBOOL(
% 1.33/1.70 hAPP( c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus(
% 1.33/1.70 X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.33/1.70 ( X ), Z ), U ), Y ) ) ) }.
% 1.33/1.70 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.33/1.70 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.33/1.70 ( X ), Z ), U ), Y ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq
% 1.33/1.70 ( X, T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.33/1.70 W ) ), U ), Y ) ) ) }.
% 1.33/1.70 { ! class_Rings_Oordered__ring( X ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, T ), c_Groups_Oplus__class_Oplus( X
% 1.33/1.70 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.33/1.70 c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.33/1.70 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.33/1.70 ( X ), Z ), U ), Y ) ) ) }.
% 1.33/1.70 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.33/1.70 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 1.33/1.70 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 1.33/1.70 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 1.33/1.70 ( X, Z, W ) ), U ), Y ) ) }.
% 1.33/1.70 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 1.33/1.70 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.33/1.70 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.33/1.70 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.33/1.70 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.33/1.70 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 1.33/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.33/1.70 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.33/1.70 X, W, Z ) ), U ), T ), Y ) }.
% 1.33/1.70 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.33/1.70 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 1.33/1.70 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.33/1.70 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.33/1.70 ( X ), Z ), U ), Y ) ) }.
% 1.33/1.70 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 1.33/1.70 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 1.33/1.70 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 1.33/1.70 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 1.33/1.70 .
% 1.33/1.70 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.33/1.70 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 1.33/1.70 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 1.33/1.70 ) }.
% 1.33/1.70 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.33/1.70 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 1.33/1.70 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 1.33/1.70 ) }.
% 1.33/1.70 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.33/1.70 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Y, Z ),
% 1.33/1.70 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 1.33/1.70 ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.33/1.70 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.33/1.70 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Z, Y ),
% 1.33/1.70 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 1.33/1.70 ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.33/1.70 { ! class_Groups_Oordered__ab__group__add__abs( X ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 1.33/1.70 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ), c_Groups_Oplus__class_Oplus
% 1.33/1.70 ( X, c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y )
% 1.33/1.70 ) ) ) }.
% 1.33/1.70 { ! class_Groups_Oordered__ab__group__add__abs( X ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 1.33/1.70 c_Groups_Ominus__class_Ominus( X, c_Groups_Oplus__class_Oplus( X, U, T )
% 1.33/1.70 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ) ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, c_Groups_Oabs__class_Oabs( X,
% 1.33/1.70 c_Groups_Ominus__class_Ominus( X, U, Z ) ), c_Groups_Oabs__class_Oabs( X
% 1.33/1.70 , c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) ) ) }.
% 1.33/1.70 { ! class_Rings_Osemiring__1( X ), hAPP( c_Nat_Osemiring__1__class_Oof__nat
% 1.33/1.70 ( X ), c_Nat_OSuc( Y ) ) = c_Groups_Oplus__class_Oplus( X,
% 1.33/1.70 c_Groups_Oone__class_Oone( X ), hAPP( c_Nat_Osemiring__1__class_Oof__nat
% 1.33/1.70 ( X ), Y ) ) }.
% 1.33/1.70 { ! class_RealVector_Oreal__normed__vector( X ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.33/1.70 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.33/1.70 ( X, Y ) ) ), c_RealVector_Onorm__class_Onorm( X,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ) ) }.
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.33/1.70 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.33/1.70 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.33/1.70 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.33/1.70 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.33/1.70 tc_Int_Oint ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.70 tc_Int_Oint, Y ), X ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), X ) )
% 1.33/1.70 , c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.33/1.70 tc_Int_Oint ) ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.33/1.70 tc_Int_Oint ) ) ), X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.33/1.70 X ) }.
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.33/1.70 tc_Int_Oint ) ) ), X ) ) }.
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.33/1.70 tc_Int_Oint ) ) ), X ) ) }.
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), X =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP(
% 1.33/1.70 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), c_Nat_OSuc( skol41( X
% 1.33/1.70 , Y ) ) ) ) }.
% 1.33/1.70 { ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP(
% 1.33/1.70 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), c_Nat_OSuc( Z ) ) ),
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.33/1.70 { hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), c_Nat_OSuc( X )
% 1.33/1.70 ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oone__class_Oone
% 1.33/1.70 ( tc_Int_Oint ), hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint )
% 1.33/1.70 , X ) ) }.
% 1.33/1.70 { ! class_Rings_Olinordered__semiring__1( X ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), Y ) ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, T ), Y ) ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.70 , U ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( X ) ), W ) ), ! c_Groups_Oplus__class_Oplus
% 1.33/1.70 ( X, U, W ) = c_Groups_Oone__class_Oone( X ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.33/1.70 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), W ), T ) ) ), Y ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ),
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.33/1.70 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.33/1.70 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 1.33/1.70 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.33/1.70 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.33/1.70 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), !
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.33/1.70 tc_Int_Oint ), Z ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.70 tc_Int_Oint, Z ), W ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.70 tc_Int_Oint, Y ), U ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ) ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ) ), ! hBOOL
% 1.33/1.70 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ),
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), !
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ), T ) ) }.
% 1.33/1.70 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), ! hBOOL(
% 1.33/1.70 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oplus__class_Oplus
% 1.33/1.70 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.33/1.70 Z ), Y ), X ) ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ),
% 1.33/1.70 ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), T ) ), !
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.33/1.70 tc_Int_Oint ), Z ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.70 tc_Int_Oint, Z ), W ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.70 tc_Int_Oint, U ), Y ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ) ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ) ), ! hBOOL
% 1.33/1.70 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), !
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T ), Y ) ) }.
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.33/1.70 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.33/1.70 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL(
% 1.33/1.70 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), !
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.33/1.70 tc_Int_Oint ), Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.70 tc_Int_Oint, Y ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oplus__class_Oplus
% 1.33/1.70 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.33/1.70 Z ), Y ), X ) ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ),
% 1.33/1.70 ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.33/1.70 ( tc_Int_Oint ), Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.70 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ) }.
% 1.33/1.70 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 1.33/1.70 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.33/1.70 ( X, T, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( X ) ), U ) ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.70 , W ) ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 1.33/1.70 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless( X,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.33/1.70 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 1.33/1.70 ), Y ) }.
% 1.33/1.70 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP
% 1.33/1.70 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 1.33/1.70 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.33/1.70 Y ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), c_Nat_OSuc( hAPP(
% 1.33/1.70 c_Int_Onat, X ) ) = hAPP( c_Int_Onat, c_Groups_Oplus__class_Oplus(
% 1.33/1.70 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.33/1.70 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.33/1.70 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 1.33/1.70 ( tc_Int_Oint ) ), Y ) ) }.
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.33/1.70 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.33/1.70 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 1.33/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y ),
% 1.33/1.70 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 1.33/1.70 alpha13( X, Z ) }.
% 1.33/1.70 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 1.33/1.70 alpha33( X, Y, Z ) }.
% 1.33/1.70 { ! alpha13( X, Z ), ! alpha33( X, Y, Z ), hBOOL( hAPP( Z,
% 1.33/1.70 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ) }.
% 1.33/1.70 { ! alpha33( X, Y, Z ), alpha44( X, Y, Z ) }.
% 1.33/1.70 { ! alpha33( X, Y, Z ), alpha49( X, Y, Z ) }.
% 1.33/1.70 { ! alpha44( X, Y, Z ), ! alpha49( X, Y, Z ), alpha33( X, Y, Z ) }.
% 1.33/1.70 { ! alpha49( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha53( X, Y, Z ) }.
% 1.33/1.70 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha49( X, Y, Z ) }.
% 1.33/1.70 { ! alpha53( X, Y, Z ), alpha49( X, Y, Z ) }.
% 1.33/1.70 { ! alpha53( X, Y, Z ), ! alpha56( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( Z, skol42( T, U, Z ) ) ), alpha53( X, Y, Z ) }.
% 1.33/1.70 { alpha56( X, Y, skol42( X, Y, Z ) ), alpha53( X, Y, Z ) }.
% 1.33/1.70 { ! alpha56( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.33/1.70 skol43( X, T, U ) ) }.
% 1.33/1.70 { ! alpha56( X, Y, Z ), alpha58( X, Y, Z, skol43( X, Y, Z ) ) }.
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T ), ! alpha58( X, Y, Z
% 1.33/1.70 , T ), alpha56( X, Y, Z ) }.
% 1.33/1.70 { ! alpha58( X, Y, Z, T ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.70 tc_Int_Oint, T ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.33/1.70 { ! alpha58( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.33/1.70 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 1.33/1.70 .
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T ),
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), ! Y =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha58( X,
% 1.33/1.70 Y, Z, T ) }.
% 1.33/1.70 { ! alpha44( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha50( X, Y, Z ) }.
% 1.33/1.70 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.33/1.70 tc_Int_Oint ), X ), alpha44( X, Y, Z ) }.
% 1.33/1.70 { ! alpha50( X, Y, Z ), alpha44( X, Y, Z ) }.
% 1.33/1.70 { ! alpha50( X, Y, Z ), ! alpha54( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( Z, skol44( T, U, Z ) ) ), alpha50( X, Y, Z ) }.
% 1.33/1.70 { alpha54( X, Y, skol44( X, Y, Z ) ), alpha50( X, Y, Z ) }.
% 1.33/1.70 { ! alpha54( X, Y, Z ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.70 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), skol45( T, U,
% 1.33/1.70 W ) ) ) }.
% 1.33/1.70 { ! alpha54( X, Y, Z ), alpha57( X, Y, Z, skol45( X, Y, Z ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), T ) ), ! alpha57( X, Y, Z,
% 1.33/1.70 T ), alpha54( X, Y, Z ) }.
% 1.33/1.70 { ! alpha57( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X
% 1.33/1.70 ) }.
% 1.33/1.70 { ! alpha57( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.33/1.70 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 1.33/1.70 .
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X ), ! Y =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha57( X,
% 1.33/1.70 Y, Z, T ) }.
% 1.33/1.70 { ! alpha13( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.33/1.70 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.33/1.70 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha13( X, Y ) }.
% 1.33/1.70 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), alpha13
% 1.33/1.70 ( X, Y ) }.
% 1.33/1.70 { ! T = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), alpha62( X,
% 1.33/1.70 Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), Z =
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.33/1.70 tc_Int_Oint, T, Z ) = Y }.
% 1.33/1.70 { ! T = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), alpha62( X,
% 1.33/1.70 Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ), ! hBOOL( hAPP
% 1.33/1.70 ( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X ),
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), Z =
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.33/1.70 tc_Int_Oint, T, Z ) = Y }.
% 1.33/1.70 { ! alpha62( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 1.33/1.70 { ! alpha62( X, Y ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.70 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), !
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.33/1.70 ( tc_Int_Oint ), Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.70 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), alpha62
% 1.33/1.70 ( X, Y ) }.
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.33/1.70 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y )
% 1.33/1.70 , alpha62( X, Y ) }.
% 1.33/1.70 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.33/1.70 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Z )
% 1.33/1.70 ), Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus
% 1.33/1.70 ( X, Z, Y ), T ) }.
% 1.33/1.70 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.33/1.70 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Z )
% 1.33/1.70 ), Y ), c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus
% 1.33/1.70 ( X, Z, Y ) ) }.
% 1.33/1.70 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.33/1.70 , c_Groups_Ominus__class_Ominus( X, Z, Y ), T ), !
% 1.33/1.70 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y
% 1.33/1.70 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X,
% 1.33/1.70 c_Groups_Ominus__class_Ominus( X, T, Z ) ), Y ) }.
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.33/1.70 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol46( Z, Y ) ) ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), T ) ), ! hBOOL( hAPP( Y, U
% 1.33/1.70 ) ), hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP(
% 1.33/1.70 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.33/1.70 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus(
% 1.33/1.70 tc_Int_Oint, skol46( X, Y ), X ) ) ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z ) ), ! hBOOL( hAPP( Y, T
% 1.33/1.70 ) ), hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint, T, hAPP(
% 1.33/1.70 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) ) }.
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.33/1.70 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol47( Z, T ) ) }.
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.33/1.70 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 1.33/1.70 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol47( X, Y ) ), X ) =
% 1.33/1.70 Y }.
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.33/1.70 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), ! hAPP( hAPP(
% 1.33/1.70 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), X ) = Y, Z =
% 1.33/1.70 skol47( X, Y ) }.
% 1.33/1.70 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 1.33/1.70 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 1.33/1.70 ) ) }.
% 1.33/1.70 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 1.33/1.70 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 1.33/1.70 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ) ), X ) =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.33/1.70 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.33/1.70 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.70 , X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol48( X, Y ) ) }.
% 1.33/1.70 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 1.33/1.70 { ! c_RealDef_Opositive( X ), ! c_RealDef_Opositive( Y ),
% 1.33/1.70 c_RealDef_Opositive( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X, Y
% 1.33/1.70 ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 1.33/1.70 X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ) ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) ) }.
% 1.33/1.70 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.33/1.70 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.33/1.70 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.33/1.70 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.33/1.70 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.33/1.70 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 1.33/1.70 ( tc_Nat_Onat ) ) = X }.
% 1.33/1.70 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.33/1.70 tc_Nat_Onat ), X ) = X }.
% 1.33/1.70 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.33/1.70 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.33/1.70 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.33/1.70 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 1.33/1.70 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.33/1.70 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 1.33/1.70 , X ) }.
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.33/1.70 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 1.33/1.70 .
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.33/1.70 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 1.33/1.70 .
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.33/1.70 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 1.33/1.70 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.33/1.70 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 1.33/1.70 .
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.33/1.70 ( tc_Nat_Onat, Y, X ), X ) }.
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.33/1.70 ( tc_Nat_Onat, Y, X ), Y ) }.
% 1.33/1.70 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 1.33/1.70 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 1.33/1.70 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.33/1.70 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.33/1.70 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.33/1.70 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 1.33/1.70 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 1.33/1.70 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 1.33/1.70 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 1.33/1.70 { hAPP( c_RealDef_Oreal( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.33/1.70 tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.33/1.70 hAPP( c_RealDef_Oreal( tc_Nat_Onat ), Y ), hAPP( c_RealDef_Oreal(
% 1.33/1.70 tc_Nat_Onat ), X ) ) }.
% 1.33/1.70 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.70 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ) ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.33/1.70 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 1.33/1.70 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) ) }.
% 1.33/1.70 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.33/1.70 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.33/1.70 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 1.33/1.70 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.33/1.70 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 1.33/1.70 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.33/1.70 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.33/1.70 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 1.33/1.70 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.33/1.70 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 1.33/1.70 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.33/1.70 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.33/1.70 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.33/1.70 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.33/1.70 tc_Nat_Onat, Y, X ), Y ) = X }.
% 1.33/1.70 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.33/1.70 tc_Nat_Onat, Y, X ), X ) = Y }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.70 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.70 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ), X ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ), X ) ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.70 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), Z )
% 1.33/1.70 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ) ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.70 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.70 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.70 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.70 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.70 , X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol49( X, Y ) ) }.
% 1.33/1.70 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) ) }.
% 1.33/1.70 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.33/1.70 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 1.33/1.70 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.33/1.70 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.33/1.70 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 1.33/1.70 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 1.33/1.70 tc_Nat_Onat, Z, Y ) ) }.
% 1.33/1.70 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.33/1.70 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 1.33/1.70 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.33/1.70 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.33/1.70 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.33/1.70 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha14( X, Y ), alpha34( X
% 1.33/1.70 , Y ) }.
% 1.33/1.70 { ! alpha14( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.33/1.70 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.33/1.70 { ! alpha34( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.33/1.70 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.33/1.70 { ! alpha34( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.33/1.70 { ! alpha34( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.33/1.70 tc_Nat_Onat ) ) }.
% 1.33/1.70 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha34( X, Y ) }.
% 1.33/1.70 { ! alpha14( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.33/1.70 tc_Nat_Onat ) ) }.
% 1.33/1.70 { ! alpha14( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.33/1.70 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha14( X, Y ) }.
% 1.33/1.70 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha15( X, Y ),
% 1.33/1.70 alpha35( X, Y ) }.
% 1.33/1.70 { ! alpha15( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.33/1.70 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 1.33/1.70 { ! alpha35( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.33/1.70 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 1.33/1.70 { ! alpha35( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.33/1.70 { ! alpha35( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.33/1.70 tc_Nat_Onat ) ) }.
% 1.33/1.70 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha35( X, Y ) }.
% 1.33/1.70 { ! alpha15( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.33/1.70 tc_Nat_Onat ) ) }.
% 1.33/1.70 { ! alpha15( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.33/1.70 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha15( X, Y ) }.
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.33/1.70 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.33/1.70 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.33/1.70 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.33/1.70 tc_Nat_Onat, Y, X ) ) }.
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.33/1.70 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.33/1.70 tc_Nat_Onat, Y, X ) ) }.
% 1.33/1.70 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.33/1.70 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.33/1.70 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol50( X, Y ) ) ) }.
% 1.33/1.70 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.33/1.70 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 1.33/1.70 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.33/1.70 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.33/1.70 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 1.33/1.70 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.33/1.70 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 1.33/1.70 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.33/1.70 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.33/1.70 tc_Nat_Onat, Z, X ), Y ) }.
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.33/1.70 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 1.33/1.70 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 1.33/1.70 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.33/1.70 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.33/1.70 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.33/1.70 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 1.33/1.70 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.33/1.70 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 1.33/1.70 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 1.33/1.70 tc_Polynomial_Opoly( X ), Y, Z ) ) = c_Polynomial_Odegree( X, Y ) }.
% 1.33/1.70 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.33/1.70 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 1.33/1.70 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 1.33/1.70 tc_Polynomial_Opoly( X ), Z, Y ) ) = c_Polynomial_Odegree( X, Y ) }.
% 1.33/1.70 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.33/1.70 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 1.33/1.70 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 1.33/1.70 X, c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }
% 1.33/1.70 .
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.70 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.33/1.70 tc_Nat_Onat, Z, Y ), X ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) ), hBOOL( hAPP
% 1.33/1.70 ( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.70 , hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ),
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.33/1.70 tc_Nat_Onat, X, Z ), Y ) ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.70 , c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.70 , c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.33/1.70 tc_Nat_Onat, Z, X ), Y ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.70 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ),
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.70 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z ),
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.70 , c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.33/1.70 ( tc_Nat_Onat, X, Y ), Y ) = X }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.70 , ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.70 , ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.70 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.33/1.70 ( tc_Nat_Onat, Z, X ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z
% 1.33/1.70 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.70 , c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.33/1.70 ( tc_Nat_Onat, X, Y ), Z ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ), Y ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.70 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.33/1.70 ( tc_Nat_Onat, X, Z ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Z ) }.
% 1.33/1.70 { ! class_Groups_Ocomm__monoid__add( X ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 1.33/1.70 Z ) ), Y ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.70 tc_Nat_Onat, c_Polynomial_Odegree( X, T ) ), Y ) ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, T ) ) ), Y ) )
% 1.33/1.70 }.
% 1.33/1.70 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP(
% 1.33/1.70 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ), hAPP(
% 1.33/1.70 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) = hAPP(
% 1.33/1.70 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.33/1.70 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP(
% 1.33/1.70 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ), hAPP(
% 1.33/1.70 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) = hAPP(
% 1.33/1.70 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.33/1.70 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP(
% 1.33/1.70 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Z ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP(
% 1.33/1.70 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ), X ) ) =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP(
% 1.33/1.70 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) }.
% 1.33/1.70 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.33/1.70 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.33/1.70 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 1.33/1.70 { ! class_RealVector_Oreal__normed__vector( X ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.70 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 1.33/1.70 Y ) ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.33/1.70 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.33/1.70 ( X, Y ) ) ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.33/1.70 , alpha16( X, Y, Z ) }.
% 1.33/1.70 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.33/1.70 , alpha36( X, Y, Z ) }.
% 1.33/1.70 { ! alpha16( X, Y, Z ), ! alpha36( X, Y, Z ), hBOOL( hAPP( Z,
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.33/1.70 { ! alpha36( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.33/1.70 T ), hBOOL( hAPP( Z, T ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( Z, skol51( T, U, Z ) ) ), alpha36( X, Y, Z ) }.
% 1.33/1.70 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol51( X, Y, Z ) ),
% 1.33/1.70 alpha36( X, Y, Z ) }.
% 1.33/1.70 { ! alpha16( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 1.33/1.70 ), hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.33/1.70 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha16( X, Y, Z ) }
% 1.33/1.70 .
% 1.33/1.70 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha16
% 1.33/1.70 ( X, Y, Z ) }.
% 1.33/1.70 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.33/1.70 , ! alpha17( X, Y, Z ) }.
% 1.33/1.70 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.33/1.70 , ! alpha37( X, Y, Z ) }.
% 1.33/1.70 { alpha17( X, Y, Z ), alpha37( X, Y, Z ), hBOOL( hAPP( Z,
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.33/1.70 { ! alpha37( X, Y, Z ), ! hBOOL( hAPP( Z, skol52( T, U, Z ) ) ) }.
% 1.33/1.70 { ! alpha37( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.33/1.70 skol52( X, Y, Z ) ) }.
% 1.33/1.70 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 1.33/1.70 ) ), alpha37( X, Y, Z ) }.
% 1.33/1.70 { ! alpha17( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 1.33/1.70 }.
% 1.33/1.70 { ! alpha17( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 1.33/1.70 tc_Nat_Onat ) ) ) }.
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha17( X, Y, Z ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.70 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc(
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Z ) =
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.70 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, c_Nat_OSuc(
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) =
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.33/1.70 tc_Nat_Onat, Z, Y ), c_Nat_OSuc( X ) ) }.
% 1.33/1.70 { hAPP( c_RealDef_Oreal( tc_Nat_Onat ), c_Nat_OSuc( X ) ) =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( c_RealDef_Oreal(
% 1.33/1.70 tc_Nat_Onat ), X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.70 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) ), hBOOL(
% 1.33/1.70 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) ), Z ) ) }
% 1.33/1.70 .
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.70 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) ), Z ) ),
% 1.33/1.70 hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.70 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.33/1.70 ( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.33/1.70 X ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) =
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.33/1.70 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.70 , ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.70 , ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.70 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) ), hBOOL(
% 1.33/1.70 hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.70 , ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) ), hBOOL
% 1.33/1.70 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.70 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.33/1.70 ( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.33/1.70 Y ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) =
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, T,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.70 , ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ), T =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.70 , ! T = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) }.
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs
% 1.33/1.70 ( tc_RealDef_Oreal, X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 1.33/1.70 , X ) }.
% 1.33/1.70 { ! class_Rings_Ocomm__semiring__0( X ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 1.33/1.70 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z
% 1.33/1.70 ), Y ) ) ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.33/1.70 c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) ) ) ) }.
% 1.33/1.70 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.33/1.70 tc_Polynomial_Opoly( X ) ), Z = c_Groups_Ozero__class_Ozero(
% 1.33/1.70 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X, Y ),
% 1.33/1.70 c_Polynomial_Odegree( X, Z ) ) }.
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( c_RealDef_Oreal(
% 1.33/1.70 tc_Nat_Onat ), Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ),
% 1.33/1.70 hAPP( c_RealDef_Oreal( tc_Nat_Onat ), X ) ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( c_RealDef_Oreal(
% 1.33/1.70 tc_Nat_Onat ), Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ),
% 1.33/1.70 hAPP( c_RealDef_Oreal( tc_Nat_Onat ), X ) ) ),
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.33/1.70 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = X }.
% 1.33/1.70 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.33/1.70 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.70 , c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( c_RealDef_Oreal
% 1.33/1.70 ( tc_Nat_Onat ), Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP
% 1.33/1.70 ( c_RealDef_Oreal( tc_Nat_Onat ), X ), c_Groups_Oone__class_Oone(
% 1.33/1.70 tc_RealDef_Oreal ) ) ) }.
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( c_RealDef_Oreal
% 1.33/1.70 ( tc_Nat_Onat ), Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP
% 1.33/1.70 ( c_RealDef_Oreal( tc_Nat_Onat ), X ), c_Groups_Oone__class_Oone(
% 1.33/1.70 tc_RealDef_Oreal ) ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.70 tc_Nat_Onat, Y ), X ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.70 , ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.33/1.70 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.70 , ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.33/1.70 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 1.33/1.70 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.70 , ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ), X ) )
% 1.33/1.70 , ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.33/1.70 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 1.33/1.70 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 1.33/1.70 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 1.33/1.70 ( tc_RealDef_Oreal ), c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) )
% 1.33/1.70 ) }.
% 1.33/1.70 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.33/1.70 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 1.33/1.70 ( tc_Nat_Onat ) ) ), X ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ), hAPP( c_Int_Onat,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) ) =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( c_Int_Onat, X ), hAPP(
% 1.33/1.70 c_Int_Onat, Y ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y ) ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( c_Int_Onat, X ), hAPP(
% 1.33/1.70 c_Int_Onat, Y ) ) = hAPP( c_Int_Onat, c_Groups_Oplus__class_Oplus(
% 1.33/1.70 tc_Int_Oint, X, Y ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 1.33/1.70 alpha18( X, Z ) }.
% 1.33/1.70 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 1.33/1.70 alpha38( X, Y, Z ) }.
% 1.33/1.70 { ! alpha18( X, Z ), ! alpha38( X, Y, Z ), hBOOL( hAPP( Z,
% 1.33/1.70 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ) }.
% 1.33/1.70 { ! alpha38( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.33/1.70 alpha45( X, Y, Z ) }.
% 1.33/1.70 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha38( X, Y, Z ) }.
% 1.33/1.70 { ! alpha45( X, Y, Z ), alpha38( X, Y, Z ) }.
% 1.33/1.70 { ! alpha45( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, X
% 1.33/1.70 ), alpha51( X, Y, Z, T ) }.
% 1.33/1.70 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol53( X, T, U ), X ),
% 1.33/1.70 alpha45( X, Y, Z ) }.
% 1.33/1.70 { ! alpha51( X, Y, Z, skol53( X, Y, Z ) ), alpha45( X, Y, Z ) }.
% 1.33/1.70 { ! alpha51( X, Y, Z, T ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.33/1.70 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 1.33/1.70 hBOOL( hAPP( Z, U ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( Z, skol54( U, W, Z, V0 ) ) ), alpha51( X, Y, Z, T ) }.
% 1.33/1.70 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol54( X, Y, Z, T ) )
% 1.33/1.70 , T ), alpha51( X, Y, Z, T ) }.
% 1.33/1.70 { ! alpha18( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.33/1.70 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.33/1.70 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha18( X, Y ) }.
% 1.33/1.70 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha18
% 1.33/1.70 ( X, Y ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( c_RealDef_Oreal
% 1.33/1.70 ( tc_Nat_Onat ), Y ) ), X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal
% 1.33/1.70 ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 1.33/1.70 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), Y ) ) ) }.
% 1.33/1.70 { c_Int_Onat__aux( Y, X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP
% 1.33/1.70 ( c_Int_Onat, Y ), X ) }.
% 1.33/1.70 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.33/1.70 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 1.33/1.70 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ) ) ),
% 1.33/1.70 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) }.
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( c_RealDef_Oreal
% 1.33/1.70 ( tc_Nat_Onat ), Y ), X ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( c_RealDef_Oreal(
% 1.33/1.70 tc_Nat_Onat ), Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) ),
% 1.33/1.70 c_RComplete_Onatceiling( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.33/1.70 Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ),
% 1.33/1.70 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 1.33/1.70 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatceiling( X ),
% 1.33/1.70 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.33/1.70 { c_RComplete_Onatceiling( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 1.33/1.70 ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.33/1.70 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), c_RComplete_Onatceiling( X
% 1.33/1.70 ) ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 1.33/1.70 X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.33/1.70 c_RComplete_Onatceiling( Y ) ), c_RComplete_Onatceiling( X ) ) ) }.
% 1.33/1.70 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ),
% 1.33/1.70 hAPP( c_RealDef_Oreal( tc_Nat_Onat ), c_RComplete_Onatceiling( X ) ) ) )
% 1.33/1.70 }.
% 1.33/1.70 { c_RComplete_Onatceiling( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 1.33/1.70 = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.33/1.70 { c_RComplete_Onatceiling( hAPP( c_RealDef_Oreal( tc_Nat_Onat ), X ) ) = X
% 1.33/1.70 }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ),
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ),
% 1.33/1.70 c_RComplete_Onatceiling( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.33/1.70 }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 1.33/1.70 hAPP( c_RealDef_Oreal( tc_Nat_Onat ), X ) ) ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 1.33/1.70 Y ) ), X ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 1.33/1.70 X ) ), Y ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.70 tc_RealDef_Oreal, X ), hAPP( c_RealDef_Oreal( tc_Nat_Onat ), Y ) ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ), hAPP(
% 1.33/1.70 c_RealDef_Oreal( tc_Nat_Onat ), Y ) ) ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 1.33/1.70 X ) ), Y ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.33/1.70 c_RComplete_Onatceiling( X ) ), c_Groups_Oone__class_Oone( tc_Nat_Onat )
% 1.33/1.70 ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X
% 1.33/1.70 ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ),
% 1.33/1.70 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 1.33/1.70 X ) ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP
% 1.33/1.70 ( c_RealDef_Oreal( tc_Nat_Onat ), Y ) ), X ) ), c_RComplete_Onatceiling(
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, hAPP( c_RealDef_Oreal
% 1.33/1.70 ( tc_Nat_Onat ), Y ) ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.33/1.70 c_RComplete_Onatceiling( X ), Y ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ),
% 1.33/1.70 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 1.33/1.70 , hAPP( c_RealDef_Oreal( tc_Nat_Onat ), Y ) ) ) =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatceiling( X ), Y
% 1.33/1.70 ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 1.33/1.70 c_RealDef_Oreal( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus(
% 1.33/1.70 tc_Nat_Onat, skol55( X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) )
% 1.33/1.70 , X ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ),
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, hAPP( c_RealDef_Oreal
% 1.33/1.70 ( tc_Nat_Onat ), skol55( X ) ) ) }.
% 1.33/1.70 { ! c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) =
% 1.33/1.70 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ),
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.70 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, X,
% 1.33/1.70 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) ),
% 1.33/1.70 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.70 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, X,
% 1.33/1.70 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) ),
% 1.33/1.70 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.70 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, X, c_Complex_Oii ) ),
% 1.33/1.70 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.70 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, X, c_Complex_Oii ) )
% 1.33/1.70 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.33/1.70 { ! c_Complex_Oii = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.33/1.70 { ! c_Complex_Oii = c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 1.33/1.70 { X = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), Y =
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 1.33/1.70 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex
% 1.33/1.70 , c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 1.33/1.70 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), X ), hAPP( hAPP(
% 1.33/1.70 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol56( X, Y ) ), Y
% 1.33/1.70 ) ) ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.33/1.70 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 1.33/1.70 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ), skol57( X, U
% 1.33/1.70 , W, T ) ) ), ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, T ),
% 1.33/1.70 V0 ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.70 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, V0 ) ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 1.33/1.70 ( tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) )
% 1.33/1.70 ) ) }.
% 1.33/1.70 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 1.33/1.70 ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.70 c_RealVector_Onorm__class_Onorm( Y, c_Groups_Ominus__class_Ominus( Y,
% 1.33/1.70 hAPP( Z, T ), hAPP( Z, skol57( X, Y, Z, T ) ) ) ),
% 1.33/1.70 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, T ), U ) ),
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.70 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, U ) ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 1.33/1.70 ( tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) )
% 1.33/1.70 ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ),
% 1.33/1.70 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 1.33/1.70 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( X ),
% 1.33/1.70 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.33/1.70 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.33/1.70 , U = c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), T ), Y )
% 1.33/1.70 }.
% 1.33/1.70 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.33/1.70 , alpha46( X, Y, Z, T ) }.
% 1.33/1.70 { ! class_Fields_Ofield( X ), ! U = c_Groups_Oplus__class_Oplus(
% 1.33/1.70 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.33/1.70 tc_Polynomial_Opoly( X ) ), Z ), T ), Y ), ! alpha46( X, Y, Z, T ),
% 1.33/1.70 c_Polynomial_Opdivmod__rel( X, U, T, Z, Y ) }.
% 1.33/1.70 { ! alpha46( X, Y, Z, T ), alpha19( X, Z, T ) }.
% 1.33/1.70 { ! alpha46( X, Y, Z, T ), alpha39( X, Y, T ) }.
% 1.33/1.70 { ! alpha19( X, Z, T ), ! alpha39( X, Y, T ), alpha46( X, Y, Z, T ) }.
% 1.33/1.70 { ! alpha39( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 1.33/1.70 tc_Polynomial_Opoly( X ) ), alpha47( X, Y, Z ) }.
% 1.33/1.70 { ! Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha39( X
% 1.33/1.70 , Y, Z ) }.
% 1.33/1.70 { ! alpha47( X, Y, Z ), alpha39( X, Y, Z ) }.
% 1.33/1.70 { ! alpha47( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 1.33/1.70 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.33/1.70 c_Polynomial_Odegree( X, Y ), c_Polynomial_Odegree( X, Z ) ) }.
% 1.33/1.70 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha47( X
% 1.33/1.70 , Y, Z ) }.
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Y
% 1.33/1.70 ), c_Polynomial_Odegree( X, Z ) ), alpha47( X, Y, Z ) }.
% 1.33/1.70 { ! alpha19( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.33/1.70 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 1.33/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha19( X,
% 1.33/1.70 Y, Z ) }.
% 1.33/1.70 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha19( X
% 1.33/1.70 , Y, Z ) }.
% 1.33/1.70 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X, Y,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) }.
% 1.33/1.70 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.33/1.70 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Z =
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Y = T }
% 1.33/1.70 .
% 1.33/1.70 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.33/1.70 tc_Polynomial_Opoly( X ) ), ! Y = T, c_Polynomial_Opdivmod__rel( X, T,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ) }.
% 1.33/1.70 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Z =
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Y =
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.33/1.70 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.33/1.70 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opdivmod__rel( X,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ) }.
% 1.33/1.70 { c_RComplete_Onatfloor( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) )
% 1.33/1.70 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.33/1.70 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), c_RComplete_Onatfloor( X )
% 1.33/1.70 ) ) }.
% 1.33/1.70 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.33/1.70 , ! c_Polynomial_Opdivmod__rel( X, Z, V1, V0, W ),
% 1.33/1.70 c_Polynomial_Opdivmod__rel( X, U, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), V1 ), V0
% 1.33/1.70 , c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), W ), Y )
% 1.33/1.70 ) }.
% 1.33/1.70 { c_RComplete_Onatfloor( hAPP( c_RealDef_Oreal( tc_Nat_Onat ), X ) ) = X }
% 1.33/1.70 .
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 1.33/1.70 X ) ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.33/1.70 c_RComplete_Onatfloor( Y ) ), c_RComplete_Onatfloor( X ) ) ) }.
% 1.33/1.70 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, Y, U )
% 1.33/1.70 , c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), T, Z ) = Y }.
% 1.33/1.70 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, Y, U )
% 1.33/1.70 , ! c_Polynomial_Opdivmod__rel( X, T, Z, W, V0 ), Y = W }.
% 1.33/1.70 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 1.33/1.70 , ! c_Polynomial_Opdivmod__rel( X, T, Z, V0, W ), Y = W }.
% 1.33/1.70 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.33/1.70 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Z = V0 }.
% 1.33/1.70 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.33/1.70 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Y = W }.
% 1.33/1.70 { c_RComplete_Onatfloor( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 1.33/1.70 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ),
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ),
% 1.33/1.70 c_RComplete_Onatfloor( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 1.33/1.70 .
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 1.33/1.70 c_RealDef_Oreal( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ) ), X ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP
% 1.33/1.70 ( c_RealDef_Oreal( tc_Nat_Onat ), Y ) ), X ) ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ),
% 1.33/1.70 c_RComplete_Onatfloor( X ) ) ) }.
% 1.33/1.70 { ! X = hAPP( c_RealDef_Oreal( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) )
% 1.33/1.70 , c_RComplete_Onatfloor( hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.33/1.70 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP( c_Power_Opower__class_Opower
% 1.33/1.70 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ), Y ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ),
% 1.33/1.70 c_RComplete_Onatfloor( X ) ) ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 1.33/1.70 c_RealDef_Oreal( tc_Nat_Onat ), Y ) ), X ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 1.33/1.70 c_RealDef_Oreal( tc_Nat_Onat ), Y ) ), X ) ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y ),
% 1.33/1.70 c_RComplete_Onatfloor( X ) ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.33/1.70 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), c_RComplete_Onatfloor( X ) )
% 1.33/1.70 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.70 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.70 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Groups_Oone__class_Oone
% 1.33/1.70 ( tc_Nat_Onat ) ), c_RComplete_Onatfloor( X ) ) ) }.
% 1.33/1.70 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( c_RealDef_Oreal(
% 1.33/1.70 tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ), c_Groups_Oone__class_Oone(
% 1.33/1.70 tc_RealDef_Oreal ) ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP
% 1.33/1.70 ( c_RealDef_Oreal( tc_Nat_Onat ), Y ) ), X ) ), c_RComplete_Onatfloor(
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, hAPP( c_RealDef_Oreal
% 1.33/1.70 ( tc_Nat_Onat ), Y ) ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.33/1.70 c_RComplete_Onatfloor( X ), Y ) }.
% 1.33/1.70 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X,
% 1.33/1.70 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), hAPP( c_RealDef_Oreal(
% 1.33/1.70 tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), !
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, hAPP( c_RealDef_Oreal
% 1.33/1.70 ( tc_Nat_Onat ), Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.33/1.70 c_RComplete_Onatfloor( X ), Y ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_RComplete_Onatfloor( X )
% 1.33/1.70 ), c_RComplete_Onatfloor( Y ) ) ), c_RComplete_Onatfloor( hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ),
% 1.33/1.70 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 1.33/1.70 hAPP( c_RealDef_Oreal( tc_Nat_Onat ), Y ) ) ) =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( X ), Y )
% 1.33/1.70 }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( Y ),
% 1.33/1.70 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), X ) ),
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, hAPP( c_RealDef_Oreal
% 1.33/1.70 ( tc_Nat_Onat ), X ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP
% 1.33/1.70 ( c_RealDef_Oreal( tc_Nat_Onat ), Y ) ), X ) ), !
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( c_RealDef_Oreal(
% 1.33/1.70 tc_Nat_Onat ), Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ),
% 1.33/1.70 c_RComplete_Onatfloor( X ) = Y }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.70 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) ), !
% 1.33/1.70 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.33/1.70 tc_Nat_Onat ), Y ), c_RComplete_Onatfloor(
% 1.33/1.70 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X, hAPP(
% 1.33/1.70 c_RealDef_Oreal( tc_Nat_Onat ), Y ) ) ) = c_Divides_Odiv__class_Odiv(
% 1.33/1.70 tc_Nat_Onat, c_RComplete_Onatfloor( X ), Y ) }.
% 1.33/1.70 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ),
% 1.33/1.70 c_Complex_Orcis( Z, Y ) ), X ) = c_Complex_Orcis( hAPP( hAPP(
% 1.33/1.70 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( c_RealDef_Oreal
% 1.33/1.70 ( tc_Nat_Onat ), X ) ), Y ) ) }.
% 1.33/1.70 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X, Y
% 1.33/1.70 , c_Groups_Oone__class_Oone( X ) ) = Y }.
% 1.33/1.70 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 1.33/1.70 c_RealDef_Oreal( tc_Nat_Onat ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat,
% 1.33/1.70 Y, X ) ) ), c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, hAPP(
% 1.33/1.70 c_RealDef_Oreal( tc_Nat_Onat ), Y ), hAPP( c_RealDef_Oreal( tc_Nat_Onat )
% 1.33/1.70 , X ) ) ) ) }.
% 1.33/1.70 { ! class_RealVector_Oreal__normed__field( X ),
% 1.33/1.70 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T, Z
% 1.33/1.70 ), Y ) = c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide
% 1.33/1.70 ( X, T, Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.33/1.70 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.33/1.70 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 1.33/1.70 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.33/1.70 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.33/1.70 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 1.33/1.70 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.33/1.70 Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.33/1.70 { ! class_Fields_Ofield__inverse__zero( X ), !
% 1.33/1.70 class_RealVector_Oreal__normed__field( X ),
% 1.33/1.70 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Odivide( X, Z
% 1.33/1.70 , Y ) ) = c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 1.33/1.70 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.33/1.70 ( X, Y ) ) }.
% 1.33/1.70 { ! class_RealVector_Oreal__normed__field( X ),
% 1.33/1.70 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X, T,
% 1.33/1.70 Z ), Y ) = c_Groups_Ominus__class_Ominus( X,
% 1.33/1.70 c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 1.33/1.70 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.33/1.70 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ) ), alpha20( X
% 1.33/1.70 , Y ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.33/1.70 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ) ), alpha40( X
% 1.33/1.70 , Y ) }.
% 1.33/1.70 { ! alpha20( X, Y ), ! alpha40( X, Y ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.33/1.70 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ) ) }.
% 1.33/1.70 { ! alpha40( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.70 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y )
% 1.33/1.70 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X )
% 1.33/1.70 , c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), Y ) ), alpha40( X, Y )
% 1.33/1.70 }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X ),
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ), alpha40( X, Y ) }.
% 1.33/1.70 { ! alpha20( X, Y ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.70 tc_RealDef_Oreal, Y ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) )
% 1.33/1.70 ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y ),
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) ), alpha20( X, Y ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X ) ), alpha20( X, Y )
% 1.33/1.70 }.
% 1.33/1.70 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( Z, Y ), hAPP( hAPP
% 1.33/1.70 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.33/1.70 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( Z, X ), hAPP( Z, Y
% 1.33/1.70 ) ), c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, Y ) ) ), Y ) )
% 1.33/1.70 = c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( Z, X ), hAPP(
% 1.33/1.70 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.33/1.70 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( Z, X ), hAPP( Z, Y
% 1.33/1.70 ) ), c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, Y ) ) ), X ) )
% 1.33/1.70 }.
% 1.33/1.70 { ! class_Rings_Odivision__ring( X ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), T ), c_Rings_Oinverse__class_Odivide
% 1.33/1.70 ( X, Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 1.33/1.70 { c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ) =
% 1.33/1.70 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X, Y ) }.
% 1.33/1.70 { ! class_RealVector_Oreal__normed__field( X ), Y =
% 1.33/1.70 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 1.33/1.70 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 1.33/1.70 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 1.33/1.70 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.33/1.70 ( X, Y ) ) }.
% 1.33/1.70 { ! class_RealVector_Oreal__normed__field( X ),
% 1.33/1.70 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.33/1.70 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.33/1.70 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.33/1.70 }.
% 1.33/1.70 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.33/1.70 c_Rings_Oinverse__class_Odivide( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.70 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.33/1.70 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 1.33/1.70 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X, T
% 1.33/1.70 , Z ) ), Y ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.33/1.70 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.33/1.70 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.33/1.70 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.33/1.70 hAPP( c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide
% 1.33/1.70 ( X, T, Y ) ), Z ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.33/1.70 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.33/1.70 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.33/1.70 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.33/1.70 , ! T = c_Rings_Oinverse__class_Odivide( X, Z, Y ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 1.33/1.70 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.33/1.70 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 1.33/1.70 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.33/1.70 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.33/1.70 , ! c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z, T = hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 1.33/1.70 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.33/1.70 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.33/1.70 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 1.33/1.70 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.33/1.70 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.33/1.70 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 1.33/1.70 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.33/1.70 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 1.33/1.70 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.33/1.70 { ! class_RealVector_Oreal__field( X ), c_Rings_Oinverse__class_Odivide( X
% 1.33/1.70 , c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), W ), U ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) =
% 1.33/1.70 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.33/1.70 ( X ), W ), c_Rings_Oinverse__class_Odivide( X,
% 1.33/1.70 c_Groups_Ominus__class_Ominus( X, U, Z ), Y ) ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.33/1.70 c_Groups_Ominus__class_Ominus( X, W, T ), Y ) ), Z ) ) }.
% 1.33/1.70 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.33/1.70 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), hAPP
% 1.33/1.70 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.33/1.70 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.33/1.70 c_Groups_Oone__class_Oone( X ), Z ) ), Y ) }.
% 1.33/1.70 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.33/1.70 , ! c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 1.33/1.70 c_Groups_Oone__class_Oone( X ), Z = Y }.
% 1.33/1.70 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.33/1.70 , ! Z = Y, c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 1.33/1.70 c_Groups_Oone__class_Oone( X ) }.
% 1.33/1.70 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.33/1.70 , c_Rings_Oinverse__class_Odivide( X, Y, Y ) = c_Groups_Oone__class_Oone
% 1.33/1.70 ( X ) }.
% 1.33/1.70 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 1.33/1.70 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 1.33/1.70 Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.33/1.70 { ! class_Rings_Odivision__ring__inverse__zero( X ), Y =
% 1.33/1.70 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 1.33/1.70 Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.33/1.70 { c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, c_Complex_Orcis( Y
% 1.33/1.70 , X ) ) = c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ) }.
% 1.33/1.70 { c_Complex_Orcis( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) =
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.33/1.70 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! hBOOL
% 1.33/1.70 ( hAPP( c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T ), Z ) ), hAPP
% 1.33/1.70 ( hAPP( c_Power_Opower__class_Opower( X ), Y ),
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, T ) ) =
% 1.33/1.70 c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.33/1.70 c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 1.33/1.70 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.33/1.70 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.33/1.70 c_Complex_Orcis( T, Z ) ), c_Complex_Orcis( Y, X ) ) = c_Complex_Orcis(
% 1.33/1.70 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), T ), Y ),
% 1.33/1.70 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 1.33/1.70 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.33/1.70 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, hAPP( c_RealDef_Oreal
% 1.33/1.70 ( tc_Nat_Onat ), Y ), hAPP( c_RealDef_Oreal( tc_Nat_Onat ), X ) ), hAPP(
% 1.33/1.70 c_RealDef_Oreal( tc_Nat_Onat ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat,
% 1.33/1.70 Y, X ) ) ) ) ) }.
% 1.33/1.70 { hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.33/1.70 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.33/1.70 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, hAPP( c_RealDef_Oreal
% 1.33/1.70 ( tc_Nat_Onat ), Y ), hAPP( c_RealDef_Oreal( tc_Nat_Onat ), X ) ), hAPP(
% 1.33/1.70 c_RealDef_Oreal( tc_Nat_Onat ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat,
% 1.33/1.70 Y, X ) ) ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) }.
% 1.33/1.70 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, T ),
% 1.33/1.70 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) ), alpha41( X, Y, Z, T ) }.
% 1.33/1.70 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, T ),
% 1.33/1.70 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) ), alpha48( X, Y, Z, T ) }.
% 1.33/1.70 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha41( X, Y, Z
% 1.33/1.70 , T ), ! alpha48( X, Y, Z, T ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, T ),
% 1.33/1.70 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) ) }.
% 1.33/1.70 { ! alpha48( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( X ), Y ), alpha52( X, Y, Z, T ) }.
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.33/1.70 , alpha48( X, Y, Z, T ) }.
% 1.33/1.70 { ! alpha52( X, Y, Z, T ), alpha48( X, Y, Z, T ) }.
% 1.33/1.70 { ! alpha52( X, Y, Z, T ), alpha55( X, Y, Z, T ) }.
% 1.33/1.70 { ! alpha52( X, Y, Z, T ), alpha21( X, Y, T ) }.
% 1.33/1.70 { ! alpha55( X, Y, Z, T ), ! alpha21( X, Y, T ), alpha52( X, Y, Z, T ) }.
% 1.33/1.70 { ! alpha55( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( X ) ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 1.33/1.70 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.33/1.70 alpha55( X, Y, Z, T ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ), hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), alpha55( X, Y, Z, T ) }
% 1.33/1.70 .
% 1.33/1.70 { ! alpha41( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( X ), Y ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) ) }.
% 1.33/1.70 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.33/1.70 alpha41( X, Y, Z, T ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.33/1.70 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) ), alpha41( X, Y, Z,
% 1.33/1.70 T ) }.
% 1.33/1.70 { ! alpha21( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.33/1.70 c_Groups_Ozero__class_Ozero( X ) ), hBOOL( hAPP(
% 1.33/1.70 c_Orderings_Oord__class_Oless__eq( X, Z ), c_Groups_Ozero__class_Ozero( X
% 1.33/1.70 ) ) ) }.
% 1.33/1.70 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 1.33/1.70 , alpha21( X, Y, Z ) }.
% 1.33/1.70 { ! hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq( X, Z ),
% 1.33/1.70 c_Groups_Ozero__class_Ozero( X ) ) ), alpha21( X, Y, Z ) }.
% 1.33/1.70 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.33/1.70 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 1.33/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { class_Groups_Ocancel__comm__monoid__add( tc_Complex_Ocomplex ) }.
% 1.33/1.70 { class_Rings_Ocomm__ring( tc_Complex_Ocomplex ) }.
% 1.33/1.70 { class_Groups_Ocancel__comm__monoid__add( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Rings_Ocomm__ring( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 1.33/1.70 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 1.33/1.70 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 1.33/1.70 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 1.33/1.70 ) ) }.
% 1.33/1.70 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 1.33/1.70 .
% 1.33/1.70 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 1.33/1.70 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.33/1.70 tc_Int_Oint ) }.
% 1.33/1.70 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.33/1.70 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 1.33/1.70 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 1.33/1.70 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 1.33/1.70 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 1.33/1.70 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 1.33/1.70 { class_Groups_Oordered__ab__group__add__abs( tc_Int_Oint ) }.
% 1.33/1.70 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 1.33/1.70 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 1.33/1.70 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.33/1.70 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 1.33/1.70 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 1.33/1.70 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 1.33/1.70 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 1.33/1.70 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 1.33/1.70 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 1.33/1.70 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 1.33/1.70 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 1.33/1.70 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 1.33/1.70 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 1.33/1.70 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 1.33/1.70 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 1.33/1.70 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 1.33/1.70 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 1.33/1.70 { class_Rings_Oordered__ring__abs( tc_Int_Oint ) }.
% 1.33/1.70 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 1.33/1.70 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 1.33/1.70 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 1.33/1.70 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 1.33/1.70 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 1.33/1.70 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 1.33/1.70 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 1.33/1.70 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 1.33/1.70 { class_Nat_Osemiring__char__0( tc_Int_Oint ) }.
% 1.33/1.70 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 1.33/1.70 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 1.33/1.70 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 1.33/1.70 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 1.33/1.70 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 1.33/1.70 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 1.33/1.70 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 1.33/1.70 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 1.33/1.70 { class_Rings_Osemiring__1( tc_Int_Oint ) }.
% 1.33/1.70 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 1.33/1.70 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 1.33/1.70 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 1.33/1.70 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 1.33/1.70 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 1.33/1.70 { class_Orderings_Oord( tc_Int_Oint ) }.
% 1.33/1.70 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 1.33/1.70 { class_Power_Opower( tc_Int_Oint ) }.
% 1.33/1.70 { class_Groups_Ozero( tc_Int_Oint ) }.
% 1.33/1.70 { class_Rings_Oring( tc_Int_Oint ) }.
% 1.33/1.70 { class_Rings_Oidom( tc_Int_Oint ) }.
% 1.33/1.70 { class_Groups_Oone( tc_Int_Oint ) }.
% 1.33/1.70 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.33/1.70 tc_Nat_Onat ) }.
% 1.33/1.70 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.33/1.70 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 1.33/1.70 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 1.33/1.70 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 1.33/1.70 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.33/1.70 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 1.33/1.70 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.33/1.70 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 1.33/1.70 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 1.33/1.70 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 1.33/1.70 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 1.33/1.70 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 1.33/1.70 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 1.33/1.70 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 1.33/1.70 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 1.33/1.70 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 1.33/1.70 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 1.33/1.70 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 1.33/1.70 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 1.33/1.70 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 1.33/1.70 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 1.33/1.70 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 1.33/1.70 { class_Nat_Osemiring__char__0( tc_Nat_Onat ) }.
% 1.33/1.70 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 1.33/1.70 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 1.33/1.70 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 1.33/1.70 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 1.33/1.70 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 1.33/1.70 { class_Rings_Osemiring__1( tc_Nat_Onat ) }.
% 1.33/1.70 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 1.33/1.70 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 1.33/1.70 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 1.33/1.70 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 1.33/1.70 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 1.33/1.70 { class_Power_Opower( tc_Nat_Onat ) }.
% 1.33/1.70 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 1.33/1.70 { class_Groups_Oone( tc_Nat_Onat ) }.
% 1.33/1.70 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 1.33/1.70 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 1.33/1.70 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 1.33/1.70 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.33/1.70 tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_RealDef_Oreal ) }
% 1.33/1.70 .
% 1.33/1.70 { class_Rings_Olinordered__comm__semiring__strict( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Fields_Olinordered__field__inverse__zero( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Rings_Olinordered__semiring__1__strict( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_RealVector_Oreal__normed__div__algebra( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Rings_Olinordered__semiring__strict( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Rings_Odivision__ring__inverse__zero( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_RealVector_Oreal__normed__algebra__1( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Groups_Oordered__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Groups_Oordered__ab__group__add__abs( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_RealVector_Oreal__normed__algebra( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Groups_Oordered__comm__monoid__add( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Groups_Olinordered__ab__group__add( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Groups_Ocancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Rings_Oring__1__no__zero__divisors( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Rings_Oordered__cancel__semiring( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_RealVector_Oreal__normed__vector( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Rings_Olinordered__ring__strict( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_RealVector_Oreal__normed__field( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Rings_Oring__no__zero__divisors( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Rings_Oordered__comm__semiring( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Rings_Olinordered__semiring__1( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Groups_Oordered__ab__group__add( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Groups_Ocancel__semigroup__add( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Rings_Olinordered__semiring( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Fields_Ofield__inverse__zero( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Rings_Olinordered__semidom( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Groups_Oab__semigroup__mult( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Groups_Ocomm__monoid__mult( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Groups_Oab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Rings_Oordered__semiring( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Rings_Oordered__ring__abs( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Rings_Ono__zero__divisors( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Groups_Ocomm__monoid__add( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Rings_Olinordered__ring( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Rings_Olinordered__idom( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Rings_Ocomm__semiring__1( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Rings_Ocomm__semiring__0( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_RealVector_Oreal__field( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Rings_Odivision__ring( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Rings_Ocomm__semiring( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Nat_Osemiring__char__0( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Groups_Oab__group__add( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Rings_Ozero__neq__one( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Rings_Oordered__ring( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Orderings_Opreorder( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Orderings_Olinorder( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Groups_Omonoid__mult( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Rings_Ocomm__ring__1( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Groups_Omonoid__add( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Rings_Osemiring__1( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Rings_Osemiring__0( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Groups_Ogroup__add( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Rings_Omult__zero( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Orderings_Oorder( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Rings_Osemiring( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Orderings_Oord( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Rings_Oring__1( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Fields_Ofield( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Power_Opower( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Groups_Ozero( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Rings_Oring( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Rings_Oidom( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Groups_Oone( tc_RealDef_Oreal ) }.
% 1.33/1.70 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.33/1.70 tc_Complex_Ocomplex ) }.
% 1.33/1.70 { class_RealVector_Oreal__normed__div__algebra( tc_Complex_Ocomplex ) }.
% 1.33/1.70 { class_Rings_Odivision__ring__inverse__zero( tc_Complex_Ocomplex ) }.
% 1.33/1.70 { class_RealVector_Oreal__normed__algebra__1( tc_Complex_Ocomplex ) }.
% 1.33/1.70 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 1.33/1.70 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.33/1.70 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.33/1.70 { class_RealVector_Oreal__normed__vector( tc_Complex_Ocomplex ) }.
% 1.33/1.70 { class_RealVector_Oreal__normed__field( tc_Complex_Ocomplex ) }.
% 1.33/1.70 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.33/1.70 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.33/1.70 { class_Fields_Ofield__inverse__zero( tc_Complex_Ocomplex ) }.
% 1.33/1.70 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 1.33/1.70 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 1.33/1.70 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.33/1.70 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.33/1.70 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 1.33/1.70 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 1.33/1.70 { class_Rings_Ocomm__semiring__0( tc_Complex_Ocomplex ) }.
% 1.33/1.70 { class_RealVector_Oreal__field( tc_Complex_Ocomplex ) }.
% 1.33/1.70 { class_Rings_Odivision__ring( tc_Complex_Ocomplex ) }.
% 1.33/1.70 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 1.33/1.70 { class_Nat_Osemiring__char__0( tc_Complex_Ocomplex ) }.
% 1.33/1.70 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 1.33/1.70 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 1.33/1.70 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 1.33/1.70 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 1.33/1.70 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 1.33/1.70 { class_Rings_Osemiring__1( tc_Complex_Ocomplex ) }.
% 1.33/1.70 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 1.33/1.70 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 1.33/1.70 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 1.33/1.70 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 1.33/1.70 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 1.33/1.70 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 1.33/1.70 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 1.33/1.70 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 1.33/1.70 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 1.33/1.70 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 1.33/1.70 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 1.33/1.70 { ! class_Rings_Oidom( X ),
% 1.33/1.70 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.33/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Rings_Olinordered__idom( X ),
% 1.33/1.70 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 1.33/1.70 ) ) }.
% 1.33/1.70 { ! class_Rings_Olinordered__idom( X ),
% 1.33/1.70 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 1.33/1.70 X ) ) }.
% 1.33/1.70 { ! class_Rings_Olinordered__idom( X ),
% 1.33/1.70 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 1.33/1.70 ) }.
% 1.33/1.70 { ! class_Rings_Olinordered__idom( X ),
% 1.33/1.70 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 1.33/1.70 }.
% 1.33/1.70 { ! class_Rings_Olinordered__idom( X ),
% 1.33/1.70 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Rings_Olinordered__idom( X ),
% 1.33/1.70 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Rings_Olinordered__idom( X ),
% 1.33/1.70 class_Groups_Oordered__ab__group__add__abs( tc_Polynomial_Opoly( X ) ) }
% 1.33/1.70 .
% 1.33/1.70 { ! class_Rings_Olinordered__idom( X ),
% 1.33/1.70 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Rings_Olinordered__idom( X ),
% 1.33/1.70 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.33/1.70 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 1.33/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Rings_Olinordered__idom( X ),
% 1.33/1.70 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Rings_Olinordered__idom( X ),
% 1.33/1.70 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 1.33/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Rings_Olinordered__idom( X ),
% 1.33/1.70 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Rings_Olinordered__idom( X ),
% 1.33/1.70 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Rings_Olinordered__idom( X ),
% 1.33/1.70 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.33/1.70 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 1.33/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 1.33/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 1.33/1.70 ( tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 1.33/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 1.33/1.70 ( tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 1.33/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring__abs(
% 1.33/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 1.33/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 1.33/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 1.33/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 1.33/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 1.33/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 1.33/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Fields_Ofield( X ), class_Divides_Osemiring__div(
% 1.33/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 1.33/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Rings_Olinordered__idom( X ), class_Nat_Osemiring__char__0(
% 1.33/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 1.33/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 1.33/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 1.33/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 1.33/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 1.33/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 1.33/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 1.33/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 1.33/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Osemiring__1(
% 1.33/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 1.33/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 1.33/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 1.33/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 1.33/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 1.33/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 1.33/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 1.33/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 1.33/1.70 tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.70 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 1.33/1.70 }.
% 1.33/1.70 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 1.33/1.71 ) ) }.
% 1.33/1.71 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 1.33/1.71 .
% 1.33/1.71 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 1.33/1.71 tc_Polynomial_Opoly( X ) ) }.
% 1.33/1.71 { ! c_SEQ_Osubseq( X ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.71 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol58( Z, T ) ),
% 1.33/1.71 v_thesis____ }.
% 1.33/1.71 { ! c_SEQ_Osubseq( X ), hBOOL( hAPP( c_Orderings_Oord__class_Oless__eq(
% 1.33/1.71 tc_Nat_Onat, Z ), skol77( T, U, Z ) ) ), v_thesis____ }.
% 1.33/1.71 { ! c_SEQ_Osubseq( X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.33/1.71 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.33/1.71 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, v_g____( hAPP( X,
% 1.33/1.71 skol77( X, Y, Z ) ) ), Y ) ), skol58( X, Y ) ), v_thesis____ }.
% 1.33/1.71 { ! v_thesis____ }.
% 1.33/1.71
% 1.33/1.71 *** allocated 15000 integers for clauses
% 1.33/1.71 *** allocated 22500 integers for clauses
% 1.33/1.71 *** allocated 33750 integers for clauses
% 1.33/1.71 *** allocated 50625 integers for clauses
% 1.33/1.71 *** allocated 75937 integers for clauses
% 1.33/1.71 *** allocated 113905 integers for clauses
% 1.33/1.71 percentage equality = 0.229415, percentage horn = 0.902644
% 1.33/1.71 This is a problem with some equality
% 1.33/1.71
% 1.33/1.71
% 1.33/1.71
% 1.33/1.71 Options Used:
% 1.33/1.71
% 1.33/1.71 useres = 1
% 1.33/1.71 useparamod = 1
% 1.33/1.71 useeqrefl = 1
% 1.33/1.71 useeqfact = 1
% 1.33/1.71 usefactor = 1
% 1.33/1.71 usesimpsplitting = 0
% 1.33/1.71 usesimpdemod = 5
% 1.33/1.71 usesimpres = 3
% 1.33/1.71
% 1.33/1.71 resimpinuse = 1000
% 1.33/1.71 resimpclauses = 20000
% 1.33/1.71 substype = eqrewr
% 1.33/1.71 backwardsubs = 1
% 1.33/1.71 selectoldest = 5
% 1.33/1.71
% 1.33/1.71 litorderings [0] = split
% 1.33/1.71 litorderings [1] = extend the termordering, first sorting on arguments
% 1.33/1.71
% 1.33/1.71 termordering = kbo
% 1.33/1.71
% 1.33/1.71 litapriori = 0
% 1.33/1.71 termapriori = 1
% 1.33/1.71 litaposteriori = 0
% 1.33/1.71 termaposteriori = 0
% 1.33/1.71 demodaposteriori = 0
% 1.33/1.71 ordereqreflfact = 0
% 1.33/1.71
% 1.33/1.71 litselect = negord
% 1.33/1.71
% 1.33/1.71 maxweight = 15
% 1.33/1.71 maxdepth = 30000
% 1.33/1.71 maxlength = 115
% 1.33/1.71 maxnrvars = 195
% 1.33/1.71 excuselevel = 1
% 1.33/1.71 increasemaxweight = 1
% 1.33/1.71
% 1.33/1.71 maxselected = 10000000
% 1.33/1.71 maxnrclauses = 10000000
% 1.33/1.71
% 1.33/1.71 showgenerated = 0
% 1.33/1.71 showkept = 0
% 1.33/1.71 showselected = 0
% 1.33/1.71 showdeleted = 0
% 1.33/1.71 showresimp = 1
% 1.33/1.71 showstatus = 2000
% 1.33/1.71
% 1.33/1.71 prologoutput = 0
% 1.33/1.71 nrgoals = 5000000
% 1.33/1.71 totalproof = 1
% 1.33/1.71
% 1.33/1.71 Symbols occurring in the translation:
% 1.33/1.71
% 1.33/1.71 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.33/1.71 . [1, 2] (w:1, o:221, a:1, s:1, b:0),
% 1.33/1.71 ! [4, 1] (w:0, o:117, a:1, s:1, b:0),
% 1.33/1.71 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.33/1.71 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.33/1.71 hAPP [38, 2] (w:1, o:245, a:1, s:1, b:0),
% 1.33/1.71 class_RealVector_Oreal__normed__vector [41, 1] (w:1, o:122, a:1, s:1
% 1.33/1.71 , b:0),
% 1.33/1.71 tc_RealDef_Oreal [42, 0] (w:1, o:20, a:1, s:1, b:0),
% 1.33/1.71 c_Groups_Ozero__class_Ozero [43, 1] (w:1, o:123, a:1, s:1, b:0),
% 1.33/1.71 c_RealVector_Onorm__class_Onorm [44, 2] (w:1, o:246, a:1, s:1, b:0),
% 1.33/1.71
% 1.33/1.71 c_Orderings_Oord__class_Oless [45, 3] (w:1, o:323, a:1, s:1, b:0),
% 1.33/1.71 c_SEQ_Osubseq [47, 1] (w:1, o:128, a:1, s:1, b:0),
% 1.33/1.71 tc_Nat_Onat [52, 0] (w:1, o:30, a:1, s:1, b:0),
% 1.33/1.71 c_Orderings_Oord__class_Oless__eq [53, 2] (w:1, o:248, a:1, s:1, b:0)
% 1.33/1.71 ,
% 1.33/1.71 hBOOL [54, 1] (w:1, o:129, a:1, s:1, b:0),
% 1.33/1.71 tc_Complex_Ocomplex [55, 0] (w:1, o:31, a:1, s:1, b:0),
% 1.33/1.71 v_g____ [56, 1] (w:1, o:130, a:1, s:1, b:0),
% 1.33/1.71 c_Groups_Ominus__class_Ominus [57, 3] (w:1, o:324, a:1, s:1, b:0),
% 1.33/1.71 class_Groups_Oordered__ab__group__add [61, 1] (w:1, o:134, a:1, s:1
% 1.33/1.71 , b:0),
% 1.33/1.71 class_Orderings_Opreorder [63, 1] (w:1, o:138, a:1, s:1, b:0),
% 1.33/1.71 v_r [68, 0] (w:1, o:51, a:1, s:1, b:0),
% 1.33/1.71 class_Groups_Ozero [70, 1] (w:1, o:139, a:1, s:1, b:0),
% 1.33/1.71 class_Orderings_Olinorder [72, 1] (w:1, o:140, a:1, s:1, b:0),
% 1.33/1.71 class_Orderings_Oord [74, 1] (w:1, o:136, a:1, s:1, b:0),
% 1.33/1.71 tc_fun [75, 2] (w:1, o:289, a:1, s:1, b:0),
% 1.33/1.71 class_Orderings_Oorder [77, 1] (w:1, o:137, a:1, s:1, b:0),
% 1.33/1.71 class_Groups_Oab__group__add [80, 1] (w:1, o:141, a:1, s:1, b:0),
% 1.33/1.71 class_Groups_Ogroup__add [81, 1] (w:1, o:142, a:1, s:1, b:0),
% 1.33/1.71 c_SEQ_Odecseq [84, 2] (w:1, o:290, a:1, s:1, b:0),
% 1.33/1.71 c_SEQ_Oincseq [85, 2] (w:1, o:291, a:1, s:1, b:0),
% 1.33/1.71 c_SEQ_OBseq [86, 2] (w:1, o:292, a:1, s:1, b:0),
% 1.33/1.71 c_SEQ_Omonoseq [88, 2] (w:1, o:293, a:1, s:1, b:0),
% 1.33/1.71 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [102, 2] (w:1, o:
% 1.33/1.71 294, a:1, s:1, b:0),
% 1.33/1.71 tc_Polynomial_Opoly [103, 1] (w:1, o:159, a:1, s:1, b:0),
% 1.33/1.71 c_HOL_Oequal__class_Oequal [105, 3] (w:1, o:326, a:1, s:1, b:0),
% 1.33/1.71 c_Groups_Oabs__class_Oabs [106, 2] (w:1, o:295, a:1, s:1, b:0),
% 1.33/1.71 c_RealDef_Opositive [107, 1] (w:1, o:124, a:1, s:1, b:0),
% 1.33/1.71 c_RealDef_Oreal [108, 1] (w:1, o:125, a:1, s:1, b:0),
% 1.33/1.71 class_Rings_Olinordered__semidom [111, 1] (w:1, o:162, a:1, s:1, b:0)
% 1.33/1.71 ,
% 1.33/1.71 c_Nat_Osemiring__1__class_Oof__nat [112, 1] (w:1, o:163, a:1, s:1, b:
% 1.33/1.71 0),
% 1.33/1.71 c_Power_Opower__class_Opower [114, 1] (w:1, o:164, a:1, s:1, b:0),
% 1.33/1.71 class_Rings_Oring__1__no__zero__divisors [115, 1] (w:1, o:165, a:1
% 1.33/1.71 , s:1, b:0),
% 1.33/1.71 class_Rings_Olinordered__idom [116, 1] (w:1, o:166, a:1, s:1, b:0),
% 1.33/1.71 class_Groups_Oordered__ab__group__add__abs [118, 1] (w:1, o:167, a:1
% 1.33/1.71 , s:1, b:0),
% 1.33/1.71 class_Rings_Osemiring__1 [119, 1] (w:1, o:172, a:1, s:1, b:0),
% 1.33/1.71 class_RealVector_Oreal__normed__div__algebra [120, 1] (w:1, o:173, a:
% 1.33/1.71 1, s:1, b:0),
% 1.33/1.71 class_RealVector_Oreal__normed__algebra__1 [121, 1] (w:1, o:174, a:1
% 1.33/1.71 , s:1, b:0),
% 1.33/1.71 class_Nat_Osemiring__char__0 [122, 1] (w:1, o:135, a:1, s:1, b:0),
% 1.33/1.71 class_Power_Opower [123, 1] (w:1, o:175, a:1, s:1, b:0),
% 1.33/1.71 class_Rings_Omult__zero [124, 1] (w:1, o:181, a:1, s:1, b:0),
% 1.33/1.71 class_Rings_Ono__zero__divisors [125, 1] (w:1, o:182, a:1, s:1, b:0)
% 1.33/1.71 ,
% 1.33/1.71 class_Rings_Ozero__neq__one [126, 1] (w:1, o:183, a:1, s:1, b:0),
% 1.33/1.71 class_Rings_Oring__1 [127, 1] (w:1, o:168, a:1, s:1, b:0),
% 1.33/1.71 tc_Int_Oint [128, 0] (w:1, o:94, a:1, s:1, b:0),
% 1.33/1.71 c_Nat_OSuc [129, 1] (w:1, o:184, a:1, s:1, b:0),
% 1.33/1.71 class_Rings_Osemiring__0 [139, 1] (w:1, o:171, a:1, s:1, b:0),
% 1.33/1.71 c_Nat__Transfer_Otsub [141, 2] (w:1, o:247, a:1, s:1, b:0),
% 1.33/1.71 c_Divides_Odiv__class_Odiv [142, 3] (w:1, o:327, a:1, s:1, b:0),
% 1.33/1.71 class_Divides_Osemiring__div [143, 1] (w:1, o:185, a:1, s:1, b:0),
% 1.33/1.71 c_Int_Onat [147, 0] (w:1, o:100, a:1, s:1, b:0),
% 1.33/1.71 c_Polynomial_Odegree [148, 2] (w:1, o:296, a:1, s:1, b:0),
% 1.33/1.71 c_Polynomial_Opoly__rec [149, 5] (w:1, o:397, a:1, s:1, b:0),
% 1.33/1.71 class_Fields_Ofield [150, 1] (w:1, o:131, a:1, s:1, b:0),
% 1.33/1.71 c_Nat__Transfer_Otransfer__morphism [155, 4] (w:1, o:380, a:1, s:1
% 1.33/1.71 , b:0),
% 1.33/1.71 class_Rings_Oidom [156, 1] (w:1, o:186, a:1, s:1, b:0),
% 1.33/1.71 c_Polynomial_Oorder [157, 3] (w:1, o:328, a:1, s:1, b:0),
% 1.33/1.71 class_Rings_Ocomm__semiring__0 [158, 1] (w:1, o:189, a:1, s:1, b:0),
% 1.33/1.71
% 1.33/1.71 c_Polynomial_Osynthetic__div [159, 3] (w:1, o:329, a:1, s:1, b:0),
% 1.33/1.71 c_Groups_Oone__class_Oone [160, 1] (w:1, o:190, a:1, s:1, b:0),
% 1.33/1.71 c_Groups_Otimes__class_Otimes [162, 1] (w:1, o:191, a:1, s:1, b:0),
% 1.33/1.71 class_Groups_Oab__semigroup__mult [163, 1] (w:1, o:192, a:1, s:1, b:0
% 1.33/1.71 ),
% 1.33/1.71 class_Groups_Ocomm__monoid__mult [164, 1] (w:1, o:193, a:1, s:1, b:0)
% 1.33/1.71 ,
% 1.33/1.71 class_Groups_Omonoid__mult [165, 1] (w:1, o:195, a:1, s:1, b:0),
% 1.33/1.71 class_Groups_Oone [166, 1] (w:1, o:196, a:1, s:1, b:0),
% 1.33/1.71 class_RealVector_Oreal__normed__algebra [167, 1] (w:1, o:197, a:1, s:
% 1.33/1.71 1, b:0),
% 1.33/1.71 class_Rings_Ocomm__semiring__1 [170, 1] (w:1, o:198, a:1, s:1, b:0),
% 1.33/1.71
% 1.33/1.71 class_Rings_Oring__no__zero__divisors [176, 1] (w:1, o:169, a:1, s:1
% 1.33/1.71 , b:0),
% 1.33/1.71 class_Rings_Olinordered__ring [177, 1] (w:1, o:160, a:1, s:1, b:0),
% 1.33/1.71 class_Rings_Olinordered__ring__strict [178, 1] (w:1, o:161, a:1, s:1
% 1.33/1.71 , b:0),
% 1.33/1.71 class_Rings_Oordered__cancel__semiring [179, 1] (w:1, o:199, a:1, s:1
% 1.33/1.71 , b:0),
% 1.33/1.71 class_Rings_Oordered__ring [180, 1] (w:1, o:200, a:1, s:1, b:0),
% 1.33/1.71 class_Rings_Oordered__semiring [181, 1] (w:1, o:202, a:1, s:1, b:0),
% 1.33/1.71
% 1.33/1.71 class_Rings_Oordered__comm__semiring [182, 1] (w:1, o:203, a:1, s:1
% 1.33/1.71 , b:0),
% 1.33/1.71 class_Rings_Olinordered__semiring__strict [184, 1] (w:1, o:176, a:1
% 1.33/1.71 , s:1, b:0),
% 1.33/1.71 class_Rings_Olinordered__comm__semiring__strict [185, 1] (w:1, o:177
% 1.33/1.71 , a:1, s:1, b:0),
% 1.33/1.71 class_Rings_Olinordered__semiring [186, 1] (w:1, o:178, a:1, s:1, b:0
% 1.33/1.71 ),
% 1.33/1.71 class_Rings_Oordered__ring__abs [187, 1] (w:1, o:201, a:1, s:1, b:0)
% 1.33/1.71 ,
% 1.33/1.71 c_Power_Opower_Opower [192, 3] (w:1, o:330, a:1, s:1, b:0),
% 1.33/1.71 c_Polynomial_Opcompose [197, 3] (w:1, o:331, a:1, s:1, b:0),
% 1.33/1.71 c_Groups_Oplus__class_Oplus [198, 3] (w:1, o:325, a:1, s:1, b:0),
% 1.33/1.71 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 1.33/1.71 199, 1] (w:1, o:210, a:1, s:1, b:0),
% 1.33/1.71 class_Rings_Ocomm__semiring [200, 1] (w:1, o:204, a:1, s:1, b:0),
% 1.33/1.71 class_Rings_Osemiring [202, 1] (w:1, o:205, a:1, s:1, b:0),
% 1.33/1.71 class_Groups_Olinordered__ab__group__add [203, 1] (w:1, o:194, a:1
% 1.33/1.71 , s:1, b:0),
% 1.33/1.71 class_Groups_Ocomm__monoid__add [204, 1] (w:1, o:211, a:1, s:1, b:0)
% 1.33/1.71 ,
% 1.33/1.71 class_Groups_Omonoid__add [205, 1] (w:1, o:212, a:1, s:1, b:0),
% 1.33/1.71 class_Groups_Oordered__ab__semigroup__add__imp__le [206, 1] (w:1, o:
% 1.33/1.71 213, a:1, s:1, b:0),
% 1.33/1.71 class_Groups_Oordered__ab__semigroup__add [207, 1] (w:1, o:214, a:1
% 1.33/1.71 , s:1, b:0),
% 1.33/1.71 class_Groups_Oordered__cancel__ab__semigroup__add [208, 1] (w:1, o:
% 1.33/1.71 215, a:1, s:1, b:0),
% 1.33/1.71 class_Groups_Oab__semigroup__add [209, 1] (w:1, o:216, a:1, s:1, b:0)
% 1.33/1.71 ,
% 1.33/1.71 class_Groups_Ocancel__semigroup__add [210, 1] (w:1, o:217, a:1, s:1
% 1.33/1.71 , b:0),
% 1.33/1.71 class_Groups_Ocancel__ab__semigroup__add [211, 1] (w:1, o:218, a:1
% 1.33/1.71 , s:1, b:0),
% 1.33/1.71 class_Groups_Oordered__comm__monoid__add [212, 1] (w:1, o:219, a:1
% 1.33/1.71 , s:1, b:0),
% 1.33/1.71 class_Rings_Oring [214, 1] (w:1, o:170, a:1, s:1, b:0),
% 1.33/1.71 class_Rings_Olinordered__semiring__1 [218, 1] (w:1, o:179, a:1, s:1
% 1.33/1.71 , b:0),
% 1.33/1.71 class_Rings_Olinordered__semiring__1__strict [221, 1] (w:1, o:180, a:
% 1.33/1.71 1, s:1, b:0),
% 1.33/1.71 class_Rings_Ocomm__ring__1 [222, 1] (w:1, o:187, a:1, s:1, b:0),
% 1.33/1.71 c_Int_Onat__aux [229, 2] (w:1, o:297, a:1, s:1, b:0),
% 1.33/1.71 c_RComplete_Onatceiling [230, 1] (w:1, o:126, a:1, s:1, b:0),
% 1.33/1.71 c_Complex_Oii [231, 0] (w:1, o:113, a:1, s:1, b:0),
% 1.33/1.71 c_RComplete_Onatfloor [233, 1] (w:1, o:127, a:1, s:1, b:0),
% 1.33/1.71 c_Polynomial_Opdivmod__rel [234, 5] (w:1, o:398, a:1, s:1, b:0),
% 1.33/1.71 c_Rings_Oinverse__class_Odivide [239, 3] (w:1, o:332, a:1, s:1, b:0)
% 1.33/1.71 ,
% 1.33/1.71 c_Complex_Orcis [240, 2] (w:1, o:298, a:1, s:1, b:0),
% 1.33/1.71 class_Rings_Odivision__ring [241, 1] (w:1, o:206, a:1, s:1, b:0),
% 1.33/1.71 class_RealVector_Oreal__normed__field [242, 1] (w:1, o:207, a:1, s:1
% 1.33/1.71 , b:0),
% 1.33/1.71 class_Fields_Ofield__inverse__zero [243, 1] (w:1, o:132, a:1, s:1, b:
% 1.33/1.71 0),
% 1.33/1.71 class_Rings_Odivision__ring__inverse__zero [244, 1] (w:1, o:208, a:1
% 1.33/1.71 , s:1, b:0),
% 1.33/1.71 class_RealVector_Oreal__field [246, 1] (w:1, o:209, a:1, s:1, b:0),
% 1.33/1.71 class_Fields_Olinordered__field__inverse__zero [247, 1] (w:1, o:133
% 1.33/1.71 , a:1, s:1, b:0),
% 1.33/1.71 class_Groups_Ocancel__comm__monoid__add [249, 1] (w:1, o:220, a:1, s:
% 1.33/1.71 1, b:0),
% 1.33/1.71 class_Rings_Ocomm__ring [250, 1] (w:1, o:188, a:1, s:1, b:0),
% 1.33/1.71 tc_HOL_Obool [252, 0] (w:1, o:93, a:1, s:1, b:0),
% 1.33/1.71 v_thesis____ [253, 0] (w:1, o:116, a:1, s:1, b:0),
% 1.33/1.71 alpha1 [254, 2] (w:1, o:299, a:1, s:1, b:1),
% 1.33/1.71 alpha2 [255, 3] (w:1, o:337, a:1, s:1, b:1),
% 1.33/1.71 alpha3 [256, 2] (w:1, o:306, a:1, s:1, b:1),
% 1.33/1.71 alpha4 [257, 2] (w:1, o:309, a:1, s:1, b:1),
% 1.33/1.71 alpha5 [258, 2] (w:1, o:312, a:1, s:1, b:1),
% 1.33/1.71 alpha6 [259, 2] (w:1, o:313, a:1, s:1, b:1),
% 1.33/1.71 alpha7 [260, 2] (w:1, o:317, a:1, s:1, b:1),
% 1.33/1.71 alpha8 [261, 2] (w:1, o:318, a:1, s:1, b:1),
% 1.33/1.71 alpha9 [262, 3] (w:1, o:338, a:1, s:1, b:1),
% 1.33/1.71 alpha10 [263, 3] (w:1, o:333, a:1, s:1, b:1),
% 1.33/1.71 alpha11 [264, 4] (w:1, o:381, a:1, s:1, b:1),
% 1.33/1.71 alpha12 [265, 4] (w:1, o:382, a:1, s:1, b:1),
% 1.33/1.71 alpha13 [266, 2] (w:1, o:319, a:1, s:1, b:1),
% 1.33/1.71 alpha14 [267, 2] (w:1, o:320, a:1, s:1, b:1),
% 1.33/1.71 alpha15 [268, 2] (w:1, o:321, a:1, s:1, b:1),
% 1.33/1.71 alpha16 [269, 3] (w:1, o:334, a:1, s:1, b:1),
% 1.33/1.71 alpha17 [270, 3] (w:1, o:335, a:1, s:1, b:1),
% 1.33/1.71 alpha18 [271, 2] (w:1, o:322, a:1, s:1, b:1),
% 1.33/1.71 alpha19 [272, 3] (w:1, o:336, a:1, s:1, b:1),
% 1.33/1.71 alpha20 [273, 2] (w:1, o:300, a:1, s:1, b:1),
% 1.33/1.71 alpha21 [274, 3] (w:1, o:339, a:1, s:1, b:1),
% 1.99/2.37 alpha22 [275, 2] (w:1, o:301, a:1, s:1, b:1),
% 1.99/2.37 alpha23 [276, 3] (w:1, o:340, a:1, s:1, b:1),
% 1.99/2.37 alpha24 [277, 2] (w:1, o:302, a:1, s:1, b:1),
% 1.99/2.37 alpha25 [278, 2] (w:1, o:303, a:1, s:1, b:1),
% 1.99/2.37 alpha26 [279, 2] (w:1, o:304, a:1, s:1, b:1),
% 1.99/2.37 alpha27 [280, 2] (w:1, o:305, a:1, s:1, b:1),
% 1.99/2.37 alpha28 [281, 3] (w:1, o:341, a:1, s:1, b:1),
% 1.99/2.37 alpha29 [282, 3] (w:1, o:342, a:1, s:1, b:1),
% 1.99/2.37 alpha30 [283, 3] (w:1, o:343, a:1, s:1, b:1),
% 1.99/2.37 alpha31 [284, 4] (w:1, o:383, a:1, s:1, b:1),
% 1.99/2.37 alpha32 [285, 4] (w:1, o:384, a:1, s:1, b:1),
% 1.99/2.37 alpha33 [286, 3] (w:1, o:344, a:1, s:1, b:1),
% 1.99/2.37 alpha34 [287, 2] (w:1, o:307, a:1, s:1, b:1),
% 1.99/2.37 alpha35 [288, 2] (w:1, o:308, a:1, s:1, b:1),
% 1.99/2.37 alpha36 [289, 3] (w:1, o:345, a:1, s:1, b:1),
% 1.99/2.37 alpha37 [290, 3] (w:1, o:346, a:1, s:1, b:1),
% 1.99/2.37 alpha38 [291, 3] (w:1, o:347, a:1, s:1, b:1),
% 1.99/2.37 alpha39 [292, 3] (w:1, o:348, a:1, s:1, b:1),
% 1.99/2.37 alpha40 [293, 2] (w:1, o:310, a:1, s:1, b:1),
% 1.99/2.37 alpha41 [294, 4] (w:1, o:385, a:1, s:1, b:1),
% 1.99/2.37 alpha42 [295, 2] (w:1, o:311, a:1, s:1, b:1),
% 1.99/2.37 alpha43 [296, 4] (w:1, o:386, a:1, s:1, b:1),
% 1.99/2.37 alpha44 [297, 3] (w:1, o:349, a:1, s:1, b:1),
% 1.99/2.37 alpha45 [298, 3] (w:1, o:350, a:1, s:1, b:1),
% 1.99/2.37 alpha46 [299, 4] (w:1, o:387, a:1, s:1, b:1),
% 1.99/2.37 alpha47 [300, 3] (w:1, o:351, a:1, s:1, b:1),
% 1.99/2.37 alpha48 [301, 4] (w:1, o:388, a:1, s:1, b:1),
% 1.99/2.37 alpha49 [302, 3] (w:1, o:352, a:1, s:1, b:1),
% 1.99/2.37 alpha50 [303, 3] (w:1, o:353, a:1, s:1, b:1),
% 1.99/2.37 alpha51 [304, 4] (w:1, o:389, a:1, s:1, b:1),
% 1.99/2.37 alpha52 [305, 4] (w:1, o:390, a:1, s:1, b:1),
% 1.99/2.37 alpha53 [306, 3] (w:1, o:354, a:1, s:1, b:1),
% 1.99/2.37 alpha54 [307, 3] (w:1, o:355, a:1, s:1, b:1),
% 1.99/2.37 alpha55 [308, 4] (w:1, o:391, a:1, s:1, b:1),
% 1.99/2.37 alpha56 [309, 3] (w:1, o:356, a:1, s:1, b:1),
% 1.99/2.37 alpha57 [310, 4] (w:1, o:392, a:1, s:1, b:1),
% 1.99/2.37 alpha58 [311, 4] (w:1, o:393, a:1, s:1, b:1),
% 1.99/2.37 alpha59 [312, 3] (w:1, o:357, a:1, s:1, b:1),
% 1.99/2.37 alpha60 [313, 2] (w:1, o:314, a:1, s:1, b:1),
% 1.99/2.37 alpha61 [314, 2] (w:1, o:315, a:1, s:1, b:1),
% 1.99/2.37 alpha62 [315, 2] (w:1, o:316, a:1, s:1, b:1),
% 1.99/2.37 alpha63 [316, 3] (w:1, o:358, a:1, s:1, b:1),
% 1.99/2.37 skol1 [317, 2] (w:1, o:249, a:1, s:1, b:1),
% 1.99/2.37 skol2 [318, 0] (w:1, o:18, a:1, s:1, b:1),
% 1.99/2.37 skol3 [319, 1] (w:1, o:148, a:1, s:1, b:1),
% 1.99/2.37 skol4 [320, 3] (w:1, o:360, a:1, s:1, b:1),
% 1.99/2.37 skol5 [321, 2] (w:1, o:256, a:1, s:1, b:1),
% 1.99/2.37 skol6 [322, 2] (w:1, o:260, a:1, s:1, b:1),
% 1.99/2.37 skol7 [323, 2] (w:1, o:269, a:1, s:1, b:1),
% 1.99/2.37 skol8 [324, 2] (w:1, o:271, a:1, s:1, b:1),
% 1.99/2.37 skol9 [325, 2] (w:1, o:274, a:1, s:1, b:1),
% 1.99/2.37 skol10 [326, 2] (w:1, o:275, a:1, s:1, b:1),
% 1.99/2.37 skol11 [327, 3] (w:1, o:361, a:1, s:1, b:1),
% 1.99/2.37 skol12 [328, 4] (w:1, o:394, a:1, s:1, b:1),
% 1.99/2.37 skol13 [329, 3] (w:1, o:362, a:1, s:1, b:1),
% 1.99/2.37 skol14 [330, 2] (w:1, o:276, a:1, s:1, b:1),
% 1.99/2.37 skol15 [331, 2] (w:1, o:277, a:1, s:1, b:1),
% 1.99/2.37 skol16 [332, 2] (w:1, o:278, a:1, s:1, b:1),
% 1.99/2.37 skol17 [333, 3] (w:1, o:363, a:1, s:1, b:1),
% 1.99/2.37 skol18 [334, 3] (w:1, o:364, a:1, s:1, b:1),
% 1.99/2.37 skol19 [335, 3] (w:1, o:365, a:1, s:1, b:1),
% 1.99/2.37 skol20 [336, 2] (w:1, o:279, a:1, s:1, b:1),
% 1.99/2.37 skol21 [337, 2] (w:1, o:280, a:1, s:1, b:1),
% 1.99/2.37 skol22 [338, 1] (w:1, o:143, a:1, s:1, b:1),
% 1.99/2.37 skol23 [339, 2] (w:1, o:281, a:1, s:1, b:1),
% 1.99/2.37 skol24 [340, 1] (w:1, o:144, a:1, s:1, b:1),
% 1.99/2.37 skol25 [341, 2] (w:1, o:282, a:1, s:1, b:1),
% 1.99/2.37 skol26 [342, 1] (w:1, o:145, a:1, s:1, b:1),
% 1.99/2.37 skol27 [343, 1] (w:1, o:146, a:1, s:1, b:1),
% 1.99/2.37 skol28 [344, 1] (w:1, o:147, a:1, s:1, b:1),
% 1.99/2.37 skol29 [345, 3] (w:1, o:366, a:1, s:1, b:1),
% 1.99/2.37 skol30 [346, 2] (w:1, o:283, a:1, s:1, b:1),
% 1.99/2.37 skol31 [347, 1] (w:1, o:149, a:1, s:1, b:1),
% 1.99/2.37 skol32 [348, 1] (w:1, o:150, a:1, s:1, b:1),
% 1.99/2.37 skol33 [349, 2] (w:1, o:284, a:1, s:1, b:1),
% 1.99/2.37 skol34 [350, 3] (w:1, o:359, a:1, s:1, b:1),
% 1.99/2.37 skol35 [351, 2] (w:1, o:285, a:1, s:1, b:1),
% 1.99/2.37 skol36 [352, 2] (w:1, o:286, a:1, s:1, b:1),
% 11.00/11.37 skol37 [353, 1] (w:1, o:151, a:1, s:1, b:1),
% 11.00/11.37 skol38 [354, 2] (w:1, o:287, a:1, s:1, b:1),
% 11.00/11.37 skol39 [355, 2] (w:1, o:288, a:1, s:1, b:1),
% 11.00/11.37 skol40 [356, 2] (w:1, o:250, a:1, s:1, b:1),
% 11.00/11.37 skol41 [357, 2] (w:1, o:251, a:1, s:1, b:1),
% 11.00/11.37 skol42 [358, 3] (w:1, o:367, a:1, s:1, b:1),
% 11.00/11.37 skol43 [359, 3] (w:1, o:368, a:1, s:1, b:1),
% 11.00/11.37 skol44 [360, 3] (w:1, o:369, a:1, s:1, b:1),
% 11.00/11.37 skol45 [361, 3] (w:1, o:370, a:1, s:1, b:1),
% 11.00/11.37 skol46 [362, 2] (w:1, o:252, a:1, s:1, b:1),
% 11.00/11.37 skol47 [363, 2] (w:1, o:253, a:1, s:1, b:1),
% 11.00/11.37 skol48 [364, 2] (w:1, o:254, a:1, s:1, b:1),
% 11.00/11.37 skol49 [365, 2] (w:1, o:255, a:1, s:1, b:1),
% 11.00/11.37 skol50 [366, 2] (w:1, o:257, a:1, s:1, b:1),
% 11.00/11.37 skol51 [367, 3] (w:1, o:371, a:1, s:1, b:1),
% 11.00/11.37 skol52 [368, 3] (w:1, o:372, a:1, s:1, b:1),
% 11.00/11.37 skol53 [369, 3] (w:1, o:373, a:1, s:1, b:1),
% 11.00/11.37 skol54 [370, 4] (w:1, o:395, a:1, s:1, b:1),
% 11.00/11.37 skol55 [371, 1] (w:1, o:152, a:1, s:1, b:1),
% 11.00/11.37 skol56 [372, 2] (w:1, o:258, a:1, s:1, b:1),
% 11.00/11.37 skol57 [373, 4] (w:1, o:396, a:1, s:1, b:1),
% 11.00/11.37 skol58 [374, 2] (w:1, o:259, a:1, s:1, b:1),
% 11.00/11.37 skol59 [375, 0] (w:1, o:19, a:1, s:1, b:1),
% 11.00/11.37 skol60 [376, 1] (w:1, o:153, a:1, s:1, b:1),
% 11.00/11.37 skol61 [377, 2] (w:1, o:261, a:1, s:1, b:1),
% 11.00/11.37 skol62 [378, 2] (w:1, o:262, a:1, s:1, b:1),
% 11.00/11.37 skol63 [379, 3] (w:1, o:374, a:1, s:1, b:1),
% 11.00/11.37 skol64 [380, 2] (w:1, o:263, a:1, s:1, b:1),
% 11.00/11.37 skol65 [381, 2] (w:1, o:264, a:1, s:1, b:1),
% 11.00/11.37 skol66 [382, 2] (w:1, o:265, a:1, s:1, b:1),
% 11.00/11.37 skol67 [383, 2] (w:1, o:266, a:1, s:1, b:1),
% 11.00/11.37 skol68 [384, 2] (w:1, o:267, a:1, s:1, b:1),
% 11.00/11.37 skol69 [385, 2] (w:1, o:268, a:1, s:1, b:1),
% 11.00/11.37 skol70 [386, 3] (w:1, o:375, a:1, s:1, b:1),
% 11.00/11.37 skol71 [387, 2] (w:1, o:270, a:1, s:1, b:1),
% 11.00/11.37 skol72 [388, 3] (w:1, o:376, a:1, s:1, b:1),
% 11.00/11.37 skol73 [389, 1] (w:1, o:154, a:1, s:1, b:1),
% 11.00/11.37 skol74 [390, 1] (w:1, o:155, a:1, s:1, b:1),
% 11.00/11.37 skol75 [391, 1] (w:1, o:156, a:1, s:1, b:1),
% 11.00/11.37 skol76 [392, 1] (w:1, o:157, a:1, s:1, b:1),
% 11.00/11.37 skol77 [393, 3] (w:1, o:377, a:1, s:1, b:1),
% 11.00/11.37 skol78 [394, 1] (w:1, o:158, a:1, s:1, b:1),
% 11.00/11.37 skol79 [395, 3] (w:1, o:378, a:1, s:1, b:1),
% 11.00/11.37 skol80 [396, 3] (w:1, o:379, a:1, s:1, b:1),
% 11.00/11.37 skol81 [397, 2] (w:1, o:272, a:1, s:1, b:1),
% 11.00/11.37 skol82 [398, 2] (w:1, o:273, a:1, s:1, b:1).
% 11.00/11.37
% 11.00/11.37
% 11.00/11.37 Starting Search:
% 11.00/11.37
% 11.00/11.37 *** allocated 170857 integers for clauses
% 11.00/11.37 Resimplifying inuse:
% 11.00/11.37 Done
% 11.00/11.37
% 11.00/11.37
% 11.00/11.37 Intermediate Status:
% 11.00/11.37 Generated: 2826
% 11.00/11.37 Kept: 2038
% 11.00/11.37 Inuse: 25
% 11.00/11.37 Deleted: 1
% 11.00/11.37 Deletedinuse: 0
% 11.00/11.37
% 11.00/11.37 *** allocated 256285 integers for clauses
% 11.00/11.37 *** allocated 170857 integers for termspace/termends
% 11.00/11.37 Resimplifying inuse:
% 11.00/11.37 Done
% 11.00/11.37
% 11.00/11.37
% 11.00/11.37 Intermediate Status:
% 11.00/11.37 Generated: 6803
% 11.00/11.37 Kept: 4086
% 11.00/11.37 Inuse: 174
% 11.00/11.37 Deleted: 2
% 11.00/11.37 Deletedinuse: 0
% 11.00/11.37
% 11.00/11.37 Resimplifying inuse:
% 11.00/11.37 Done
% 11.00/11.37
% 11.00/11.37 *** allocated 384427 integers for clauses
% 11.00/11.37 Resimplifying inuse:
% 11.00/11.37 Done
% 11.00/11.37
% 11.00/11.37 *** allocated 256285 integers for termspace/termends
% 11.00/11.37
% 11.00/11.37 Intermediate Status:
% 11.00/11.37 Generated: 12491
% 11.00/11.37 Kept: 6770
% 11.00/11.37 Inuse: 301
% 11.00/11.37 Deleted: 5
% 11.00/11.37 Deletedinuse: 0
% 11.00/11.37
% 11.00/11.37 Resimplifying inuse:
% 11.00/11.37 Done
% 11.00/11.37
% 11.00/11.37 *** allocated 576640 integers for clauses
% 11.00/11.37 Resimplifying inuse:
% 11.00/11.37 Done
% 11.00/11.37
% 11.00/11.37 *** allocated 384427 integers for termspace/termends
% 11.00/11.37
% 11.00/11.37 Intermediate Status:
% 11.00/11.37 Generated: 16991
% 11.00/11.37 Kept: 9538
% 11.00/11.37 Inuse: 346
% 11.00/11.37 Deleted: 6
% 11.00/11.37 Deletedinuse: 1
% 11.00/11.37
% 11.00/11.37 Resimplifying inuse:
% 11.00/11.37 Done
% 11.00/11.37
% 11.00/11.37 Resimplifying inuse:
% 11.00/11.37 Done
% 11.00/11.37
% 11.00/11.37
% 11.00/11.37 Intermediate Status:
% 11.00/11.37 Generated: 20005
% 11.00/11.37 Kept: 11553
% 11.00/11.37 Inuse: 381
% 11.00/11.37 Deleted: 6
% 11.00/11.37 Deletedinuse: 1
% 11.00/11.37
% 11.00/11.37 Resimplifying inuse:
% 11.00/11.37 Done
% 11.00/11.37
% 11.00/11.37 *** allocated 864960 integers for clauses
% 11.00/11.37 Resimplifying inuse:
% 11.00/11.37 Done
% 11.00/11.37
% 11.00/11.37
% 11.00/11.37 Intermediate Status:
% 11.00/11.37 Generated: 23603
% 11.00/11.37 Kept: 13574
% 11.00/11.37 Inuse: 438
% 11.00/11.37 Deleted: 6
% 11.00/11.37 Deletedinuse: 1
% 11.00/11.37
% 11.00/11.37 Resimplifying inuse:
% 11.00/11.37 Done
% 11.00/11.37
% 11.00/11.37 Resimplifying inuse:
% 11.00/11.37 Done
% 11.00/11.37
% 11.00/11.37 *** allocated 576640 integers for termspace/termends
% 11.00/11.37
% 11.00/11.37 Intermediate Status:
% 11.00/11.37 Generated: 27306
% 11.00/11.37 Kept: 15590
% 11.00/11.37 Inuse: 485
% 11.00/11.37 Deleted: 6
% 11.00/11.37 Deletedinuse: 1
% 11.00/11.37
% 11.00/11.37 Resimplifying inuse:
% 11.00/11.37 Done
% 11.00/11.37
% 11.00/11.37 Resimplifying inuse:
% 11.00/11.37 Done
% 11.00/11.37
% 11.00/11.37
% 11.00/11.37 Intermediate Status:
% 11.00/11.37 Generated: 36093
% 11.00/11.37 Kept: 18357
% 11.00/11.37 Inuse: 514
% 59.89/60.29 Deleted: 8
% 59.89/60.29 Deletedinuse: 1
% 59.89/60.29
% 59.89/60.29 Resimplifying inuse:
% 59.89/60.29 Done
% 59.89/60.29
% 59.89/60.29 *** allocated 1297440 integers for clauses
% 59.89/60.29 Resimplifying inuse:
% 59.89/60.29 Done
% 59.89/60.29
% 59.89/60.29 Resimplifying clauses:
% 59.89/60.29 Done
% 59.89/60.29
% 59.89/60.29
% 59.89/60.29 Intermediate Status:
% 59.89/60.29 Generated: 41945
% 59.89/60.29 Kept: 20374
% 59.89/60.29 Inuse: 545
% 59.89/60.29 Deleted: 319
% 59.89/60.29 Deletedinuse: 1
% 59.89/60.29
% 59.89/60.29 Resimplifying inuse:
% 59.89/60.29 Done
% 59.89/60.29
% 59.89/60.29 Resimplifying inuse:
% 59.89/60.29 Done
% 59.89/60.29
% 59.89/60.29
% 59.89/60.29 Intermediate Status:
% 59.89/60.29 Generated: 50512
% 59.89/60.29 Kept: 23009
% 59.89/60.29 Inuse: 603
% 59.89/60.29 Deleted: 320
% 59.89/60.29 Deletedinuse: 2
% 59.89/60.29
% 59.89/60.29 Resimplifying inuse:
% 59.89/60.29 Done
% 59.89/60.29
% 59.89/60.29 *** allocated 864960 integers for termspace/termends
% 59.89/60.29
% 59.89/60.29 Intermediate Status:
% 59.89/60.29 Generated: 53966
% 59.89/60.29 Kept: 25673
% 59.89/60.29 Inuse: 613
% 59.89/60.29 Deleted: 320
% 59.89/60.29 Deletedinuse: 2
% 59.89/60.29
% 59.89/60.29 Resimplifying inuse:
% 59.89/60.29 Done
% 59.89/60.29
% 59.89/60.29 Resimplifying inuse:
% 59.89/60.29 Done
% 59.89/60.29
% 59.89/60.29
% 59.89/60.29 Intermediate Status:
% 59.89/60.29 Generated: 62326
% 59.89/60.29 Kept: 28272
% 59.89/60.29 Inuse: 663
% 59.89/60.29 Deleted: 320
% 59.89/60.29 Deletedinuse: 2
% 59.89/60.29
% 59.89/60.29 Resimplifying inuse:
% 59.89/60.29 Done
% 59.89/60.29
% 59.89/60.29 *** allocated 1946160 integers for clauses
% 59.89/60.29 Resimplifying inuse:
% 59.89/60.29 Done
% 59.89/60.29
% 59.89/60.29
% 59.89/60.29 Intermediate Status:
% 59.89/60.29 Generated: 68838
% 59.89/60.29 Kept: 32518
% 59.89/60.29 Inuse: 678
% 59.89/60.29 Deleted: 320
% 59.89/60.29 Deletedinuse: 2
% 59.89/60.29
% 59.89/60.29 Resimplifying inuse:
% 59.89/60.29 Done
% 59.89/60.29
% 59.89/60.29 Resimplifying inuse:
% 59.89/60.29 Done
% 59.89/60.29
% 59.89/60.29
% 59.89/60.29 Intermediate Status:
% 59.89/60.29 Generated: 73229
% 59.89/60.29 Kept: 34521
% 59.89/60.29 Inuse: 710
% 59.89/60.29 Deleted: 320
% 59.89/60.29 Deletedinuse: 2
% 59.89/60.29
% 59.89/60.29 Resimplifying inuse:
% 59.89/60.29 Done
% 59.89/60.29
% 59.89/60.29
% 59.89/60.29 Intermediate Status:
% 59.89/60.29 Generated: 77674
% 59.89/60.29 Kept: 37453
% 59.89/60.29 Inuse: 718
% 59.89/60.29 Deleted: 320
% 59.89/60.29 Deletedinuse: 2
% 59.89/60.29
% 59.89/60.29 Resimplifying inuse:
% 59.89/60.29 Done
% 59.89/60.29
% 59.89/60.29 Resimplifying inuse:
% 59.89/60.29 Done
% 59.89/60.29
% 59.89/60.29 *** allocated 1297440 integers for termspace/termends
% 59.89/60.29
% 59.89/60.29 Intermediate Status:
% 59.89/60.29 Generated: 81571
% 59.89/60.29 Kept: 39466
% 59.89/60.29 Inuse: 750
% 59.89/60.29 Deleted: 320
% 59.89/60.29 Deletedinuse: 2
% 59.89/60.29
% 59.89/60.29 Resimplifying inuse:
% 59.89/60.29 Done
% 59.89/60.29
% 59.89/60.29 Resimplifying inuse:
% 59.89/60.29 Done
% 59.89/60.29
% 59.89/60.29 Resimplifying clauses:
% 59.89/60.29 Done
% 59.89/60.29
% 59.89/60.29
% 59.89/60.29 Intermediate Status:
% 59.89/60.29 Generated: 84264
% 59.89/60.29 Kept: 41472
% 59.89/60.29 Inuse: 759
% 59.89/60.29 Deleted: 389
% 59.89/60.29 Deletedinuse: 2
% 59.89/60.29
% 59.89/60.29 Resimplifying inuse:
% 59.89/60.29 Done
% 59.89/60.29
% 59.89/60.29 *** allocated 2919240 integers for clauses
% 59.89/60.29
% 59.89/60.29 Intermediate Status:
% 59.89/60.29 Generated: 91769
% 59.89/60.29 Kept: 43743
% 59.89/60.29 Inuse: 778
% 59.89/60.29 Deleted: 389
% 59.89/60.29 Deletedinuse: 2
% 59.89/60.29
% 59.89/60.29 Resimplifying inuse:
% 59.89/60.29 Done
% 59.89/60.29
% 59.89/60.29 Resimplifying inuse:
% 59.89/60.29 Done
% 59.89/60.29
% 59.89/60.29
% 59.89/60.29 Intermediate Status:
% 59.89/60.29 Generated: 97353
% 59.89/60.29 Kept: 45774
% 59.89/60.29 Inuse: 809
% 59.89/60.29 Deleted: 389
% 59.89/60.29 Deletedinuse: 2
% 59.89/60.29
% 59.89/60.29 Resimplifying inuse:
% 59.89/60.29 Done
% 59.89/60.29
% 59.89/60.29 Resimplifying inuse:
% 59.89/60.29 Done
% 59.89/60.29
% 59.89/60.29
% 59.89/60.29 Intermediate Status:
% 59.89/60.29 Generated: 103197
% 59.89/60.29 Kept: 47807
% 59.89/60.29 Inuse: 840
% 59.89/60.29 Deleted: 390
% 59.89/60.29 Deletedinuse: 3
% 59.89/60.29
% 59.89/60.29 Resimplifying inuse:
% 59.89/60.29 Done
% 59.89/60.29
% 59.89/60.29 Resimplifying inuse:
% 59.89/60.29 Done
% 59.89/60.29
% 59.89/60.29
% 59.89/60.29 Intermediate Status:
% 59.89/60.29 Generated: 108625
% 59.89/60.29 Kept: 49845
% 59.89/60.29 Inuse: 864
% 59.89/60.29 Deleted: 390
% 59.89/60.29 Deletedinuse: 3
% 59.89/60.29
% 59.89/60.29 Resimplifying inuse:
% 59.89/60.29 Done
% 59.89/60.29
% 59.89/60.29 Resimplifying inuse:
% 59.89/60.29 Done
% 59.89/60.29
% 59.89/60.29
% 59.89/60.29 Intermediate Status:
% 59.89/60.29 Generated: 114530
% 59.89/60.29 Kept: 52428
% 59.89/60.29 Inuse: 878
% 59.89/60.29 Deleted: 390
% 59.89/60.29 Deletedinuse: 3
% 59.89/60.29
% 59.89/60.29 Resimplifying inuse:
% 59.89/60.29 Done
% 59.89/60.29
% 59.89/60.29
% 59.89/60.29 Intermediate Status:
% 59.89/60.29 Generated: 123083
% 59.89/60.29 Kept: 55160
% 59.89/60.29 Inuse: 888
% 59.89/60.29 Deleted: 390
% 59.89/60.29 Deletedinuse: 3
% 59.89/60.29
% 59.89/60.29 Resimplifying inuse:
% 59.89/60.29 Done
% 59.89/60.29
% 59.89/60.29 Resimplifying inuse:
% 59.89/60.29 Done
% 59.89/60.29
% 59.89/60.29
% 59.89/60.29 Intermediate Status:
% 59.89/60.29 Generated: 128412
% 59.89/60.29 Kept: 57231
% 59.89/60.29 Inuse: 913
% 59.89/60.29 Deleted: 390
% 59.89/60.29 Deletedinuse: 3
% 59.89/60.29
% 59.89/60.29 Resimplifying inuse:
% 59.89/60.29 Done
% 59.89/60.29
% 59.89/60.29 Resimplifying inuse:
% 59.89/60.29 Done
% 59.89/60.29
% 59.89/60.29 *** allocated 1946160 integers for termspace/termends
% 59.89/60.29
% 59.89/60.29 Intermediate Status:
% 59.89/60.29 Generated: 139911
% 59.89/60.29 Kept: 60728
% 59.89/60.29 Inuse: 938
% 59.89/60.29 Deleted: 390
% 59.89/60.29 Deletedinuse: 3
% 59.89/60.29
% 59.89/60.29 Resimplifying inuse:
% 59.89/60.29 Done
% 59.89/60.29
% 59.89/60.29 Resimplifying clauses:
% 59.89/60.29 Done
% 59.89/60.29
% 59.89/60.29 Resimplifying inuse:
% 59.89/60.29 Done
% 59.89/60.29
% 59.89/60.29 *** allocated 4378860 integers for clauses
% 59.89/60.29
% 59.89/60.29 Intermediate Status:
% 59.89/60.29 Generated: 146935
% 59.89/60.29 Kept: 64596
% 59.89/60.29 Inuse: 958
% 59.89/60.29 Deleted: 517
% 59.89/60.29 Deletedinuse: 5
% 59.89/60.29
% 59.89/60.29 Resimplifying inuse:
% 59.89/60.29 Done
% 59.89/60.29
% 59.89/60.29 Resimplifying inuse:
% 59.89/60.29 Done
% 59.89/60.29
% 59.89/60.29
% 59.89/60.29 Intermediate Status:
% 59.89/60.29 Generated: 153206
% 59.89/60.29 Kept: 66852
% 59.89/60.29 Inuse: 988
% 59.89/60.29 Deleted: 517
% 59.89/60.29 Deletedinuse: 5
% 59.89/60.29
% 59.89/60.29 Resimplifying inuse:
% 59.89/60.29 Done
% 59.89/60.29
% 59.89/60.29
% 59.89/60.29 Intermediate Status:
% 59.89/60.29 Generated: 163168
% 59.89/60.29 Kept: 69706
% 59.89/60.29 Inuse: 996
% 59.89/60.29 Deleted: 517
% 59.89/60.29 Deletedinuse: 5
% 59.89/60.29
% 59.89/60.29 Resimplifying inuse:
% 59.89/60.29 Done
% 59.89/60.29
% 59.89/60.29 Resimplifying inuse:
% 59.89/60.29 Done
% 59.89/60.29
% 59.89/60.29
% 59.89/60.29 Intermediate Status:
% 59.89/60.29 Generated: 173385
% 59.89/60.29 Kept: 72695
% 59.89/60.29 Inuse: 1008
% 59.89/60.29 Deleted: 517
% 59.89/60.29 Deletedinuse: 5
% 59.89/60.29
% 59.89/60.29 Resimplifying inuse:
% 59.89/60.29 Done
% 59.89/60.29
% 59.89/60.29 Resimplifying inuse:
% 59.89/60.29 Done
% 59.89/60.29
% 59.89/60.29
% 59.89/60.29 Intermediate Status:
% 59.89/60.29 Generated: 180381
% 59.89/60.29 Kept: 74734
% 59.89/60.29 Inuse: 1028
% 59.89/60.29 Deleted: 518
% 59.89/60.29 Deletedinuse: 6
% 59.89/60.29
% 59.89/60.29 Resimplifying inuse:
% 59.89/60.29 Done
% 59.89/60.29
% 59.89/60.29
% 59.89/60.29 Intermediate Status:
% 159.47/159.96 Generated: 185480
% 159.47/159.96 Kept: 76753
% 159.47/159.96 Inuse: 1043
% 159.47/159.96 Deleted: 518
% 159.47/159.96 Deletedinuse: 6
% 159.47/159.96
% 159.47/159.96
% 159.47/159.96 Intermediate Status:
% 159.47/159.96 Generated: 189221
% 159.47/159.96 Kept: 79516
% 159.47/159.96 Inuse: 1048
% 159.47/159.96 Deleted: 518
% 159.47/159.96 Deletedinuse: 6
% 159.47/159.96
% 159.47/159.96 Resimplifying inuse:
% 159.47/159.96 Done
% 159.47/159.96
% 159.47/159.96 Resimplifying inuse:
% 159.47/159.96 Done
% 159.47/159.96
% 159.47/159.96 Resimplifying clauses:
% 159.47/159.96 Done
% 159.47/159.96
% 159.47/159.96
% 159.47/159.96 Intermediate Status:
% 159.47/159.96 Generated: 200006
% 159.47/159.96 Kept: 81658
% 159.47/159.96 Inuse: 1077
% 159.47/159.96 Deleted: 1479
% 159.47/159.96 Deletedinuse: 6
% 159.47/159.96
% 159.47/159.96 Resimplifying inuse:
% 159.47/159.96 Done
% 159.47/159.96
% 159.47/159.96 Resimplifying inuse:
% 159.47/159.96 Done
% 159.47/159.96
% 159.47/159.96 *** allocated 2919240 integers for termspace/termends
% 159.47/159.96
% 159.47/159.96 Intermediate Status:
% 159.47/159.96 Generated: 206762
% 159.47/159.96 Kept: 86012
% 159.47/159.96 Inuse: 1083
% 159.47/159.96 Deleted: 1505
% 159.47/159.96 Deletedinuse: 8
% 159.47/159.96
% 159.47/159.96 Resimplifying inuse:
% 159.47/159.96 Done
% 159.47/159.96
% 159.47/159.96 Resimplifying inuse:
% 159.47/159.96 Done
% 159.47/159.96
% 159.47/159.96
% 159.47/159.96 Intermediate Status:
% 159.47/159.96 Generated: 212189
% 159.47/159.96 Kept: 88031
% 159.47/159.96 Inuse: 1103
% 159.47/159.96 Deleted: 1524
% 159.47/159.96 Deletedinuse: 8
% 159.47/159.96
% 159.47/159.96 Resimplifying inuse:
% 159.47/159.96 Done
% 159.47/159.96
% 159.47/159.96 Resimplifying inuse:
% 159.47/159.96 Done
% 159.47/159.96
% 159.47/159.96
% 159.47/159.96 Intermediate Status:
% 159.47/159.96 Generated: 227750
% 159.47/159.96 Kept: 91884
% 159.47/159.96 Inuse: 1109
% 159.47/159.96 Deleted: 1524
% 159.47/159.96 Deletedinuse: 8
% 159.47/159.96
% 159.47/159.96 Resimplifying inuse:
% 159.47/159.96 Done
% 159.47/159.96
% 159.47/159.96 Resimplifying inuse:
% 159.47/159.96 Done
% 159.47/159.96
% 159.47/159.96
% 159.47/159.96 Intermediate Status:
% 159.47/159.96 Generated: 232926
% 159.47/159.96 Kept: 93895
% 159.47/159.96 Inuse: 1134
% 159.47/159.96 Deleted: 1524
% 159.47/159.96 Deletedinuse: 8
% 159.47/159.96
% 159.47/159.96 Resimplifying inuse:
% 159.47/159.96 Done
% 159.47/159.96
% 159.47/159.96 Resimplifying inuse:
% 159.47/159.96 Done
% 159.47/159.96
% 159.47/159.96
% 159.47/159.96 Intermediate Status:
% 159.47/159.96 Generated: 239162
% 159.47/159.96 Kept: 96135
% 159.47/159.96 Inuse: 1169
% 159.47/159.96 Deleted: 1524
% 159.47/159.96 Deletedinuse: 8
% 159.47/159.96
% 159.47/159.96 Resimplifying inuse:
% 159.47/159.96 Done
% 159.47/159.96
% 159.47/159.96 Resimplifying inuse:
% 159.47/159.96 Done
% 159.47/159.96
% 159.47/159.96 *** allocated 6568290 integers for clauses
% 159.47/159.96
% 159.47/159.96 Intermediate Status:
% 159.47/159.96 Generated: 244745
% 159.47/159.96 Kept: 98389
% 159.47/159.96 Inuse: 1189
% 159.47/159.96 Deleted: 1524
% 159.47/159.96 Deletedinuse: 8
% 159.47/159.96
% 159.47/159.96 Resimplifying inuse:
% 159.47/159.96 Done
% 159.47/159.96
% 159.47/159.96
% 159.47/159.96 Intermediate Status:
% 159.47/159.96 Generated: 249730
% 159.47/159.96 Kept: 100508
% 159.47/159.96 Inuse: 1204
% 159.47/159.96 Deleted: 1524
% 159.47/159.96 Deletedinuse: 8
% 159.47/159.96
% 159.47/159.96 Resimplifying inuse:
% 159.47/159.96 Done
% 159.47/159.96
% 159.47/159.96 Resimplifying clauses:
% 159.47/159.96 Done
% 159.47/159.96
% 159.47/159.96 Resimplifying inuse:
% 159.47/159.96 Done
% 159.47/159.96
% 159.47/159.96
% 159.47/159.96 Intermediate Status:
% 159.47/159.96 Generated: 257740
% 159.47/159.96 Kept: 102663
% 159.47/159.96 Inuse: 1244
% 159.47/159.96 Deleted: 1892
% 159.47/159.96 Deletedinuse: 10
% 159.47/159.96
% 159.47/159.96 Resimplifying inuse:
% 159.47/159.96 Done
% 159.47/159.96
% 159.47/159.96
% 159.47/159.96 Intermediate Status:
% 159.47/159.96 Generated: 264561
% 159.47/159.96 Kept: 105143
% 159.47/159.96 Inuse: 1259
% 159.47/159.96 Deleted: 1892
% 159.47/159.96 Deletedinuse: 10
% 159.47/159.96
% 159.47/159.96 Resimplifying inuse:
% 159.47/159.96 Done
% 159.47/159.96
% 159.47/159.96 Resimplifying inuse:
% 159.47/159.96 Done
% 159.47/159.96
% 159.47/159.96
% 159.47/159.96 Intermediate Status:
% 159.47/159.96 Generated: 279217
% 159.47/159.96 Kept: 109381
% 159.47/159.96 Inuse: 1279
% 159.47/159.96 Deleted: 1892
% 159.47/159.96 Deletedinuse: 10
% 159.47/159.96
% 159.47/159.96 Resimplifying inuse:
% 159.47/159.96 Done
% 159.47/159.96
% 159.47/159.96 Resimplifying inuse:
% 159.47/159.96 Done
% 159.47/159.96
% 159.47/159.96
% 159.47/159.96 Intermediate Status:
% 159.47/159.96 Generated: 293446
% 159.47/159.96 Kept: 113638
% 159.47/159.96 Inuse: 1299
% 159.47/159.96 Deleted: 1892
% 159.47/159.96 Deletedinuse: 10
% 159.47/159.96
% 159.47/159.96 Resimplifying inuse:
% 159.47/159.96 Done
% 159.47/159.96
% 159.47/159.96
% 159.47/159.96 Intermediate Status:
% 159.47/159.96 Generated: 305761
% 159.47/159.96 Kept: 117019
% 159.47/159.96 Inuse: 1309
% 159.47/159.96 Deleted: 1892
% 159.47/159.96 Deletedinuse: 10
% 159.47/159.96
% 159.47/159.96 Resimplifying inuse:
% 159.47/159.96 Done
% 159.47/159.96
% 159.47/159.96
% 159.47/159.96 Intermediate Status:
% 159.47/159.96 Generated: 316750
% 159.47/159.96 Kept: 122509
% 159.47/159.96 Inuse: 1324
% 159.47/159.96 Deleted: 1892
% 159.47/159.96 Deletedinuse: 10
% 159.47/159.96
% 159.47/159.96 Resimplifying inuse:
% 159.47/159.96 Done
% 159.47/159.96
% 159.47/159.96 Resimplifying clauses:
% 159.47/159.96 Done
% 159.47/159.96
% 159.47/159.96 *** allocated 4378860 integers for termspace/termends
% 159.47/159.96
% 159.47/159.96 Intermediate Status:
% 159.47/159.96 Generated: 327913
% 159.47/159.96 Kept: 128831
% 159.47/159.96 Inuse: 1339
% 159.47/159.96 Deleted: 1945
% 159.47/159.96 Deletedinuse: 10
% 159.47/159.96
% 159.47/159.96 Resimplifying inuse:
% 159.47/159.96 Done
% 159.47/159.96
% 159.47/159.96
% 159.47/159.96 Intermediate Status:
% 159.47/159.96 Generated: 335070
% 159.47/159.96 Kept: 132065
% 159.47/159.96 Inuse: 1349
% 159.47/159.96 Deleted: 1945
% 159.47/159.96 Deletedinuse: 10
% 159.47/159.96
% 159.47/159.97 Resimplifying inuse:
% 159.47/159.97 Done
% 159.47/159.97
% 159.47/159.97 Resimplifying inuse:
% 159.47/159.97 Done
% 159.47/159.97
% 159.47/159.97
% 159.47/159.97 Intermediate Status:
% 159.47/159.97 Generated: 340964
% 159.47/159.97 Kept: 134112
% 159.47/159.97 Inuse: 1375
% 159.47/159.97 Deleted: 1945
% 159.47/159.97 Deletedinuse: 10
% 159.47/159.97
% 159.47/159.97 Resimplifying inuse:
% 159.47/159.97 Done
% 159.47/159.97
% 159.47/159.97 Resimplifying inuse:
% 159.47/159.97 Done
% 159.47/159.97
% 159.47/159.97
% 159.47/159.97 Intermediate Status:
% 159.47/159.97 Generated: 347834
% 159.47/159.97 Kept: 136385
% 159.47/159.97 Inuse: 1384
% 159.47/159.97 Deleted: 1945
% 159.47/159.97 Deletedinuse: 10
% 159.47/159.97
% 159.47/159.97 Resimplifying inuse:
% 159.47/159.97 Done
% 159.47/159.97
% 159.47/159.97 Resimplifying inuse:
% 159.47/159.97 Done
% 159.47/159.97
% 159.47/159.97
% 159.47/159.97 Intermediate Status:
% 159.47/159.97 Generated: 353966
% 159.47/159.97 Kept: 138434
% 159.47/159.97 Inuse: 1404
% 159.47/159.97 Deleted: 1945
% 159.47/159.97 Deletedinuse: 10
% 159.47/159.97
% 159.47/159.97 Resimplifying inuse:
% 159.47/159.97 Done
% 159.47/159.97
% 159.47/159.97
% 159.47/159.97 Intermediate Status:
% 159.47/159.97 Generated: 364384
% 159.47/159.97 Kept: 143002
% 159.47/159.97 Inuse: 1429
% 159.47/159.97 Deleted: 1945
% 159.47/159.97 Deletedinuse: 10
% 159.47/159.97
% 159.47/159.97 Resimplifying inuse:
% 159.47/159.97 Done
% 159.47/159.97
% 159.47/159.97 Resimplifying clauses:
% 159.47/159.97 Done
% 159.47/159.97
% 159.47/159.97 Resimplifying inuse:
% 159.47/159.97 Done
% 159.47/159.97
% 159.47/159.97
% 159.47/159.97 Intermediate Status:
% 159.47/159.97 Generated: 372317
% 159.47/159.97 Kept: 145032
% 159.47/159.97 Inuse: 1468
% 159.47/159.97 Deleted: 2222
% 159.47/159.97 Deletedinuse: 12
% 159.47/159.97
% 159.47/159.97 Resimplifying inuse:
% 159.47/159.97 Done
% 159.47/159.97
% 159.47/159.97 Resimplifying inuse:
% 159.47/159.97 Done
% 159.47/159.97
% 159.47/159.97 *** allocated 9852435 integers for clauses
% 159.47/159.97
% 159.47/159.97 Intermediate Status:
% 159.47/159.97 Generated: 387543
% 159.47/159.97 Kept: Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------