TSTP Solution File: SWW225+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW225+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n023.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 23:21:22 EDT 2022
% Result : Timeout 300.05s 300.45s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWW225+1 : TPTP v8.1.0. Released v5.2.0.
% 0.12/0.14 % Command : bliksem %s
% 0.13/0.35 % Computer : n023.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % DateTime : Sat Jun 4 21:40:09 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.12/1.61 *** allocated 10000 integers for termspace/termends
% 1.12/1.61 *** allocated 10000 integers for clauses
% 1.12/1.61 *** allocated 10000 integers for justifications
% 1.12/1.61 *** allocated 15000 integers for termspace/termends
% 1.12/1.61 *** allocated 22500 integers for termspace/termends
% 1.12/1.61 *** allocated 33750 integers for termspace/termends
% 1.12/1.61 Bliksem 1.12
% 1.12/1.61
% 1.12/1.61
% 1.12/1.61 Automatic Strategy Selection
% 1.12/1.61
% 1.12/1.61 *** allocated 50625 integers for termspace/termends
% 1.12/1.61 *** allocated 75937 integers for termspace/termends
% 1.12/1.61 *** allocated 113905 integers for termspace/termends
% 1.12/1.61
% 1.12/1.61 Clauses:
% 1.12/1.61
% 1.12/1.61 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 1.12/1.61 { c_SEQ_Osubseq( v_f____ ) }.
% 1.12/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, v_N1____, v_N2____ ), hAPP(
% 1.12/1.61 v_f____, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, v_N1____, v_N2____ ) )
% 1.12/1.61 ) }.
% 1.12/1.61 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 1.12/1.61 , Y ) }.
% 1.12/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 1.12/1.61 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.12/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.12/1.61 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.12/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.12/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.12/1.61 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.12/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.12/1.61 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.12/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.12/1.61 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.12/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.12/1.61 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.12/1.61 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.12/1.61 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.12/1.61 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.12/1.61 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.12/1.61 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.12/1.61 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.12/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.12/1.61 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.12/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.12/1.61 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.12/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 1.12/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 1.12/1.61 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 1.12/1.61 ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 1.12/1.61 c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 1.12/1.61 }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 1.12/1.61 c_Nat_OSuc( X ) ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 1.12/1.61 ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.12/1.61 { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 1.12/1.61 , c_Nat_OSuc( X ) ) }.
% 1.12/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 1.12/1.61 .
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol2( X, Y ) ) }.
% 1.12/1.61 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.12/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.12/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 1.12/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.12/1.61 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.12/1.61 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.12/1.61 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.12/1.61 hAPP( Y, U ) ) }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.12/1.61 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.12/1.61 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 1.12/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.12/1.61 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.12/1.61 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.12/1.61 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.12/1.61 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 1.12/1.61 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 1.12/1.61 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.12/1.61 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.12/1.61 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.12/1.61 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.12/1.61 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.12/1.61 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.12/1.61 hAPP( Y, U ) ) }.
% 1.12/1.61 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.12/1.61 ( X, Z, Y ) }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.12/1.61 ( X, Y, Z ) }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.12/1.61 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 1.12/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.12/1.61 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.12/1.61 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.12/1.61 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.12/1.61 hAPP( Y, U ) ) }.
% 1.12/1.61 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 1.12/1.61 ( Z, skol3( X, Y, Z ) ), hAPP( Y, skol3( X, Y, Z ) ) ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 1.12/1.61 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.12/1.61 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 1.12/1.61 Y, T ), Z = Y }.
% 1.12/1.61 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 1.12/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.12/1.61 T, Y ), Z = Y }.
% 1.12/1.61 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.12/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.12/1.61 T, Y ), Z = Y }.
% 1.12/1.61 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.12/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.12/1.61 Y, Z ), T = Y }.
% 1.12/1.61 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 1.12/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.12/1.61 Y, Z ) }.
% 1.12/1.61 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.12/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.12/1.61 T, Y ), Z = Y }.
% 1.12/1.61 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 1.12/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.12/1.61 T, Y ) }.
% 1.12/1.61 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.12/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.12/1.61 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.12/1.61 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 1.12/1.61 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 1.12/1.61 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 1.12/1.61 { ! c_Nat_OSuc( X ) = X }.
% 1.12/1.61 { ! X = c_Nat_OSuc( X ) }.
% 1.12/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 1.12/1.61 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 1.12/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 1.12/1.61 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 1.12/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.12/1.61 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.12/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 1.12/1.61 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.12/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 1.12/1.61 c_RealDef_Oreal( tc_Nat_Onat ), Y ), hAPP( c_RealDef_Oreal( tc_Nat_Onat )
% 1.12/1.61 , X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 1.12/1.61 c_RealDef_Oreal( tc_Nat_Onat ), Y ), hAPP( c_RealDef_Oreal( tc_Nat_Onat )
% 1.12/1.61 , X ) ) }.
% 1.12/1.61 { ! c_SEQ_Osubseq( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.12/1.61 hAPP( X, Y ) ) }.
% 1.12/1.61 { hAPP( c_RealDef_Oreal( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.12/1.61 tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.12/1.61 hAPP( c_RealDef_Oreal( tc_Nat_Onat ), Y ), hAPP( c_RealDef_Oreal(
% 1.12/1.61 tc_Nat_Onat ), X ) ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol4( X, Y ) ) }.
% 1.12/1.61 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.12/1.61 hAPP( Y, skol5( X, Y ) ), hAPP( Y, c_Nat_OSuc( skol5( X, Y ) ) ) ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ), hAPP( Y, Z ) ) }.
% 1.12/1.61 { ! hAPP( c_RealDef_Oreal( tc_Nat_Onat ), Y ) = hAPP( c_RealDef_Oreal(
% 1.12/1.61 tc_Nat_Onat ), X ), Y = X }.
% 1.12/1.61 { ! Y = X, hAPP( c_RealDef_Oreal( tc_Nat_Onat ), Y ) = hAPP(
% 1.12/1.61 c_RealDef_Oreal( tc_Nat_Onat ), X ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ),
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ), Y = X }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Z ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, Z ) }.
% 1.12/1.61 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ) }.
% 1.12/1.61 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, X ) }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), ! c_SEQ_Odecseq( X, Y ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ), hAPP( Y, Z ) ) }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless__eq(
% 1.12/1.61 tc_Nat_Onat, skol6( X, Y ), skol62( X, Y ) ), c_SEQ_Odecseq( X, Y ) }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.12/1.61 hAPP( Y, skol62( X, Y ) ), hAPP( Y, skol6( X, Y ) ) ), c_SEQ_Odecseq( X,
% 1.12/1.61 Y ) }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), ! c_SEQ_Oincseq( X, Y ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, Z ), hAPP( Y, T ) ) }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless__eq(
% 1.12/1.61 tc_Nat_Onat, skol7( X, Y ), skol63( X, Y ) ), c_SEQ_Oincseq( X, Y ) }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.12/1.61 hAPP( Y, skol7( X, Y ) ), hAPP( Y, skol63( X, Y ) ) ), c_SEQ_Oincseq( X,
% 1.12/1.61 Y ) }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), ! c_SEQ_Omonoseq( X, Y ), alpha1( X, Y ),
% 1.12/1.61 alpha18( X, Y ) }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), ! alpha1( X, Y ), c_SEQ_Omonoseq( X, Y ) }
% 1.12/1.61 .
% 1.12/1.61 { ! class_Orderings_Oorder( X ), ! alpha18( X, Y ), c_SEQ_Omonoseq( X, Y )
% 1.12/1.61 }.
% 1.12/1.61 { ! alpha18( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T
% 1.12/1.61 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ), hAPP( Y, Z ) ) }
% 1.12/1.61 .
% 1.12/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol8( X, Y ), skol64( X
% 1.12/1.61 , Y ) ), alpha18( X, Y ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, skol64( X, Y ) ), hAPP(
% 1.12/1.61 Y, skol8( X, Y ) ) ), alpha18( X, Y ) }.
% 1.12/1.61 { ! alpha1( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T
% 1.12/1.61 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, Z ), hAPP( Y, T ) ) }
% 1.12/1.61 .
% 1.12/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol9( X, Y ), skol65( X
% 1.12/1.61 , Y ) ), alpha1( X, Y ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, skol9( X, Y ) ), hAPP( Y
% 1.12/1.61 , skol65( X, Y ) ) ), alpha1( X, Y ) }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), ! c_SEQ_Omonoseq( X, Y ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, Z ), hAPP( Y, c_Nat_OSuc(
% 1.12/1.61 Z ) ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, c_Nat_OSuc( T ) )
% 1.12/1.61 , hAPP( Y, T ) ) }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.12/1.61 hAPP( Y, skol10( X, Y ) ), hAPP( Y, c_Nat_OSuc( skol10( X, Y ) ) ) ),
% 1.12/1.61 c_SEQ_Omonoseq( X, Y ) }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.12/1.61 hAPP( Y, c_Nat_OSuc( skol66( X, Y ) ) ), hAPP( Y, skol66( X, Y ) ) ),
% 1.12/1.61 c_SEQ_Omonoseq( X, Y ) }.
% 1.12/1.61 { hAPP( c_RealDef_Oreal( tc_Nat_Onat ), c_Nat_OSuc( X ) ) =
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( c_RealDef_Oreal(
% 1.12/1.61 tc_Nat_Onat ), X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.12/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 1.12/1.61 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 1.12/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 1.12/1.61 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 1.12/1.61 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.12/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 1.12/1.61 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 1.12/1.61 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 1.12/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.12/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.12/1.61 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.12/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.12/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.12/1.61 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), ! c_SEQ_Oincseq( X, Y ), c_SEQ_Omonoseq( X
% 1.12/1.61 , Y ) }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), ! c_SEQ_Odecseq( X, Y ), c_SEQ_Omonoseq( X
% 1.12/1.61 , Y ) }.
% 1.12/1.61 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 1.12/1.61 c_Groups_Oone__class_Oone( X ) }.
% 1.12/1.61 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 1.12/1.61 c_Groups_Oone__class_Oone( X ) = Y }.
% 1.12/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.12/1.61 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 1.12/1.61 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 1.12/1.61 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.12/1.61 hAPP( Y, skol11( X, Y ) ), hAPP( Y, c_Nat_OSuc( skol11( X, Y ) ) ) ),
% 1.12/1.61 c_SEQ_Oincseq( X, Y ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( c_RealDef_Oreal(
% 1.12/1.61 tc_Nat_Onat ), Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP(
% 1.12/1.61 c_RealDef_Oreal( tc_Nat_Onat ), X ), c_Groups_Oone__class_Oone(
% 1.12/1.61 tc_RealDef_Oreal ) ) ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( c_RealDef_Oreal
% 1.12/1.61 ( tc_Nat_Onat ), Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP
% 1.12/1.61 ( c_RealDef_Oreal( tc_Nat_Onat ), X ), c_Groups_Oone__class_Oone(
% 1.12/1.61 tc_RealDef_Oreal ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 1.12/1.61 , X ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( c_RealDef_Oreal(
% 1.12/1.61 tc_Nat_Onat ), Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), hAPP
% 1.12/1.61 ( c_RealDef_Oreal( tc_Nat_Onat ), X ) ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( c_RealDef_Oreal(
% 1.12/1.61 tc_Nat_Onat ), Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), hAPP
% 1.12/1.61 ( c_RealDef_Oreal( tc_Nat_Onat ), X ) ), c_Orderings_Oord__class_Oless(
% 1.12/1.61 tc_Nat_Onat, Y, X ) }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless__eq(
% 1.12/1.61 tc_Nat_Onat, skol12( X, Y ), skol67( X, Y ) ), c_SEQ_Omonoseq( X, Y ) }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.12/1.61 hAPP( Y, skol67( X, Y ) ), hAPP( Y, skol12( X, Y ) ) ), c_SEQ_Omonoseq( X
% 1.12/1.61 , Y ) }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless__eq(
% 1.12/1.61 tc_Nat_Onat, skol13( X, Y ), skol68( X, Y ) ), c_SEQ_Omonoseq( X, Y ) }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.12/1.61 hAPP( Y, skol13( X, Y ) ), hAPP( Y, skol68( X, Y ) ) ), c_SEQ_Omonoseq( X
% 1.12/1.61 , Y ) }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.12/1.61 hAPP( Y, c_Nat_OSuc( skol14( X, Y ) ) ), hAPP( Y, skol14( X, Y ) ) ),
% 1.12/1.61 c_SEQ_Omonoseq( X, Y ) }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.12/1.61 hAPP( Y, skol15( X, Y ) ), hAPP( Y, c_Nat_OSuc( skol15( X, Y ) ) ) ),
% 1.12/1.61 c_SEQ_Omonoseq( X, Y ) }.
% 1.12/1.61 { hAPP( c_RealDef_Oreal( tc_Nat_Onat ), c_Nat_OSuc(
% 1.12/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) =
% 1.12/1.61 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.12/1.61 { ! class_Rings_Osemiring__1( X ), c_Nat_Osemiring__1__class_Oof__nat__aux
% 1.12/1.61 ( X, T, c_Nat_OSuc( Z ), Y ) = c_Nat_Osemiring__1__class_Oof__nat__aux( X
% 1.12/1.61 , T, Z, hAPP( T, Y ) ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc(
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Z ) =
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.12/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.12/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.12/1.61 X ) ) }.
% 1.12/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.12/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.12/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.12/1.61 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 1.12/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 1.12/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.12/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.12/1.61 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.61 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 1.12/1.61 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = X }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.61 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 1.12/1.61 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 1.12/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 1.12/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.12/1.61 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.12/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.12/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.12/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.61 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol16( X ) ) }.
% 1.12/1.61 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.12/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.12/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 1.12/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.12/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.12/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 1.12/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha2( X, Y ) }.
% 1.12/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.12/1.61 { ! alpha2( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.12/1.61 c_Nat_OSuc( X ) ) }.
% 1.12/1.61 { ! alpha2( X, Y ), Y = c_Nat_OSuc( skol17( Z, Y ) ) }.
% 1.12/1.61 { ! alpha2( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol17( X,
% 1.12/1.61 Y ), X ) }.
% 1.12/1.61 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 1.12/1.61 ), alpha2( X, Y ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.12/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 1.12/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.12/1.61 Y ) }.
% 1.12/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.12/1.61 tc_Nat_Onat ), X ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.61 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 1.12/1.61 .
% 1.12/1.61 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 1.12/1.61 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 1.12/1.61 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.12/1.61 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.12/1.61 Y ), ! Z = Y }.
% 1.12/1.61 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.12/1.61 Z ), ! Z = Y }.
% 1.12/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.12/1.61 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 1.12/1.61 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.12/1.61 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.12/1.61 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 1.12/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.12/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.12/1.61 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.12/1.61 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 1.12/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 1.12/1.61 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.12/1.61 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.61 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.12/1.61 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.12/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.12/1.61 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 1.12/1.61 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.12/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 1.12/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 1.12/1.61 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 1.12/1.61 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.12/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 1.12/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.12/1.61 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 1.12/1.61 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.12/1.61 ) }.
% 1.12/1.61 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.12/1.61 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.12/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.12/1.61 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 1.12/1.61 ( X ) ) }.
% 1.12/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.12/1.61 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.12/1.61 , Z, Y ) }.
% 1.12/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.12/1.61 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.12/1.61 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.12/1.61 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.12/1.61 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 1.12/1.61 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.12/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.12/1.61 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 1.12/1.61 { ! class_Rings_Osemiring__1( X ), c_Nat_Osemiring__1__class_Oof__nat__aux
% 1.12/1.61 ( X, Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) = Y }.
% 1.12/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.12/1.61 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 1.12/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.12/1.61 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.12/1.61 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 1.12/1.61 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.12/1.61 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.61 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 1.12/1.61 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 1.12/1.61 ) ) = X }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.61 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.12/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.12/1.61 ( tc_Nat_Onat, Y, X ), Y ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 1.12/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.12/1.61 , ! Z = Y }.
% 1.12/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.12/1.61 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.12/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.12/1.61 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.12/1.61 , ! Z = Y }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.12/1.61 , ! Y = Z }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.12/1.61 ( tc_Nat_Onat, Y, Z ), X ) }.
% 1.12/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.12/1.61 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.12/1.61 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.12/1.61 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 1.12/1.61 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 1.12/1.61 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 1.12/1.61 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 1.12/1.61 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.12/1.61 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.12/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.12/1.61 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.12/1.61 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.12/1.61 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.12/1.61 ) }.
% 1.12/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.12/1.61 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.12/1.61 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.12/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.12/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.12/1.61 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.12/1.61 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 1.12/1.61 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.12/1.61 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 1.12/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.12/1.61 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.12/1.61 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.12/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.12/1.61 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.12/1.61 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 1.12/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.12/1.61 tc_Nat_Onat ), X ) }.
% 1.12/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.12/1.61 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.12/1.61 { alpha48( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 1.12/1.61 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.12/1.61 { alpha48( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 1.12/1.61 ( X, Y ), Z ) ) }.
% 1.12/1.61 { ! alpha48( X, Y, Z ), alpha51( X, Y, Z ), Z = Y }.
% 1.12/1.61 { ! alpha48( X, Y, Z ), alpha51( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 1.12/1.61 ) ) }.
% 1.12/1.61 { ! alpha51( X, Y, Z ), alpha48( X, Y, Z ) }.
% 1.12/1.61 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha48( X, Y, Z ) }.
% 1.12/1.61 { ! alpha51( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 1.12/1.61 }.
% 1.12/1.61 { ! alpha51( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 1.12/1.61 X, Y ), Z ) ), alpha51( X, Y, Z ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.12/1.61 ( tc_Nat_Onat, Y, Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z )
% 1.12/1.61 ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.12/1.61 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.12/1.61 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.12/1.61 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.12/1.61 ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.12/1.61 tc_Nat_Onat, Z, X ), Y ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.12/1.61 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 1.12/1.61 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 1.12/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 1.12/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.12/1.61 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 1.12/1.61 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.12/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.12/1.61 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 1.12/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.12/1.61 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 1.12/1.61 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.12/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.12/1.61 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.12/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.12/1.61 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.12/1.61 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.12/1.61 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.12/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.12/1.61 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.12/1.61 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.12/1.61 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.12/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.12/1.61 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 1.12/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 1.12/1.61 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.12/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 1.12/1.61 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.12/1.61 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.12/1.61 , alpha3( X, Y, Z ) }.
% 1.12/1.61 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.12/1.61 , alpha19( X, Y, Z ) }.
% 1.12/1.61 { ! alpha3( X, Y, Z ), ! alpha19( X, Y, Z ), hBOOL( hAPP( Z,
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.12/1.61 { ! alpha19( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.12/1.61 T ), hBOOL( hAPP( Z, T ) ) }.
% 1.12/1.61 { ! hBOOL( hAPP( Z, skol18( T, U, Z ) ) ), alpha19( X, Y, Z ) }.
% 1.12/1.61 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol18( X, Y, Z ) ),
% 1.12/1.61 alpha19( X, Y, Z ) }.
% 1.12/1.61 { ! alpha3( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 1.12/1.61 , hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.12/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha3( X, Y, Z ) }.
% 1.12/1.61 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha3
% 1.12/1.61 ( X, Y, Z ) }.
% 1.12/1.61 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.12/1.61 , ! alpha4( X, Y, Z ) }.
% 1.12/1.61 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.12/1.61 , ! alpha20( X, Y, Z ) }.
% 1.12/1.61 { alpha4( X, Y, Z ), alpha20( X, Y, Z ), hBOOL( hAPP( Z,
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.12/1.61 { ! alpha20( X, Y, Z ), ! hBOOL( hAPP( Z, skol19( T, U, Z ) ) ) }.
% 1.12/1.61 { ! alpha20( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.12/1.61 skol19( X, Y, Z ) ) }.
% 1.12/1.61 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 1.12/1.61 ) ), alpha20( X, Y, Z ) }.
% 1.12/1.61 { ! alpha4( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }
% 1.12/1.61 .
% 1.12/1.61 { ! alpha4( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 1.12/1.61 tc_Nat_Onat ) ) ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 1.12/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha4( X, Y, Z ) }.
% 1.12/1.61 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 1.12/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( c_RealDef_Oreal
% 1.12/1.61 ( tc_Nat_Onat ), Y ), hAPP( c_RealDef_Oreal( tc_Nat_Onat ), X ) ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( c_RealDef_Oreal(
% 1.12/1.61 tc_Nat_Onat ), Y ), hAPP( c_RealDef_Oreal( tc_Nat_Onat ), X ) ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.61 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.12/1.61 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.12/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.61 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.12/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.12/1.61 tc_Nat_Onat, Y, X ) ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.61 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.12/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.12/1.61 tc_Nat_Onat, Y, X ) ) }.
% 1.12/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = X }.
% 1.12/1.61 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.12/1.61 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 1.12/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.12/1.61 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.12/1.61 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.12/1.61 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.12/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.12/1.61 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.12/1.61 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.12/1.61 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.12/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.12/1.61 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.12/1.61 ) ) }.
% 1.12/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.12/1.61 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.12/1.61 ) ) }.
% 1.12/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.12/1.61 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.12/1.61 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 1.12/1.61 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.12/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.12/1.61 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.12/1.61 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 1.12/1.61 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.12/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.12/1.61 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.12/1.61 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.12/1.61 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.12/1.61 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.12/1.61 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 1.12/1.61 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.12/1.61 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 1.12/1.61 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.12/1.61 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 1.12/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.12/1.61 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.12/1.61 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.12/1.61 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.12/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.12/1.61 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.12/1.61 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.12/1.61 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.12/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.12/1.61 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.12/1.61 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.12/1.61 , ! Z = Y }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.12/1.61 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.12/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.12/1.61 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.12/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.12/1.61 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.12/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.12/1.61 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.12/1.61 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.12/1.61 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.12/1.61 ( X, Z, Y ) }.
% 1.12/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.12/1.61 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.12/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.12/1.61 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.12/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.12/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 1.12/1.61 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.12/1.61 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.12/1.61 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.12/1.61 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.12/1.61 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.12/1.61 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.12/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.12/1.61 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.12/1.61 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.12/1.61 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.12/1.61 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.12/1.61 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.12/1.61 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.12/1.61 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.12/1.61 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.12/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.12/1.61 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.12/1.61 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.12/1.61 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.12/1.61 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.12/1.61 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.12/1.61 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.12/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.12/1.61 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 1.12/1.61 ( X, T, Y ) }.
% 1.12/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 1.12/1.61 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.12/1.61 , Y, Z ) ) }.
% 1.12/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.12/1.61 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 1.12/1.61 ( X, Z, Y ) }.
% 1.12/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.12/1.61 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.12/1.61 , T, Y ) ) }.
% 1.12/1.61 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.12/1.61 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 1.12/1.61 , Y, T ) ) }.
% 1.12/1.61 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.12/1.61 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.12/1.61 , T, Y ) ) }.
% 1.12/1.61 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.12/1.61 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 1.12/1.61 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 1.12/1.61 , T ) ) }.
% 1.12/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 1.12/1.61 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 1.12/1.61 ( X, Z, Y ) }.
% 1.12/1.61 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.12/1.61 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 1.12/1.61 ( X, Z, Y ) }.
% 1.12/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.12/1.61 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 1.12/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.12/1.61 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.12/1.61 ( tc_Nat_Onat, Z, Y ), X ) }.
% 1.12/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.12/1.61 tc_Nat_Onat, Y, X ), X ) = Y }.
% 1.12/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.12/1.61 tc_Nat_Onat, Y, X ), Y ) = X }.
% 1.12/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.12/1.61 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.12/1.61 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.12/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.12/1.61 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 1.12/1.61 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.12/1.61 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ),
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.12/1.61 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.12/1.61 ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! X = Z,
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 1.12/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 1.12/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.12/1.61 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 1.12/1.61 }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 1.12/1.61 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.12/1.61 X ) ) }.
% 1.12/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 1.12/1.61 .
% 1.12/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.12/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 1.12/1.61 .
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 1.12/1.61 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 1.12/1.61 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), ! Y = X }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), Y = X,
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), Y = X }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 1.12/1.61 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.12/1.61 ( tc_Nat_Onat, Y, X ), Y ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.12/1.61 ( tc_Nat_Onat, Y, X ), X ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.12/1.61 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 1.12/1.61 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.12/1.61 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 1.12/1.61 .
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.12/1.61 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 1.12/1.61 .
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.12/1.61 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 1.12/1.61 .
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.12/1.61 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 1.12/1.61 , X ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.12/1.61 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.12/1.61 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.12/1.61 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.12/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.12/1.61 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.12/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.12/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.12/1.61 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.12/1.61 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.12/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.12/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 1.12/1.61 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 1.12/1.61 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.12/1.61 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.12/1.61 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.12/1.61 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.12/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.12/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.12/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.12/1.61 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.12/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.12/1.61 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 1.12/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 1.12/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.12/1.61 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.12/1.61 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 1.12/1.61 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.12/1.61 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.12/1.61 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.12/1.61 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.12/1.61 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.12/1.61 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.12/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.12/1.61 tc_Nat_Onat ), X ) = X }.
% 1.12/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 1.12/1.61 ( tc_Nat_Onat ) ) = X }.
% 1.12/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.12/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.12/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.12/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.12/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.12/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.12/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 1.12/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.12/1.61 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.12/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 1.12/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 1.12/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 1.12/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.12/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 1.12/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.12/1.61 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.12/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.12/1.61 { ! c_SEQ_Osubseq( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z
% 1.12/1.61 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( X, Y ), hAPP( X, Z
% 1.12/1.61 ) ) }.
% 1.12/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol20( X ), skol69( X ) ),
% 1.12/1.61 c_SEQ_Osubseq( X ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( X, skol20( X ) ),
% 1.12/1.61 hAPP( X, skol69( X ) ) ), c_SEQ_Osubseq( X ) }.
% 1.12/1.61 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 1.12/1.61 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.12/1.61 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 1.12/1.61 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 1.12/1.61 , Y, T ) ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 1.12/1.61 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.12/1.61 tc_Nat_Onat, X, Z ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Z ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.12/1.61 tc_Nat_Onat, X, Y ), Z ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ), Y ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.12/1.61 tc_Nat_Onat, Z, X ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X =
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X =
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.12/1.61 tc_Nat_Onat, X, Y ), Y ) = X }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.12/1.61 tc_Nat_Onat, Z, X ), Y ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.12/1.61 tc_Nat_Onat, X, Z ), Y ) ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 1.12/1.61 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.12/1.61 tc_Nat_Onat, Z, Y ), X ) }.
% 1.12/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.12/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol21( X, Y ) ) ) }.
% 1.12/1.61 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X = Y }
% 1.12/1.61 .
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y,
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.12/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.12/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.12/1.61 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.12/1.61 ) }.
% 1.12/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.12/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.12/1.61 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 1.12/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 1.12/1.61 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.12/1.61 ) }.
% 1.12/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.12/1.61 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 1.12/1.61 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.12/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.12/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.12/1.61 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.12/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 1.12/1.61 ) }.
% 1.12/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.12/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.12/1.61 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 1.12/1.61 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 1.12/1.61 .
% 1.12/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.12/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.12/1.61 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 1.12/1.61 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.12/1.61 .
% 1.12/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.12/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.12/1.61 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 1.12/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 1.12/1.61 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.12/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.12/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 1.12/1.61 Y, Z ) ) }.
% 1.12/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.12/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 1.12/1.61 Z, Y ) ) }.
% 1.12/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.12/1.61 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.12/1.61 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.12/1.61 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.12/1.61 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 1.12/1.61 ) ) }.
% 1.12/1.61 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.12/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 1.12/1.61 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.12/1.61 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.12/1.61 { hAPP( c_RealDef_Oreal( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 1.12/1.61 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.12/1.61 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.12/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha5( X, Y ), alpha21
% 1.12/1.61 ( X, Y ) }.
% 1.12/1.61 { ! alpha5( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.12/1.61 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 1.12/1.61 { ! alpha21( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.12/1.61 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 1.12/1.61 { ! alpha21( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.12/1.61 { ! alpha21( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.12/1.61 tc_Nat_Onat ) ) }.
% 1.12/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 1.12/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha21( X, Y ) }.
% 1.12/1.61 { ! alpha5( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.12/1.61 tc_Nat_Onat ) ) }.
% 1.12/1.61 { ! alpha5( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.12/1.61 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.12/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha5( X, Y ) }.
% 1.12/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.12/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha6( X, Y ), alpha22( X
% 1.12/1.61 , Y ) }.
% 1.12/1.61 { ! alpha6( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.12/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.12/1.61 { ! alpha22( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.12/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.12/1.61 { ! alpha22( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.12/1.61 { ! alpha22( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.12/1.61 tc_Nat_Onat ) ) }.
% 1.12/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 1.12/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha22( X, Y ) }.
% 1.12/1.61 { ! alpha6( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.12/1.61 tc_Nat_Onat ) ) }.
% 1.12/1.61 { ! alpha6( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.12/1.61 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.12/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha6( X, Y ) }.
% 1.12/1.61 { ! c_SEQ_Osubseq( X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( X
% 1.12/1.61 , Y ), hAPP( X, c_Nat_OSuc( Y ) ) ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( X, skol22( X ) ),
% 1.12/1.61 hAPP( X, c_Nat_OSuc( skol22( X ) ) ) ), c_SEQ_Osubseq( X ) }.
% 1.12/1.61 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, c_Nat_OSuc(
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) =
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.12/1.62 tc_Nat_Onat, Z, Y ), c_Nat_OSuc( X ) ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.12/1.62 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.12/1.62 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.12/1.62 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 1.12/1.62 ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.12/1.62 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 1.12/1.62 .
% 1.12/1.62 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.12/1.62 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__semidom( X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.12/1.62 c_Groups_Oone__class_Oone( X ) ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__semidom( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.12/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 1.12/1.62 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.12/1.62 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 1.12/1.62 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 1.12/1.62 ) ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.12/1.62 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.12/1.62 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 1.12/1.62 ) ) }.
% 1.12/1.62 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), v_d____ ) }.
% 1.12/1.62 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), v_r ) }.
% 1.12/1.62 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( c_RealDef_Oreal(
% 1.12/1.62 tc_Nat_Onat ), X ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 1.12/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 1.12/1.62 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 1.12/1.62 .
% 1.12/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 1.12/1.62 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 1.12/1.62 }.
% 1.12/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.12/1.62 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 1.12/1.62 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 1.12/1.62 { ! c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) =
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.12/1.62 { hAPP( c_RealDef_Oreal( tc_Nat_Onat ), c_Groups_Ozero__class_Ozero(
% 1.12/1.62 tc_Nat_Onat ) ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.12/1.62 { ! hAPP( c_RealDef_Oreal( tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero
% 1.12/1.62 ( tc_RealDef_Oreal ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.12/1.62 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_RealDef_Oreal(
% 1.12/1.62 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( c_RealDef_Oreal
% 1.12/1.62 ( tc_Nat_Onat ), X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }
% 1.12/1.62 .
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), hAPP(
% 1.12/1.62 c_RealDef_Oreal( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus(
% 1.12/1.62 tc_Nat_Onat, X, Y ) ) = c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.12/1.62 hAPP( c_RealDef_Oreal( tc_Nat_Onat ), X ), hAPP( c_RealDef_Oreal(
% 1.12/1.62 tc_Nat_Onat ), Y ) ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.12/1.62 X, Y, Z ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 1.12/1.62 c_RealDef_Oreal( tc_Nat_Onat ), X ), c_Groups_Ozero__class_Ozero(
% 1.12/1.62 tc_RealDef_Oreal ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.12/1.62 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 1.12/1.62 c_RealDef_Oreal( tc_Nat_Onat ), X ), c_Groups_Ozero__class_Ozero(
% 1.12/1.62 tc_RealDef_Oreal ) ) }.
% 1.12/1.62 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( c_RealDef_Oreal(
% 1.12/1.62 tc_Nat_Onat ), c_Nat_OSuc( X ) ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( c_RealDef_Oreal(
% 1.12/1.62 tc_Nat_Onat ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.62 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( c_RealDef_Oreal(
% 1.12/1.62 tc_Nat_Onat ), X ) ) }.
% 1.12/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.12/1.62 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.12/1.62 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.12/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.12/1.62 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.12/1.62 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 1.12/1.62 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 1.12/1.62 c_Groups_Oone__class_Oone( X ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, Z ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, Y ) ), Z ) }.
% 1.12/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.12/1.62 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 1.12/1.62 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus(
% 1.12/1.62 X, U, Z ), c_Groups_Ominus__class_Ominus( X, T, Y ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( c_RealDef_Oreal
% 1.12/1.62 ( tc_Nat_Onat ), Y ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 1.12/1.62 tc_RealDef_Oreal, X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP
% 1.12/1.62 ( c_RealDef_Oreal( tc_Nat_Onat ), Y ), c_Groups_Oone__class_Oone(
% 1.12/1.62 tc_RealDef_Oreal ) ) ), c_RComplete_Onatceiling( X ) =
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone(
% 1.12/1.62 tc_Nat_Onat ) ) }.
% 1.12/1.62 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.12/1.62 hAPP( X, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol23( Z, Y
% 1.12/1.62 ), Y ) }.
% 1.12/1.62 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.12/1.62 hAPP( X, Y ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.12/1.62 skol23( X, Y ) ), ! hBOOL( hAPP( X, Z ) ) }.
% 1.12/1.62 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.12/1.62 hAPP( X, Y ) ), hBOOL( hAPP( X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 1.12/1.62 , skol23( X, Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.62 ( tc_Nat_Onat ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ),
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) = c_Nat_OSuc(
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ),
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 1.12/1.62 { ! class_Groups_Ozero( X ), !
% 1.12/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.62 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.12/1.62 tc_Polynomial_Opoly( X ) ),
% 1.12/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X,
% 1.12/1.62 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.12/1.62 { c_RComplete_Onatceiling( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 1.12/1.62 ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.12/1.62 { ! class_Int_Onumber( X ), ! c_Int_Onumber__class_Onumber__of( X, Z ) = Y
% 1.12/1.62 , Y = c_Int_Onumber__class_Onumber__of( X, Z ) }.
% 1.12/1.62 { ! class_Int_Onumber( X ), ! Y = c_Int_Onumber__class_Onumber__of( X, Z )
% 1.12/1.62 , c_Int_Onumber__class_Onumber__of( X, Z ) = Y }.
% 1.12/1.62 { ! class_Int_Onumber__ring( X ), ! class_Int_Oring__char__0( X ), !
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( X, Z ) =
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( X, Y ), Z = Y }.
% 1.12/1.62 { ! class_Int_Onumber__ring( X ), ! class_Int_Oring__char__0( X ), ! Z = Y
% 1.12/1.62 , c_Int_Onumber__class_Onumber__of( X, Z ) =
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( X, Y ) }.
% 1.12/1.62 { c_RComplete_Onatceiling( hAPP( c_RealDef_Oreal( tc_Nat_Onat ), X ) ) = X
% 1.12/1.62 }.
% 1.12/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.12/1.62 c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 1.12/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 1.12/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.12/1.62 c_Groups_Oabs__class_Oabs( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 1.12/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 1.12/1.62 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.12/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oabs__class_Oabs( X, Y
% 1.12/1.62 ) ) }.
% 1.12/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.12/1.62 c_Groups_Oabs__class_Oabs( X, c_Groups_Oplus__class_Oplus( X,
% 1.12/1.62 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ) )
% 1.12/1.62 = c_Groups_Oplus__class_Oplus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 1.12/1.62 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 1.12/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.12/1.62 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 1.12/1.62 = c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z )
% 1.12/1.62 ) }.
% 1.12/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.12/1.62 c_Groups_Oabs__class_Oabs( X, c_Groups_Oabs__class_Oabs( X, Y ) ) =
% 1.12/1.62 c_Groups_Oabs__class_Oabs( X, Y ) }.
% 1.12/1.62 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 1.12/1.62 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, Y ) }.
% 1.12/1.62 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, Y ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 1.12/1.62 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 1.12/1.62 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Z
% 1.12/1.62 ), c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y ) }.
% 1.12/1.62 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Z
% 1.12/1.62 ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 1.12/1.62 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( X, T ), c_Groups_Oplus__class_Oplus( X
% 1.12/1.62 , c_Int_Onumber__class_Onumber__of( X, Z ), Y ) ) =
% 1.12/1.62 c_Groups_Oplus__class_Oplus( X, c_Int_Onumber__class_Onumber__of( X,
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, T, Z ) ), Y ) }.
% 1.12/1.62 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( X, Z ),
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 1.12/1.62 tc_Int_Oint, Z, Y ) ) }.
% 1.12/1.62 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ) =
% 1.12/1.62 c_Groups_Oplus__class_Oplus( X, c_Int_Onumber__class_Onumber__of( X, Z )
% 1.12/1.62 , c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 1.12/1.62 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ) =
% 1.12/1.62 c_Groups_Ominus__class_Ominus( X, c_Int_Onumber__class_Onumber__of( X, Z
% 1.12/1.62 ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 1.12/1.62 { c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, hAPP( c_RealDef_Oreal(
% 1.12/1.62 tc_Nat_Onat ), X ) ) = hAPP( c_RealDef_Oreal( tc_Nat_Onat ), X ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.12/1.62 c_RComplete_Onatceiling( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.12/1.62 }.
% 1.12/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RComplete_Onatceiling( X )
% 1.12/1.62 ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 1.12/1.62 Y ), c_RComplete_Onatceiling( X ) ) }.
% 1.12/1.62 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, hAPP(
% 1.12/1.62 c_RealDef_Oreal( tc_Nat_Onat ), c_RComplete_Onatceiling( X ) ) ) }.
% 1.12/1.62 { c_RComplete_Onatceiling( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 1.12/1.62 = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.12/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.12/1.62 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 1.12/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Y ),
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.12/1.62 }.
% 1.12/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq( X,
% 1.12/1.62 c_Groups_Oabs__class_Oabs( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.12/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.12/1.62 ), c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 1.12/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, Y ),
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.12/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.12/1.62 c_Groups_Oabs__class_Oabs( X, Y ) ), ! Y = c_Groups_Ozero__class_Ozero( X
% 1.12/1.62 ) }.
% 1.12/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ), Y =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 1.12/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.12/1.62 c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 1.12/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 1.12/1.62 c_Groups_Oplus__class_Oplus( X, Z, Y ) ), c_Groups_Oplus__class_Oplus( X
% 1.12/1.62 , c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 1.12/1.62 ) }.
% 1.12/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 1.12/1.62 c_Groups_Ominus__class_Ominus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 1.12/1.62 c_Groups_Oabs__class_Oabs( X, Y ) ) ), c_Groups_Oabs__class_Oabs( X,
% 1.12/1.62 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 1.12/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 1.12/1.62 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 1.12/1.62 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 1.12/1.62 ) }.
% 1.12/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 1.12/1.62 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 1.12/1.62 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z ) )
% 1.12/1.62 ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.12/1.62 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Z )
% 1.12/1.62 ), Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus
% 1.12/1.62 ( X, Z, Y ), T ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.12/1.62 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Z )
% 1.12/1.62 ), Y ), c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus
% 1.12/1.62 ( X, Z, Y ) ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.12/1.62 , c_Groups_Ominus__class_Ominus( X, Z, Y ), T ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y
% 1.12/1.62 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X,
% 1.12/1.62 c_Groups_Ominus__class_Ominus( X, T, Z ) ), Y ) }.
% 1.12/1.62 { ! class_Int_Onumber( X ), ! class_Orderings_Olinorder( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 1.12/1.62 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 1.12/1.62 ), c_Int_Onumber__class_Onumber__of( X, Z ) ) }.
% 1.12/1.62 { ! class_Int_Onumber( X ), ! class_Orderings_Olinorder( X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 1.12/1.62 ), c_Int_Onumber__class_Onumber__of( X, Z ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 1.12/1.62 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 1.12/1.62 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( X, T ), c_Groups_Ominus__class_Ominus(
% 1.12/1.62 X, c_Int_Onumber__class_Onumber__of( X, Z ), Y ) ) =
% 1.12/1.62 c_Groups_Ominus__class_Ominus( X, c_Int_Onumber__class_Onumber__of( X,
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, T, Z ) ), Y ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, hAPP(
% 1.12/1.62 c_RealDef_Oreal( tc_Nat_Onat ), X ) ), c_Orderings_Oord__class_Oless__eq
% 1.12/1.62 ( tc_Nat_Onat, c_RComplete_Onatceiling( Y ), X ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 1.12/1.62 X ), Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, hAPP(
% 1.12/1.62 c_RealDef_Oreal( tc_Nat_Onat ), Y ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, hAPP(
% 1.12/1.62 c_RealDef_Oreal( tc_Nat_Onat ), Y ) ), c_Orderings_Oord__class_Oless__eq
% 1.12/1.62 ( tc_Nat_Onat, c_RComplete_Onatceiling( X ), Y ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 1.12/1.62 c_RealDef_Oreal( tc_Nat_Onat ), Y ), X ), c_RComplete_Onatceiling(
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, hAPP( c_RealDef_Oreal
% 1.12/1.62 ( tc_Nat_Onat ), Y ) ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.12/1.62 c_RComplete_Onatceiling( X ), Y ) }.
% 1.12/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 1.12/1.62 c_Groups_Ominus__class_Ominus( X, Z, Y ) ), c_Groups_Oplus__class_Oplus(
% 1.12/1.62 X, c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 1.12/1.62 ) }.
% 1.12/1.62 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 1.12/1.62 c_Groups_Ominus__class_Ominus( X, c_Groups_Oplus__class_Oplus( X, U, T )
% 1.12/1.62 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ), c_Groups_Oplus__class_Oplus
% 1.12/1.62 ( X, c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, U, Z
% 1.12/1.62 ) ), c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T,
% 1.12/1.62 Y ) ) ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs
% 1.12/1.62 ( tc_RealDef_Oreal, X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 1.12/1.62 , X ) }.
% 1.12/1.62 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 1.12/1.62 ( tc_RealDef_Oreal ), c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) )
% 1.12/1.62 ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling
% 1.12/1.62 ( X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 1.12/1.62 X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.12/1.62 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 1.12/1.62 , hAPP( c_RealDef_Oreal( tc_Nat_Onat ), Y ) ) ) =
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatceiling( X ), Y
% 1.12/1.62 ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.12/1.62 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 1.12/1.62 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatceiling( X ),
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.12/1.62 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_w____ ), v_r ) }
% 1.12/1.62 .
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 1.12/1.62 c_RealDef_Oreal( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus(
% 1.12/1.62 tc_Nat_Onat, skol24( X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), X
% 1.12/1.62 ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, hAPP( c_RealDef_Oreal
% 1.12/1.62 ( tc_Nat_Onat ), skol24( X ) ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.12/1.62 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( X ),
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol25( T, U, W ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, T ) ), skol25( X, Y,
% 1.12/1.62 Z ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, T ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, T ) ), skol25( X, Y,
% 1.12/1.62 Z ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, T, Z ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 1.12/1.62 c_RealDef_Oreal( tc_Nat_Onat ), skol26( X ) ), X ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, hAPP( c_RealDef_Oreal
% 1.12/1.62 ( tc_Nat_Onat ), c_Nat_OSuc( skol26( X ) ) ) ) }.
% 1.12/1.62 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_g____( X ) ), v_r
% 1.12/1.62 ) }.
% 1.12/1.62 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.12/1.62 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.12/1.62 tc_Int_Oint ), X ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.12/1.62 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.12/1.62 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 1.12/1.62 }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.12/1.62 tc_Int_Oint ) ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 1.12/1.62 ( tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 1.12/1.62 .
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 1.12/1.62 ( tc_Int_Oint ) ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.12/1.62 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 1.12/1.62 = X }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.12/1.62 tc_Int_Oint ) ) ) }.
% 1.12/1.62 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.12/1.62 tc_Int_Oint ) ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.12/1.62 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 1.12/1.62 }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.12/1.62 tc_Int_Oint ) ), X ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.12/1.62 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.12/1.62 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.12/1.62 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.12/1.62 tc_Int_Oint ) ), X ) }.
% 1.12/1.62 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.12/1.62 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oabs__class_Oabs(
% 1.12/1.62 tc_Int_Oint, X ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.12/1.62 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oabs__class_Oabs(
% 1.12/1.62 tc_Int_Oint, X ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) }.
% 1.12/1.62 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 1.12/1.62 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.12/1.62 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 1.12/1.62 .
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.12/1.62 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 1.12/1.62 .
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.12/1.62 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 1.12/1.62 ( tc_Int_Oint ) ) = X }.
% 1.12/1.62 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.12/1.62 tc_Int_Oint ), X ) = X }.
% 1.12/1.62 { c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) =
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) }.
% 1.12/1.62 { c_RComplete_Onatfloor( c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal
% 1.12/1.62 , X ) ) = c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 1.12/1.62 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.12/1.62 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 1.12/1.62 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 1.12/1.62 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 1.12/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 1.12/1.62 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 1.12/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 1.12/1.62 { c_RComplete_Onatfloor( hAPP( c_RealDef_Oreal( tc_Nat_Onat ), X ) ) = X }
% 1.12/1.62 .
% 1.12/1.62 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ),
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) }.
% 1.12/1.62 { c_RComplete_Onatceiling( c_Int_Onumber__class_Onumber__of(
% 1.12/1.62 tc_RealDef_Oreal, X ) ) = c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 1.12/1.62 X ) }.
% 1.12/1.62 { c_RComplete_Onatfloor( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) )
% 1.12/1.62 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.12/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) )
% 1.12/1.62 }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatfloor( Y
% 1.12/1.62 ), c_RComplete_Onatfloor( X ) ) }.
% 1.12/1.62 { c_RComplete_Onatfloor( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_RComplete_Onatfloor
% 1.12/1.62 ( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 1.12/1.62 c_RealDef_Oreal( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ), X ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 1.12/1.62 c_RealDef_Oreal( tc_Nat_Onat ), Y ), X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_RComplete_Onatfloor
% 1.12/1.62 ( X ) ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol27( X, Y, Z ) ) ), Z ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), hAPP( c_RealDef_Oreal
% 1.12/1.62 ( tc_Nat_Onat ), c_Nat_OSuc( skol70( X, Y ) ) ) ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol77( X, Y, Z ) ) ), hAPP
% 1.12/1.62 ( c_RealDef_Oreal( tc_Nat_Onat ), c_Nat_OSuc( Z ) ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol79( T, U ) ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol77( X, Y, Z ) ) ), hAPP
% 1.12/1.62 ( c_RealDef_Oreal( tc_Nat_Onat ), c_Nat_OSuc( Z ) ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), skol79( X, Y ) ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol28( X, Y, Z ) ) ), Z ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), hAPP( c_RealDef_Oreal
% 1.12/1.62 ( tc_Nat_Onat ), c_Nat_OSuc( skol71( X, Y ) ) ) ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol78( X, Y, Z ) ) ), hAPP
% 1.12/1.62 ( c_RealDef_Oreal( tc_Nat_Onat ), c_Nat_OSuc( Z ) ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol80( T, U ) ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol78( X, Y, Z ) ) ), hAPP
% 1.12/1.62 ( c_RealDef_Oreal( tc_Nat_Onat ), c_Nat_OSuc( Z ) ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, T ) ), skol80( X, Y ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_RComplete_Onatfloor
% 1.12/1.62 ( X ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 1.12/1.62 c_RealDef_Oreal( tc_Nat_Onat ), Y ), X ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 1.12/1.62 c_RealDef_Oreal( tc_Nat_Onat ), Y ), X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_RComplete_Onatfloor
% 1.12/1.62 ( X ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Groups_Oone__class_Oone
% 1.12/1.62 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ) }.
% 1.12/1.62 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( c_RealDef_Oreal(
% 1.12/1.62 tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ), c_Groups_Oone__class_Oone(
% 1.12/1.62 tc_RealDef_Oreal ) ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 1.12/1.62 c_RealDef_Oreal( tc_Nat_Onat ), Y ), X ), c_RComplete_Onatfloor(
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, hAPP( c_RealDef_Oreal
% 1.12/1.62 ( tc_Nat_Onat ), Y ) ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.12/1.62 c_RComplete_Onatfloor( X ), Y ) }.
% 1.12/1.62 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X,
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), hAPP( c_RealDef_Oreal(
% 1.12/1.62 tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, hAPP( c_RealDef_Oreal
% 1.12/1.62 ( tc_Nat_Onat ), Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.12/1.62 c_RComplete_Onatfloor( X ), Y ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.12/1.62 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 1.12/1.62 hAPP( c_RealDef_Oreal( tc_Nat_Onat ), Y ) ) ) =
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( X ), Y )
% 1.12/1.62 }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( Y ),
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, hAPP( c_RealDef_Oreal
% 1.12/1.62 ( tc_Nat_Onat ), X ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 1.12/1.62 c_RealDef_Oreal( tc_Nat_Onat ), Y ), X ), ! c_Orderings_Oord__class_Oless
% 1.12/1.62 ( tc_RealDef_Oreal, X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.12/1.62 hAPP( c_RealDef_Oreal( tc_Nat_Onat ), Y ), c_Groups_Oone__class_Oone(
% 1.12/1.62 tc_RealDef_Oreal ) ) ), c_RComplete_Onatfloor( X ) = Y }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.12/1.62 ( X, Y ) ) ), c_RealVector_Onorm__class_Onorm( X,
% 1.12/1.62 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X,
% 1.12/1.62 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 1.12/1.62 , Y ) ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, U,
% 1.12/1.62 Z ) ), c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 1.12/1.62 ( X, T, Y ) ) ) ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.12/1.62 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 1.12/1.62 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.12/1.62 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 1.12/1.62 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 1.12/1.62 Y ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.12/1.62 ( X, Y ) ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, v_N1____, X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, v_g____( hAPP(
% 1.12/1.62 v_f____, X ) ), v_z____ ) ), v_d____ ) }.
% 1.12/1.62 { c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) = X }.
% 1.12/1.62 { c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, X ) =
% 1.12/1.62 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) }.
% 1.12/1.62 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 1.12/1.62 ( tc_Int_Oint ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 1.12/1.62 Y ) ) = c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 1.12/1.62 ( X, Y, Z ) ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Oabs__class_Oabs
% 1.12/1.62 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ) ) =
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, Y ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, Y ) = c_Groups_Ozero__class_Ozero(
% 1.12/1.62 tc_RealDef_Oreal ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X, Y )
% 1.12/1.62 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 1.12/1.62 tc_RealDef_Oreal ) ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oone__class_Oone( X ) ) =
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.12/1.62 { ! class_Int_Onumber__ring( X ), !
% 1.12/1.62 class_RealVector_Oreal__normed__algebra__1( X ),
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, c_Int_Onumber__class_Onumber__of( X,
% 1.12/1.62 Y ) ) = c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, Y ) ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 1.12/1.62 tc_RealDef_Oreal ) ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 1.12/1.62 tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ),
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, Y ) ), ! Y =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless(
% 1.12/1.62 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 1.12/1.62 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.12/1.62 ( X, Y ) ) ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, U
% 1.12/1.62 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, T ) ) }.
% 1.12/1.62 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ) ),
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.12/1.62 tc_Int_Oint, X, Y ) ) }.
% 1.12/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 1.12/1.62 tc_Int_Oint ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol29( X ), Y ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, v_g____( hAPP(
% 1.12/1.62 v_f____, Y ) ), v_z____ ) ), X ) }.
% 1.12/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 1.12/1.62 tc_Int_Oint ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol30, X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, v_g____( hAPP(
% 1.12/1.62 v_f____, X ) ), v_z____ ) ), v_d____ ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol31, X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, v_g____( hAPP(
% 1.12/1.62 v_f____, X ) ), v_z____ ) ), v_d____ ) }.
% 1.12/1.62 { c_Nat__Numeral_Oneg( c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) )
% 1.12/1.62 , ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.12/1.62 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y
% 1.12/1.62 , c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, X ) ) ) =
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatceiling( Y ),
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) }.
% 1.12/1.62 { c_Nat__Numeral_Oneg( c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) )
% 1.12/1.62 , ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.12/1.62 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, X ) ) ) =
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( Y ),
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) }.
% 1.12/1.62 { ! c_Nat__Numeral_Oneg( c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.12/1.62 { ! c_Nat__Numeral_Oneg( c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.12/1.62 { c_Nat__Numeral_Oneg( X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint
% 1.12/1.62 , c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), ! c_Nat__Numeral_Oneg( X
% 1.12/1.62 ) }.
% 1.12/1.62 { ! c_Nat__Numeral_Oneg( X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X
% 1.12/1.62 , c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Nat__Numeral_Oneg( X ) }
% 1.12/1.62 .
% 1.12/1.62 { ! c_Nat__Numeral_Oneg( c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X )
% 1.12/1.62 ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.12/1.62 { ! c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) =
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ), alpha7( X, Y ) }.
% 1.12/1.62 { ! c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) =
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ), alpha23( X, Y ) }.
% 1.12/1.62 { ! alpha7( X, Y ), ! alpha23( X, Y ), c_Int_Onumber__class_Onumber__of(
% 1.12/1.62 tc_Nat_Onat, Y ) = c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) }.
% 1.12/1.62 { ! alpha23( X, Y ), c_Nat__Numeral_Oneg( c_Int_Onumber__class_Onumber__of
% 1.12/1.62 ( tc_Int_Oint, Y ) ), alpha33( X, Y ) }.
% 1.12/1.62 { ! c_Nat__Numeral_Oneg( c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y )
% 1.12/1.62 ), alpha23( X, Y ) }.
% 1.12/1.62 { ! alpha33( X, Y ), alpha23( X, Y ) }.
% 1.12/1.62 { ! alpha33( X, Y ), alpha38( X, Y ) }.
% 1.12/1.62 { ! alpha33( X, Y ), alpha42( X, Y ) }.
% 1.12/1.62 { ! alpha38( X, Y ), ! alpha42( X, Y ), alpha33( X, Y ) }.
% 1.12/1.62 { ! alpha42( X, Y ), c_Nat__Numeral_Oneg( c_Int_Onumber__class_Onumber__of
% 1.12/1.62 ( tc_Int_Oint, X ) ), Y = X }.
% 1.12/1.62 { ! c_Nat__Numeral_Oneg( c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X )
% 1.12/1.62 ), alpha42( X, Y ) }.
% 1.12/1.62 { ! Y = X, alpha42( X, Y ) }.
% 1.12/1.62 { ! alpha38( X, Y ), ! c_Nat__Numeral_Oneg(
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ),
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ) =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.12/1.62 { c_Nat__Numeral_Oneg( c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) )
% 1.12/1.62 , alpha38( X, Y ) }.
% 1.12/1.62 { ! c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ) =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha38( X, Y ) }.
% 1.12/1.62 { ! alpha7( X, Y ), ! c_Nat__Numeral_Oneg( c_Int_Onumber__class_Onumber__of
% 1.12/1.62 ( tc_Int_Oint, Y ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ),
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.12/1.62 { c_Nat__Numeral_Oneg( c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ) )
% 1.12/1.62 , alpha7( X, Y ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ),
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha7( X, Y ) }.
% 1.12/1.62 { ! c_Nat__Numeral_Oneg( c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Z )
% 1.12/1.62 ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Z ),
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ), X ) ) =
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ), X ) }.
% 1.12/1.62 { c_Nat__Numeral_Oneg( c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Z ) )
% 1.12/1.62 , ! c_Nat__Numeral_Oneg( c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y
% 1.12/1.62 ) ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Z ),
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ), X ) ) =
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Z ), X ) }.
% 1.12/1.62 { c_Nat__Numeral_Oneg( c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Z ) )
% 1.12/1.62 , c_Nat__Numeral_Oneg( c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y )
% 1.12/1.62 ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Z ),
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ), X ) ) =
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) }.
% 1.12/1.62 { ! c_Nat__Numeral_Oneg( c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X )
% 1.12/1.62 ), hAPP( c_RealDef_Oreal( tc_Nat_Onat ),
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.12/1.62 { c_Nat__Numeral_Oneg( c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) )
% 1.12/1.62 , hAPP( c_RealDef_Oreal( tc_Nat_Onat ), c_Int_Onumber__class_Onumber__of
% 1.12/1.62 ( tc_Nat_Onat, X ) ) = c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal
% 1.12/1.62 , X ) }.
% 1.12/1.62 { c_Nat__Numeral_Oneg( c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) )
% 1.12/1.62 , ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ), c_RComplete_Onatfloor
% 1.12/1.62 ( Y ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, X ), Y ) }.
% 1.12/1.62 { c_Nat__Numeral_Oneg( c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) )
% 1.12/1.62 , ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, X ), Y ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ), c_RComplete_Onatfloor
% 1.12/1.62 ( Y ) ) }.
% 1.12/1.62 { c_Nat__Numeral_Oneg( c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) )
% 1.12/1.62 , ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 1.12/1.62 Y ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, X ) ) }.
% 1.12/1.62 { c_Nat__Numeral_Oneg( c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) )
% 1.12/1.62 , ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, X ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 1.12/1.62 Y ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) }.
% 1.12/1.62 { ! c_Nat__Numeral_Oneg( c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y )
% 1.12/1.62 ), c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ), X ) ) =
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 1.12/1.62 tc_Nat_Onat ), X ) }.
% 1.12/1.62 { c_Nat__Numeral_Oneg( c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ) )
% 1.12/1.62 , c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ), X ) ) =
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_Osucc( Y ) ), X ) }
% 1.12/1.62 .
% 1.12/1.62 { ! c_Nat__Numeral_Oneg( c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X )
% 1.12/1.62 ), c_Nat_OSuc( c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.12/1.62 { c_Nat__Numeral_Oneg( c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) )
% 1.12/1.62 , c_Nat_OSuc( c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_Osucc( X ) ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 1.12/1.62 ), c_Orderings_Oord__class_Oless__eq( X, T, skol32( X, U, W, T ) ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, T, V0 ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, V0 ) ),
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 1.12/1.62 ( tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) )
% 1.12/1.62 ) ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 1.12/1.62 ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( Y, c_Groups_Ominus__class_Ominus( Y,
% 1.12/1.62 hAPP( Z, T ), hAPP( Z, skol32( X, Y, Z, T ) ) ) ),
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, U ) ),
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 1.12/1.62 ( tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) )
% 1.12/1.62 ) ) }.
% 1.12/1.62 { ! c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) =
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, X,
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) ),
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, X,
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) ),
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, X, c_Complex_Oii ) ),
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, X, c_Complex_Oii ) )
% 1.12/1.62 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.12/1.62 { ! c_Complex_Oii = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.12/1.62 { ! c_Complex_Oii = c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 1.12/1.62 { ! c_Complex_Oii = c_Int_Onumber__class_Onumber__of( tc_Complex_Ocomplex,
% 1.12/1.62 X ) }.
% 1.12/1.62 { c_Int_Osucc( X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, X,
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.12/1.62 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.12/1.62 c_Int_Osucc( Y ) ) = c_Groups_Oplus__class_Oplus( X,
% 1.12/1.62 c_Groups_Oone__class_Oone( X ), c_Int_Onumber__class_Onumber__of( X, Y )
% 1.12/1.62 ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.12/1.62 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 1.12/1.62 tc_Int_Oint, X, Y ) }.
% 1.12/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.12/1.62 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint
% 1.12/1.62 ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), hAPP( c_RealDef_Oreal
% 1.12/1.62 ( tc_Nat_Onat ), c_Nat_OSuc( skol33( X, Y ) ) ) ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol72( X, Y, Z ) ) ), hAPP
% 1.12/1.62 ( c_RealDef_Oreal( tc_Nat_Onat ), c_Nat_OSuc( Z ) ) ), c_SEQ_OBseq( X, Y
% 1.12/1.62 ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), hAPP( c_RealDef_Oreal
% 1.12/1.62 ( tc_Nat_Onat ), c_Nat_OSuc( skol34( X, Y ) ) ) ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol73( X, Y, Z ) ) ), hAPP
% 1.12/1.62 ( c_RealDef_Oreal( tc_Nat_Onat ), c_Nat_OSuc( Z ) ) ), c_SEQ_OBseq( X, Y
% 1.12/1.62 ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol35( Z, T ) ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), skol35( X, Y ) ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol74( X, Y, Z ) ) ), Z ),
% 1.12/1.62 c_SEQ_OBseq( X, Y ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Nat__Transfer_Otsub( X, Y )
% 1.12/1.62 ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.12/1.62 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 1.12/1.62 tc_Int_Oint, X, Y ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol36( Z, T ) ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), skol36( X, Y ) ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( Z, skol37( X, Y, Z ) ) ), Y ),
% 1.12/1.62 c_SEQ_OBseq( X, Z ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls ),
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 1.12/1.62 tc_Nat_Onat ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.12/1.62 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls ),
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 1.12/1.62 tc_Nat_Onat ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_Osucc( X ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls ),
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ),
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone(
% 1.12/1.62 tc_Nat_Onat ) }.
% 1.12/1.62 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls ),
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ),
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) =
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_Osucc( X ) ) }.
% 1.12/1.62 { c_Int_OPls = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.12/1.62 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Int_OPls, X ) = X }.
% 1.12/1.62 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Int_OPls ) = X }.
% 1.12/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OPls )
% 1.12/1.62 }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, c_Int_OPls ) }
% 1.12/1.62 .
% 1.12/1.62 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Int_OPls ) = X }.
% 1.12/1.62 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.12/1.62 c_Int_OPls ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.12/1.62 { ! class_Int_Onumber__ring( X ), c_Groups_Ozero__class_Ozero( X ) =
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( X, c_Int_OPls ) }.
% 1.12/1.62 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( X, c_Int_OPls ), Y ) = Y }.
% 1.12/1.62 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( X, c_Int_OPls ) ) = Y }.
% 1.12/1.62 { c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OPls ) =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.12/1.62 { c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) =
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OPls ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.12/1.62 { c_Groups_Ozero__class_Ozero( tc_Int_Oint ) =
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OPls ) }.
% 1.12/1.62 { ! c_Nat__Numeral_Oneg( c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 1.12/1.62 c_Int_OPls ) ) }.
% 1.12/1.62 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) =
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ),
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) =
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) }.
% 1.12/1.62 { ! c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ),
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ), alpha8( X, Y ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.12/1.62 { ! alpha8( X, Y ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) }.
% 1.12/1.62 { ! alpha8( X, Y ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ) }.
% 1.12/1.62 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), alpha8( X, Y ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ), alpha8( X
% 1.12/1.62 , Y ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OPls ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OPls ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) }.
% 1.12/1.62 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 1.12/1.62 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OPls ) }.
% 1.12/1.62 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OPls ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 1.12/1.62 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.12/1.62 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, Y ) }.
% 1.12/1.62 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, Y ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 1.12/1.62 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 1.12/1.62 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 1.12/1.62 tc_Int_Oint, Y, c_Int_OPls ) }.
% 1.12/1.62 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 1.12/1.62 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.12/1.62 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.12/1.62 ( tc_Int_Oint, c_Int_OPls, Y ) }.
% 1.12/1.62 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, Y ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.62 ( tc_Nat_Onat ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.12/1.62 tc_Nat_Onat ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ),
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) }.
% 1.12/1.62 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls ),
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) }.
% 1.12/1.62 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls ),
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 1.12/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OPls ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ),
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ),
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = c_Groups_Ozero__class_Ozero
% 1.12/1.62 ( tc_Nat_Onat ) }.
% 1.12/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ),
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ),
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) =
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_Opred( X ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ),
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_Opred( X ) ) ) }.
% 1.12/1.62 { c_Complex_Oexpi( c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) =
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 1.12/1.62 { c_Int_Osucc( c_Int_Opred( X ) ) = X }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_Opred( Y ), X ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_Opred( Y ), X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 1.12/1.62 { c_Int_Opred( X ) = c_Groups_Ominus__class_Ominus( tc_Int_Oint, X,
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.12/1.62 { ! c_Nat__Numeral_Oneg( c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 1.12/1.62 c_Int_Opred( X ) ) ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X )
% 1.12/1.62 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.12/1.62 { ! c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Nat__Numeral_Oneg(
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_Opred( X ) ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.12/1.62 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Groups_Oplus__class_Oplus
% 1.12/1.62 ( tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint,
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ),
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ), Y ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.12/1.62 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Z,
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Groups_Oplus__class_Oplus
% 1.12/1.62 ( tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint,
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, Z ) ),
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ) ) }.
% 1.12/1.62 { ! class_Int_Onumber__ring( X ), ! c_Orderings_Oord__class_Oless__eq(
% 1.12/1.62 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ) ), hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( X ), c_Int_Onumber__class_Onumber__of
% 1.12/1.62 ( tc_Nat_Onat, Y ) ) = c_Int_Onumber__class_Onumber__of( X, Y ) }.
% 1.12/1.62 { ! class_Int_Onumber__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 1.12/1.62 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ) ), hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( X ), c_Int_Onumber__class_Onumber__of
% 1.12/1.62 ( tc_Nat_Onat, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.12/1.62 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 1.12/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Z ) ), Y ), hAPP( hAPP
% 1.12/1.62 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Z ) ), X ) ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.12/1.62 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.12/1.62 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.12/1.62 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.12/1.62 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.12/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.12/1.62 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.12/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.12/1.62 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.12/1.62 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.12/1.62 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 1.12/1.62 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.12/1.62 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 1.12/1.62 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.12/1.62 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.12/1.62 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 1.12/1.62 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 1.12/1.62 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.12/1.62 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 1.12/1.62 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.12/1.62 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.12/1.62 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.12/1.62 ( X ), c_Int_Onumber__class_Onumber__of( X, T ) ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.12/1.62 Z ) ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), Z ) ) ), Y ) }.
% 1.12/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ) ),
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) =
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.12/1.62 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.12/1.62 ( X ), c_Int_Onumber__class_Onumber__of( X, Z ) ),
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ) }.
% 1.12/1.62 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X, hAPP
% 1.12/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ) = hAPP(
% 1.12/1.62 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( X, Z ) ),
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 1.12/1.62 { ! c_Nat__Numeral_Oneg( hAPP( c_Nat_Osemiring__1__class_Oof__nat(
% 1.12/1.62 tc_Int_Oint ), X ) ) }.
% 1.12/1.62 { c_Groups_Oabs__class_Oabs( tc_Int_Oint, hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) = hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 1.12/1.62 ( c_Nat_Osemiring__1__class_Oof__nat( X ), Y ) ) = hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( X ), Y ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.12/1.62 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.12/1.62 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.12/1.62 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.12/1.62 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.12/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.12/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.12/1.62 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 1.12/1.62 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 1.12/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.12/1.62 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 1.12/1.62 ) ), T ), Y ) }.
% 1.12/1.62 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.12/1.62 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.12/1.62 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.12/1.62 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.12/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.12/1.62 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.12/1.62 ), U = Z, T = Y }.
% 1.12/1.62 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.12/1.62 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.12/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.12/1.62 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.12/1.62 ) }.
% 1.12/1.62 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.12/1.62 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.12/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.12/1.62 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.12/1.62 ) }.
% 1.12/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.12/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 1.12/1.62 ) ), Z ) }.
% 1.12/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.12/1.62 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.12/1.62 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.12/1.62 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.12/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.12/1.62 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.12/1.62 ) }.
% 1.12/1.62 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.12/1.62 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.12/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.12/1.62 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.12/1.62 ), ! U = T }.
% 1.12/1.62 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.12/1.62 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.12/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.12/1.62 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.12/1.62 ), ! Z = Y }.
% 1.12/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.12/1.62 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__idom( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 1.12/1.62 c_Groups_Oabs__class_Oabs( X, Y ) ) = hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 1.12/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 1.12/1.62 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 1.12/1.62 { c_RealDef_Oreal( tc_Nat_Onat ) = c_Nat_Osemiring__1__class_Oof__nat(
% 1.12/1.62 tc_RealDef_Oreal ) }.
% 1.12/1.62 { c_RealDef_Oreal( tc_Nat_Onat ) = c_Nat_Osemiring__1__class_Oof__nat(
% 1.12/1.62 tc_RealDef_Oreal ) }.
% 1.12/1.62 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.12/1.62 { ! class_Nat_Osemiring__char__0( X ), ! hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( X ), Z ) = hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( X ), Y ), Z = Y }.
% 1.12/1.62 { ! class_Nat_Osemiring__char__0( X ), ! Z = Y, hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( X ), Z ) = hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( X ), Y ) }.
% 1.12/1.62 { ! class_Rings_Osemiring__1( X ), hAPP( c_Nat_Osemiring__1__class_Oof__nat
% 1.12/1.62 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y )
% 1.12/1.62 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( X ), Z ) ), hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( X ), Y ) ) }.
% 1.12/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.12/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 1.12/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.12/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 1.12/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.12/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 1.12/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.12/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 1.12/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 1.12/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.12/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 1.12/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 1.12/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.12/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( X ), Y ) ) = hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_RealDef_Oreal ), Y ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 1.12/1.62 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 1.12/1.62 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 1.12/1.62 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 1.12/1.62 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ) ) }.
% 1.12/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 1.12/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 1.12/1.62 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.12/1.62 = Y }.
% 1.12/1.62 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.12/1.62 = Y }.
% 1.12/1.62 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.12/1.62 = Y }.
% 1.12/1.62 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.12/1.62 = Y }.
% 1.12/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.12/1.62 = Y }.
% 1.12/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.12/1.62 = Y }.
% 1.12/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Int_OPls ), X
% 1.12/1.62 ) = c_Int_OPls }.
% 1.12/1.62 { ! class_Rings_Olinordered__semidom( X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.12/1.62 hAPP( c_Nat_Osemiring__1__class_Oof__nat( X ), Y ) ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__semidom( X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.12/1.62 hAPP( c_Nat_Osemiring__1__class_Oof__nat( X ), Y ) ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.12/1.62 ( X, hAPP( c_Nat_Osemiring__1__class_Oof__nat( X ), Y ),
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.12/1.62 { ! class_Rings_Osemiring__1( X ), hAPP( c_Nat_Osemiring__1__class_Oof__nat
% 1.12/1.62 ( X ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.12/1.62 ( X, hAPP( c_Nat_Osemiring__1__class_Oof__nat( X ), Z ), hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( X ), Y ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.12/1.62 ( tc_Nat_Onat, Z, Y ), c_Orderings_Oord__class_Oless( X, hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( X ), Z ), hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( X ), Y ) ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.12/1.62 ( X, hAPP( c_Nat_Osemiring__1__class_Oof__nat( X ), Z ), hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( X ), Y ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.12/1.62 ( tc_Nat_Onat, Z, Y ), c_Orderings_Oord__class_Oless( X, hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( X ), Z ), hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( X ), Y ) ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__semidom( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( X ), Z ), hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( X ), Y ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__semidom( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( X ), Z ), hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( X ), Y ) ) }.
% 1.12/1.62 { ! class_Rings_Osemiring__1( X ), hAPP( c_Nat_Osemiring__1__class_Oof__nat
% 1.12/1.62 ( X ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ) =
% 1.12/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( c_Nat_Osemiring__1__class_Oof__nat
% 1.12/1.62 ( X ), Z ), hAPP( c_Nat_Osemiring__1__class_Oof__nat( X ), Y ) ) }.
% 1.12/1.62 { ! class_Rings_Osemiring__1( X ), hAPP( c_Nat_Osemiring__1__class_Oof__nat
% 1.12/1.62 ( X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) =
% 1.12/1.62 c_Groups_Oone__class_Oone( X ) }.
% 1.12/1.62 { c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ),
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.12/1.62 { hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ),
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.12/1.62 { ! hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.12/1.62 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 1.12/1.62 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.12/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha9( X, Y
% 1.12/1.62 , Z ), alpha24( X, Y, Z ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha9( X, Y, Z ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.12/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha24( X, Y, Z ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.12/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.12/1.62 { ! alpha24( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.12/1.62 { ! alpha24( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.12/1.62 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ) ), alpha24( X, Y, Z ) }.
% 1.12/1.62 { ! alpha9( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.12/1.62 { ! alpha9( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.12/1.62 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ), Y ), alpha9( X, Y, Z ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.12/1.62 ( X ) ), alpha10( X, Y, Z ), alpha25( X, Y, Z ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha10( X, Y, Z ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.12/1.62 ( X ) ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha25( X, Y, Z ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.12/1.62 ( X ) ) }.
% 1.12/1.62 { ! alpha25( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.12/1.62 { ! alpha25( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.12/1.62 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.12/1.62 ( X ), Y ), alpha25( X, Y, Z ) }.
% 1.12/1.62 { ! alpha10( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.12/1.62 { ! alpha10( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.12/1.62 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ) ), alpha10( X, Y, Z ) }.
% 1.12/1.62 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.12/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.12/1.62 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.12/1.62 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.12/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.12/1.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.12/1.62 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.12/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.12/1.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.12/1.62 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.12/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.12/1.62 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.12/1.62 ( X ) ) }.
% 1.12/1.62 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.12/1.62 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 1.12/1.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.12/1.62 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.12/1.62 { ! class_Rings_Oordered__semiring( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.12/1.62 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.12/1.62 { ! class_Rings_Oordered__semiring( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.12/1.62 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.12/1.62 { ! class_Rings_Oordered__comm__semiring( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.12/1.62 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.12/1.62 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.12/1.62 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.12/1.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.12/1.62 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.12/1.62 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.12/1.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.12/1.62 { ! class_Rings_Oordered__semiring( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.12/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.12/1.62 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.12/1.62 { ! class_Rings_Oordered__semiring( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.12/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.12/1.62 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.12/1.62 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.12/1.62 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.12/1.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.12/1.62 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.12/1.62 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.12/1.62 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.12/1.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.12/1.62 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.12/1.62 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.12/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.12/1.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.12/1.62 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 1.12/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.12/1.62 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.12/1.62 ( X ) ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 1.12/1.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha11( X, Y, Z, T ),
% 1.12/1.62 alpha26( X, Y, Z, T ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha11( X, Y, Z, T ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha26( X, Y, Z, T ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.12/1.62 { ! alpha26( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.12/1.62 { ! alpha26( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.12/1.62 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha26( X, Y, Z, T ) }.
% 1.12/1.62 { ! alpha11( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.12/1.62 { ! alpha11( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.12/1.62 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha11( X, Y, Z, T ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha12( X, Y, Z, T ),
% 1.12/1.62 alpha27( X, Y, Z, T ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha12( X, Y, Z, T ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha27( X, Y, Z, T ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.12/1.62 { ! alpha27( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.12/1.62 { ! alpha27( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 1.12/1.62 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha27( X, Y, Z, T ) }.
% 1.12/1.62 { ! alpha12( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 1.12/1.62 { ! alpha12( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 1.12/1.62 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha12( X, Y, Z, T ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.12/1.62 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.12/1.62 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 1.12/1.62 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.12/1.62 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.12/1.62 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.12/1.62 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.12/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.12/1.62 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.12/1.62 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.12/1.62 ( X ) ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.12/1.62 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.12/1.62 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.12/1.62 ( X ) ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.12/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.12/1.62 .
% 1.12/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.12/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 1.12/1.62 .
% 1.12/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.12/1.62 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.12/1.62 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 1.12/1.62 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.12/1.62 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.12/1.62 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.12/1.62 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.12/1.62 ( X ) ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.12/1.62 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.12/1.62 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.12/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.12/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.12/1.62 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 1.12/1.62 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.12/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.12/1.62 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.12/1.62 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.12/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.12/1.62 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.12/1.62 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.12/1.62 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.12/1.62 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.12/1.62 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.12/1.62 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.12/1.62 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 1.12/1.62 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.12/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), skol38( Y ) ), hBOOL( hAPP( X
% 1.12/1.62 , hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Z ) ) ) }.
% 1.12/1.62 { ! hBOOL( hAPP( X, skol38( X ) ) ), hBOOL( hAPP( X, hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) ) ) }.
% 1.12/1.62 { ! hBOOL( hAPP( X, hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint )
% 1.12/1.62 , skol75( X ) ) ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), hBOOL( hAPP( X, Y ) ) }
% 1.12/1.62 .
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), ! hBOOL( hAPP( X, Y ) )
% 1.12/1.62 , hBOOL( hAPP( X, hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint )
% 1.12/1.62 , skol39( X ) ) ) ) }.
% 1.12/1.62 { ! hBOOL( hAPP( X, hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint )
% 1.12/1.62 , Y ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), skol76( Z ) ) }.
% 1.12/1.62 { ! hBOOL( hAPP( X, hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint )
% 1.12/1.62 , Y ) ) ), hBOOL( hAPP( X, skol76( X ) ) ) }.
% 1.12/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) }.
% 1.12/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ),
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.12/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.12/1.62 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.12/1.62 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 1.12/1.62 ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.12/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.12/1.62 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.12/1.62 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 1.12/1.62 ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.12/1.62 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 1.12/1.62 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.12/1.62 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 1.12/1.62 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 1.12/1.62 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ), hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ), hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ), hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ), hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ), hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ), hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ), hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ), hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.12/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.12/1.62 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 1.12/1.62 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.12/1.62 { ! class_Int_Onumber( X ), ! class_Rings_Osemiring( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.12/1.62 ) ), c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 1.12/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.12/1.62 ( X ), T ), c_Int_Onumber__class_Onumber__of( X, Y ) ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), c_Int_Onumber__class_Onumber__of
% 1.12/1.62 ( X, Y ) ) ) }.
% 1.12/1.62 { ! class_Int_Onumber( X ), ! class_Rings_Osemiring( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.12/1.62 T ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) =
% 1.12/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.12/1.62 ( X ), c_Int_Onumber__class_Onumber__of( X, T ) ), Z ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.12/1.62 T ) ), Y ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), X =
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), skol40( X, Y ) ) ) }.
% 1.12/1.62 { ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Z ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 1.12/1.62 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ), hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) = hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ),
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.12/1.62 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ), hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) = hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ),
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.12/1.62 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Z ),
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ), X ) ) =
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ),
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) }.
% 1.12/1.62 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.12/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.12/1.62 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.12/1.62 W ) ), U ), Y ) }.
% 1.12/1.62 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.12/1.62 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.12/1.62 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.12/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.12/1.62 ( X ), Z ), U ), Y ) }.
% 1.12/1.62 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.12/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.12/1.62 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.12/1.62 Z ) ), U ), T ) = Y }.
% 1.12/1.62 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.12/1.62 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.12/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.12/1.62 ( X ), Z ), U ), Y ) }.
% 1.12/1.62 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.12/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.12/1.62 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 1.12/1.62 Z ) ), Y ) ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.12/1.62 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.12/1.62 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.12/1.62 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.12/1.62 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 1.12/1.62 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 1.12/1.62 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 1.12/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.12/1.62 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.12/1.62 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 1.12/1.62 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.12/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 1.12/1.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 1.12/1.62 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.12/1.62 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 1.12/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.12/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 1.12/1.62 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 1.12/1.62 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.12/1.62 { ! class_Int_Onumber( X ), ! class_Rings_Oring( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.12/1.62 T ) ), c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 1.12/1.62 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.12/1.62 T ) ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( X, T ) ), Y ) ) }.
% 1.12/1.62 { ! class_Int_Onumber( X ), ! class_Rings_Oring( X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 1.12/1.62 Z ) ), c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 1.12/1.62 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 1.12/1.62 ( X, Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( X, Y ) ) ) }.
% 1.12/1.62 { c_Groups_Oone__class_Oone( tc_Int_Oint ) = hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ),
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.12/1.62 { hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ),
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone(
% 1.12/1.62 tc_Int_Oint ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.12/1.62 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), ! c_Orderings_Oord__class_Oless
% 1.12/1.62 ( X, c_Groups_Oabs__class_Oabs( X, U ), T ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 1.12/1.62 c_Groups_Oabs__class_Oabs( X, U ) ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.12/1.62 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 1.12/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 1.12/1.62 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.12/1.62 { ! c_Groups_Oabs__class_Oabs( tc_Int_Oint, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) =
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 1.12/1.62 tc_Int_Oint, X ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.12/1.62 { c_Nat__Transfer_Otsub( hAPP( c_Nat_Osemiring__1__class_Oof__nat(
% 1.12/1.62 tc_Int_Oint ), Y ), hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint
% 1.12/1.62 ), X ) ) = hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ),
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 1.12/1.62 { ! class_Rings_Osemiring__1( X ), hAPP( c_Nat_Osemiring__1__class_Oof__nat
% 1.12/1.62 ( X ), c_Nat_OSuc( Y ) ) = c_Groups_Oplus__class_Oplus( X,
% 1.12/1.62 c_Groups_Oone__class_Oone( X ), hAPP( c_Nat_Osemiring__1__class_Oof__nat
% 1.12/1.62 ( X ), Y ) ) }.
% 1.12/1.62 { ! class_Rings_Oring__1( X ), ! c_Orderings_Oord__class_Oless__eq(
% 1.12/1.62 tc_Nat_Onat, Z, Y ), hAPP( c_Nat_Osemiring__1__class_Oof__nat( X ),
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ) ) =
% 1.12/1.62 c_Groups_Ominus__class_Ominus( X, hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( X ), Y ), hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( X ), Z ) ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.12/1.62 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.12/1.62 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.12/1.62 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.12/1.62 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.12/1.62 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.12/1.62 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.12/1.62 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.12/1.62 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.12/1.62 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.12/1.62 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 1.12/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.12/1.62 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 1.12/1.62 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.12/1.62 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.12/1.62 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.12/1.62 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 1.12/1.62 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.12/1.62 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.12/1.62 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.12/1.62 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ),
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.12/1.62 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ),
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.12/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 1.12/1.62 }.
% 1.12/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.12/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.12/1.62 }.
% 1.12/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.12/1.62 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.12/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 1.12/1.62 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 1.12/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.12/1.62 { hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), c_Nat_OSuc(
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) =
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 1.12/1.62 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.12/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.12/1.62 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.12/1.62 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.12/1.62 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.12/1.62 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.12/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.12/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 1.12/1.62 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.12/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.12/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 1.12/1.62 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 1.12/1.62 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.12/1.62 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.12/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.12/1.62 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 1.12/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.12/1.62 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 1.12/1.62 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.12/1.62 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.12/1.62 Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.12/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.12/1.62 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.12/1.62 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.12/1.62 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.12/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.12/1.62 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 1.12/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.12/1.62 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 1.12/1.62 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.12/1.62 , T, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.12/1.62 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 1.12/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.12/1.62 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.12/1.62 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.12/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.12/1.62 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 1.12/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 1.12/1.62 ( X, Z, W ) ), U ), Y ) ) }.
% 1.12/1.62 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 1.12/1.62 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.12/1.62 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 1.12/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.12/1.62 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.12/1.62 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.12/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.12/1.62 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.12/1.62 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.12/1.62 X, W, Z ) ), U ), T ), Y ) }.
% 1.12/1.62 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.12/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.12/1.62 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.12/1.62 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.12/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.12/1.62 ( X ), Z ), U ), Y ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), X =
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), c_Nat_OSuc( skol41( X
% 1.12/1.62 , Y ) ) ) ) }.
% 1.12/1.62 { ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), c_Nat_OSuc( Z ) ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.12/1.62 { hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), c_Nat_OSuc( X )
% 1.12/1.62 ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oone__class_Oone
% 1.12/1.62 ( tc_Int_Oint ), hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint )
% 1.12/1.62 , X ) ) }.
% 1.12/1.62 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 1.12/1.62 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 1.12/1.62 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.12/1.62 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 1.12/1.62 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 1.12/1.62 .
% 1.12/1.62 { ! class_Rings_Oordered__ring__abs( X ), alpha49( X, Z ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.12/1.62 ), c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 1.12/1.62 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 1.12/1.62 { ! class_Rings_Oordered__ring__abs( X ), alpha49( X, Z ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.12/1.62 ), c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 1.12/1.62 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 1.12/1.62 { ! alpha49( X, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.12/1.62 { ! alpha49( X, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.12/1.62 { c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.12/1.62 ), c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero
% 1.12/1.62 ( X ) ), alpha49( X, Y ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.12/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 1.12/1.62 Y ) = c_Groups_Oabs__class_Oabs( X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ), hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) ) = hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ),
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.12/1.62 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.12/1.62 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.12/1.62 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.12/1.62 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.12/1.62 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 1.12/1.62 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.12/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( X ), Y ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.12/1.62 tc_Nat_Onat ), Y ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.12/1.62 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.12/1.62 ( c_Nat_Osemiring__1__class_Oof__nat( X ), Y ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.12/1.62 ( tc_Int_Oint ), hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint )
% 1.12/1.62 , X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.62 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__semiring__1( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.12/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.12/1.62 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 1.12/1.62 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 1.12/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.12/1.62 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 1.12/1.62 ), Y ) }.
% 1.12/1.62 { ! c_Nat__Numeral_Oneg( c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X )
% 1.12/1.62 ), hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ),
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.12/1.62 { c_Nat__Numeral_Oneg( c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) )
% 1.12/1.62 , hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ),
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) }.
% 1.12/1.62 { ! class_Int_Onumber__ring( X ), ! c_Nat__Numeral_Oneg(
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ) ), hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( X ), c_Int_Onumber__class_Onumber__of
% 1.12/1.62 ( tc_Nat_Onat, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.12/1.62 { ! class_Int_Onumber__ring( X ), c_Nat__Numeral_Oneg(
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ) ), hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( X ), c_Int_Onumber__class_Onumber__of
% 1.12/1.62 ( tc_Nat_Onat, Y ) ) = c_Int_Onumber__class_Onumber__of( X, Y ) }.
% 1.12/1.62 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.12/1.62 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ), U ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 1.12/1.62 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 1.12/1.62 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 1.12/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 1.12/1.62 { ! hBOOL( hAPP( Z, hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint )
% 1.12/1.62 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) ), alpha13( X, Y
% 1.12/1.62 , Z ) }.
% 1.12/1.62 { ! hBOOL( hAPP( Z, hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint )
% 1.12/1.62 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) ), alpha28( X, Y
% 1.12/1.62 , Z ) }.
% 1.12/1.62 { ! alpha13( X, Y, Z ), ! alpha28( X, Y, Z ), hBOOL( hAPP( Z, hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ),
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) ) }.
% 1.12/1.62 { ! alpha28( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 1.12/1.62 ), hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.12/1.62 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha28( X, Y, Z ) }
% 1.12/1.62 .
% 1.12/1.62 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), alpha28
% 1.12/1.62 ( X, Y, Z ) }.
% 1.12/1.62 { ! alpha13( X, Y, Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X
% 1.12/1.62 , Y ), hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ), hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) ) ) }.
% 1.12/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), alpha13( X, Y, Z
% 1.12/1.62 ) }.
% 1.12/1.62 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ), hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) ) ), alpha13( X
% 1.12/1.62 , Y, Z ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.12/1.62 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.12/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.12/1.62 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.12/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 1.12/1.62 ( tc_Int_Oint ), Y ) }.
% 1.12/1.62 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.12/1.62 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.12/1.62 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.12/1.62 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 1.12/1.62 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 1.12/1.62 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP( hAPP
% 1.12/1.62 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), Z = Y }.
% 1.12/1.62 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 1.12/1.62 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP(
% 1.12/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) }.
% 1.12/1.62 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP( hAPP
% 1.12/1.62 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ), Z = Y }.
% 1.12/1.62 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 1.12/1.62 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP(
% 1.12/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) }.
% 1.12/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.12/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.12/1.62 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.12/1.62 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.12/1.62 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.12/1.62 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.12/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 1.12/1.62 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.12/1.62 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.12/1.62 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.12/1.62 .
% 1.12/1.62 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.12/1.62 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.12/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 1.12/1.62 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.12/1.62 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.12/1.62 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 1.12/1.62 .
% 1.12/1.62 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.12/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.12/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.12/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ) ), X ) =
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.12/1.62 { hAPP( c_RealDef_Oreal( tc_Nat_Onat ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( c_RealDef_Oreal
% 1.12/1.62 ( tc_Nat_Onat ), Y ) ), hAPP( c_RealDef_Oreal( tc_Nat_Onat ), X ) ) }.
% 1.12/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP
% 1.12/1.62 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) ), X ) =
% 1.12/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), hAPP
% 1.12/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.12/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) =
% 1.12/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y )
% 1.12/1.62 }.
% 1.12/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 1.12/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.12/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 1.12/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.12/1.62 { ! hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) = hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ), Y = X }.
% 1.12/1.62 { ! Y = X, hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) =
% 1.12/1.62 hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) }.
% 1.12/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) ), hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) = hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.12/1.62 { hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) ), hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.12/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 1.12/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 1.12/1.62 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 1.12/1.62 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.12/1.62 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 1.12/1.62 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.12/1.62 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.12/1.62 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 1.12/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.12/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.12/1.62 { ! hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) = hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ), Y = X }.
% 1.12/1.62 { ! Y = X, hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) =
% 1.12/1.62 hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) }.
% 1.12/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) ), hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) = hAPP(
% 1.12/1.62 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.12/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) = X }.
% 1.12/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 1.12/1.62 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.12/1.62 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.12/1.62 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 1.12/1.62 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.12/1.62 , Y ), X ) }.
% 1.12/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.12/1.62 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 1.12/1.62 tc_Nat_Onat ) }.
% 1.12/1.62 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 1.12/1.62 tc_Nat_Onat ) }.
% 1.12/1.62 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.12/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_RComplete_Onatfloor( X )
% 1.12/1.62 ), c_RComplete_Onatfloor( Y ) ), c_RComplete_Onatfloor( hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ) }.
% 1.12/1.62 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.12/1.62 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 1.12/1.62 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.12/1.62 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.12/1.62 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 1.12/1.62 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.12/1.62 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.12/1.62 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.62 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.12/1.62 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.62 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.12/1.62 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.62 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.12/1.62 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.12/1.62 Y ), X ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.12/1.62 tc_Nat_Onat ), Z ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.62 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 1.12/1.62 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.12/1.62 tc_Nat_Onat ), Y ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.62 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 1.12/1.62 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.12/1.62 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.12/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 1.12/1.62 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.12/1.62 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.12/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 1.12/1.62 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.12/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.12/1.62 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.12/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.12/1.62 ), X ) ) }.
% 1.12/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 1.12/1.62 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.12/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 1.12/1.62 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.12/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.12/1.62 ), X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.12/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.12/1.62 ), X ) ) }.
% 1.12/1.62 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 1.12/1.62 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.12/1.62 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.12/1.62 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.12/1.62 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.12/1.62 { c_Complex_Oexpi( c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X )
% 1.12/1.62 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.12/1.62 c_Complex_Oexpi( Y ) ), c_Complex_Oexpi( X ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.12/1.62 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 1.12/1.62 ) }.
% 1.12/1.62 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.12/1.62 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 1.12/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 1.12/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.12/1.62 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 1.12/1.62 ) }.
% 1.12/1.62 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.12/1.62 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 1.12/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 1.12/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ),
% 1.12/1.62 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Z ) ) ), Y =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.12/1.62 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, Z ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ),
% 1.12/1.62 c_RealVector_Onorm__class_Onorm( X, T ) ) ), Z =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 1.12/1.62 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.12/1.62 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 1.12/1.62 ( tc_Nat_Onat ) ) ), X ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ), hAPP( hAPP
% 1.12/1.62 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ),
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.12/1.62 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ),
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, c_Int_OPls ), hAPP( hAPP
% 1.12/1.62 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Z ) ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ), X ) ) =
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.12/1.62 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, c_Int_OPls ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Z ) ), hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ), X ) ) = hAPP( hAPP
% 1.12/1.62 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.12/1.62 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ) ), X ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.12/1.62 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.12/1.62 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.12/1.62 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.12/1.62 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.12/1.62 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.12/1.62 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 1.12/1.62 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.12/1.62 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.12/1.62 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.12/1.62 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 1.12/1.62 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.12/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 1.12/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.12/1.62 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 1.12/1.62 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 1.12/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.12/1.62 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 1.12/1.62 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.12/1.62 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 1.12/1.62 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.12/1.62 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 1.12/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.12/1.62 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.12/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 1.12/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.12/1.62 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 1.12/1.62 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 1.12/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.12/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.12/1.63 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.12/1.63 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.12/1.63 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.12/1.63 .
% 1.12/1.63 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 1.12/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 1.12/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 1.12/1.63 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 1.12/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 1.12/1.63 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.12/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 1.12/1.63 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.63 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.12/1.63 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.12/1.63 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.63 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.12/1.63 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.12/1.63 tc_Nat_Onat ), X ), Y ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.12/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 1.12/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 1.12/1.63 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.12/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 1.12/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ), T =
% 1.12/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.12/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! T =
% 1.12/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.12/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ),
% 1.12/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 1.12/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.12/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.12/1.63 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 1.12/1.63 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) =
% 1.12/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, T,
% 1.12/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.12/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.12/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 1.12/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 1.12/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.12/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 1.12/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.12/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.12/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 1.12/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.12/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 1.12/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ),
% 1.12/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.12/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.12/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.12/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z,
% 1.12/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 1.12/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.12/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.12/1.63 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 1.12/1.63 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) =
% 1.12/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.12/1.63 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.12/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.12/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 1.12/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.12/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.12/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.12/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.12/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.12/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 1.12/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 1.12/1.63 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ), X =
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.12/1.63 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 1.12/1.63 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.12/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol42( Z, T ) ) }.
% 1.12/1.63 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.12/1.63 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol42( X, Y ) ) ) }.
% 1.12/1.63 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.12/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol43( Y ) ) }.
% 1.12/1.63 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.12/1.63 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 1.12/1.63 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol43( X ) ) ) }.
% 1.12/1.63 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.12/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol44( Z, T ) ) }.
% 1.12/1.63 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.12/1.63 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol44( X, Y ) ) ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.12/1.63 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol45( Z, Y ) ) ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U ) )
% 1.12/1.63 , hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus( tc_Int_Oint, U, hAPP(
% 1.12/1.63 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.12/1.63 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus(
% 1.12/1.63 tc_Int_Oint, skol45( X, Y ), X ) ) ), ! c_Orderings_Oord__class_Oless__eq
% 1.12/1.63 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL(
% 1.12/1.63 hAPP( Y, T ) ), hBOOL( hAPP( Y, c_Groups_Ominus__class_Ominus(
% 1.12/1.63 tc_Int_Oint, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 1.12/1.63 , Z ), X ) ) ) ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.12/1.63 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol46( Z, Y ) ) ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U ) )
% 1.12/1.63 , hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP
% 1.12/1.63 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.12/1.63 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus(
% 1.12/1.63 tc_Int_Oint, skol46( X, Y ), X ) ) ), ! c_Orderings_Oord__class_Oless__eq
% 1.12/1.63 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL(
% 1.12/1.63 hAPP( Y, T ) ), hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint
% 1.12/1.63 , T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) )
% 1.12/1.63 ) ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.12/1.63 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), skol47( Y ) ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.12/1.63 ( tc_Int_Oint ), X ), X = hAPP( c_Nat_Osemiring__1__class_Oof__nat(
% 1.12/1.63 tc_Int_Oint ), skol47( X ) ) }.
% 1.12/1.63 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol48( Y ) ) }.
% 1.12/1.63 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.12/1.63 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 1.12/1.63 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol48( X ) ) ) }.
% 1.12/1.63 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol49( Z, T ) ) }.
% 1.12/1.63 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.12/1.63 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol49( X, Y ) ) ) }.
% 1.12/1.63 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol50( Z, T ) ) }.
% 1.12/1.63 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.12/1.63 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol50( X, Y ) ) ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( c_RealDef_Oreal
% 1.12/1.63 ( tc_Nat_Onat ), Y ) ), X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal
% 1.12/1.63 ) ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.12/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 1.12/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), Y ) ) }.
% 1.12/1.63 { c_Complex_Ocis( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.12/1.63 tc_RealDef_Oreal ), hAPP( c_RealDef_Oreal( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 1.12/1.63 ) ), X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.12/1.63 tc_Complex_Ocomplex ), c_Complex_Ocis( X ) ), c_Complex_Ocis( hAPP( hAPP
% 1.12/1.63 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP(
% 1.12/1.63 c_RealDef_Oreal( tc_Nat_Onat ), Y ) ), X ) ) ) }.
% 1.12/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 1.12/1.63 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.12/1.63 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 1.12/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.12/1.63 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) }.
% 1.12/1.63 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.63 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.12/1.63 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) ) }.
% 1.12/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.12/1.63 tc_Nat_Onat ) ) = Y }.
% 1.12/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 1.12/1.63 tc_Nat_Onat, Z, Y ) ) }.
% 1.12/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 1.12/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 1.12/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.12/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 1.12/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.12/1.63 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.12/1.63 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.12/1.63 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 1.12/1.63 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ) =
% 1.12/1.63 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.12/1.63 .
% 1.12/1.63 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.12/1.63 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.12/1.63 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 1.12/1.63 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ) =
% 1.12/1.63 c_Groups_Ozero__class_Ozero( X ), ! c_Int_Onumber__class_Onumber__of(
% 1.12/1.63 tc_Nat_Onat, Y ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.12/1.63 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.12/1.63 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.12/1.63 , ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.12/1.63 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) =
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Z ), c_Int_Onumber__class_Onumber__of
% 1.12/1.63 ( tc_Nat_Onat, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.12/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.12/1.63 c_Complex_Ocis( Y ) ), c_Complex_Ocis( X ) ) = c_Complex_Ocis(
% 1.12/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 1.12/1.63 { c_Complex_Ocis( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 1.12/1.63 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__semidom( X ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.12/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone
% 1.12/1.63 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ), Y ) }.
% 1.12/1.63 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), !
% 1.12/1.63 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) =
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.12/1.63 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ) =
% 1.12/1.63 c_Groups_Oone__class_Oone( X ) }.
% 1.12/1.63 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ),
% 1.12/1.63 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) =
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.12/1.63 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ) =
% 1.12/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.12/1.63 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP
% 1.12/1.63 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.12/1.63 Y ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.12/1.63 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 1.12/1.63 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 1.12/1.63 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 1.12/1.63 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 1.12/1.63 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 1.12/1.63 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 1.12/1.63 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 1.12/1.63 c_Groups_Oone__class_Oone( X ) }.
% 1.12/1.63 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.12/1.63 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 1.12/1.63 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.12/1.63 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 1.12/1.63 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 1.12/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.12/1.63 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP(
% 1.12/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) ), X ) = hAPP(
% 1.12/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.12/1.63 { hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP(
% 1.12/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) ), X ) }.
% 1.12/1.63 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP(
% 1.12/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ) ), X ) = hAPP(
% 1.12/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.63 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.12/1.63 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.12/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.12/1.63 tc_Nat_Onat ), Y ) }.
% 1.12/1.63 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.12/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.12/1.63 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 1.12/1.63 ), X ) ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.63 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.63 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.12/1.63 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.63 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.12/1.63 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.12/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.12/1.63 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 1.12/1.63 ), X ) ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 1.12/1.63 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 1.12/1.63 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 1.12/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.12/1.63 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.12/1.63 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 1.12/1.63 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.12/1.63 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.12/1.63 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 1.12/1.63 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 1.12/1.63 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.12/1.63 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), hAPP(
% 1.12/1.63 c_RealDef_Oreal( tc_Nat_Onat ), Y ) ), X ) = hAPP( c_RealDef_Oreal(
% 1.12/1.63 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 1.12/1.63 ), X ) ) }.
% 1.12/1.63 { hAPP( c_RealDef_Oreal( tc_Nat_Onat ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), hAPP( c_RealDef_Oreal(
% 1.12/1.63 tc_Nat_Onat ), Y ) ), X ) }.
% 1.12/1.63 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 1.12/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 1.12/1.63 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.12/1.63 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.63 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.12/1.63 , Y ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) ),
% 1.12/1.63 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) =
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 1.12/1.63 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 1.12/1.63 { ! c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) =
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 1.12/1.63 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ),
% 1.12/1.63 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.63 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ),
% 1.12/1.63 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) ) }.
% 1.12/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 1.12/1.63 tc_Int_Oint, Y ) ), X ) ) }.
% 1.12/1.63 { ! X = hAPP( c_RealDef_Oreal( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) )
% 1.12/1.63 , c_RComplete_Onatfloor( hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.12/1.63 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP( c_Power_Opower__class_Opower
% 1.12/1.63 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ), Y ) }.
% 1.12/1.63 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ),
% 1.12/1.63 c_Complex_Ocis( Y ) ), X ) = c_Complex_Ocis( hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( c_RealDef_Oreal
% 1.12/1.63 ( tc_Nat_Onat ), X ) ), Y ) ) }.
% 1.12/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 1.12/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.12/1.63 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 1.12/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 1.12/1.63 ( tc_Nat_Onat ) ) ) ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.12/1.63 ( tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint )
% 1.12/1.63 , c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ), ! Y =
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.12/1.63 { Y = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.12/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.12/1.63 tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 1.12/1.63 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ) }.
% 1.12/1.63 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.12/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.12/1.63 tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 1.12/1.63 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ) }.
% 1.12/1.63 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 1.12/1.63 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 1.12/1.63 ( X ) }.
% 1.12/1.63 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.12/1.63 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.12/1.63 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.12/1.63 = c_Groups_Oone__class_Oone( X ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 1.12/1.63 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), c_Groups_Oabs__class_Oabs( X, Z ) ), Y
% 1.12/1.63 ) }.
% 1.12/1.63 { ! class_Rings_Osemiring__1( X ), hAPP( c_Nat_Osemiring__1__class_Oof__nat
% 1.12/1.63 ( X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y )
% 1.12/1.63 ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 1.12/1.63 c_Nat_Osemiring__1__class_Oof__nat( X ), Z ) ), Y ) }.
% 1.12/1.63 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 1.12/1.63 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.12/1.63 tc_Nat_Onat ) ) = Y }.
% 1.12/1.63 { ! class_Rings_Olinordered__semidom( X ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.12/1.63 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.12/1.63 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__semidom( X ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.12/1.63 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.12/1.63 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 1.12/1.63 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__semidom( X ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 1.12/1.63 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.12/1.63 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.12/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 1.12/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.12/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 1.12/1.63 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.12/1.63 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.12/1.63 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.12/1.63 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.12/1.63 .
% 1.12/1.63 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.12/1.63 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.12/1.63 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.12/1.63 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.12/1.63 tc_Nat_Onat ) }.
% 1.12/1.63 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.12/1.63 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.12/1.63 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 1.12/1.63 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 1.12/1.63 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.12/1.63 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.12/1.63 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.12/1.63 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.12/1.63 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.12/1.63 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.12/1.63 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 1.12/1.63 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.12/1.63 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.12/1.63 c_Groups_Oone__class_Oone( X ) }.
% 1.12/1.63 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 1.12/1.63 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.12/1.63 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.12/1.63 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 1.12/1.63 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.12/1.63 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.12/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.12/1.63 X ), Y ), Z = Y }.
% 1.12/1.63 { ! class_Rings_Olinordered__semidom( X ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.12/1.63 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.12/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.12/1.63 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.12/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.12/1.63 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.12/1.63 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.12/1.63 ) = c_Groups_Oone__class_Oone( X ) }.
% 1.12/1.63 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.12/1.63 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless__eq(
% 1.12/1.63 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), c_Groups_Oabs__class_Oabs( X, Z ) ), Y
% 1.12/1.63 ) ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.12/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.12/1.63 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.12/1.63 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.12/1.63 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 1.12/1.63 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.12/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.12/1.63 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.12/1.63 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.12/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.12/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.12/1.63 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.12/1.63 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.12/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.12/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.12/1.63 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__semidom( X ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 1.12/1.63 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.12/1.63 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.12/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.12/1.63 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.12/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 1.12/1.63 c_Groups_Oone__class_Oone( X ) ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.12/1.63 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 1.12/1.63 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.12/1.63 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.12/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.12/1.63 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 1.12/1.63 { ! class_Rings_Olinordered__semidom( X ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.12/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 1.12/1.63 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.12/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.12/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.12/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.12/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.12/1.63 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 1.12/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 1.12/1.63 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.12/1.63 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless__eq(
% 1.12/1.63 tc_Nat_Onat, Z, Y ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ),
% 1.12/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) ) = hAPP
% 1.12/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), T ), c_Groups_Ominus__class_Ominus(
% 1.12/1.63 tc_Nat_Onat, Y, Z ) ) ), T ) }.
% 1.12/1.63 { X = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), Y =
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 1.12/1.63 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex
% 1.12/1.63 , c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 1.12/1.63 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), X ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol51( X, Y ) ), Y
% 1.12/1.63 ) ) ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.12/1.63 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 1.12/1.63 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 1.12/1.63 c_Groups_Otimes__class_Otimes( X ) ) }.
% 1.12/1.63 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 1.12/1.63 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 1.12/1.63 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 1.12/1.63 ) ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( c_RealDef_Oreal
% 1.12/1.63 ( tc_Nat_Onat ), skol52( X, Y ) ) ), X ), Y ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.12/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( c_RealDef_Oreal
% 1.12/1.63 ( tc_Nat_Onat ), c_Nat_OSuc( skol52( X, Y ) ) ) ), X ) ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.12/1.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ), Y ) = hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ),
% 1.12/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ),
% 1.12/1.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.12/1.63 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ),
% 1.12/1.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.12/1.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.12/1.63 tc_Int_Oint ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.12/1.63 Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 1.12/1.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.12/1.63 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.12/1.63 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y
% 1.12/1.63 , c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.12/1.63 tc_Int_Oint, Y, X ) ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ),
% 1.12/1.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.12/1.63 tc_Int_Oint ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.12/1.63 Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ),
% 1.12/1.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.12/1.63 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.12/1.63 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 1.12/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.12/1.63 tc_Int_Oint ), Y ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.12/1.63 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.12/1.63 tc_Int_Oint, X, Y ) ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.12/1.63 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.12/1.63 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 1.12/1.63 , Y ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.12/1.63 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 1.12/1.63 , Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.12/1.63 tc_Int_Oint, Y, X ) ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.12/1.63 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.12/1.63 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.12/1.63 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.12/1.63 tc_Int_Oint, Y, X ) ) }.
% 1.12/1.63 { ! c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha14( X, Y ) }.
% 1.12/1.63 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.12/1.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.12/1.63 { ! alpha14( X, Y ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.12/1.63 { ! alpha14( X, Y ), alpha29( X, Y ), alpha34( X, Y ) }.
% 1.12/1.63 { ! alpha29( X, Y ), alpha14( X, Y ) }.
% 1.12/1.63 { ! alpha34( X, Y ), alpha14( X, Y ) }.
% 1.12/1.63 { ! alpha34( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.12/1.63 { ! alpha34( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ), alpha34( X, Y ) }.
% 1.12/1.63 { ! alpha29( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 1.12/1.63 { ! alpha29( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), alpha29( X, Y ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.12/1.63 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.12/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ), Y ),
% 1.12/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.12/1.63 tc_Int_Oint, X, Y ), X ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.12/1.63 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, hAPP(
% 1.12/1.63 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 1.12/1.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.12/1.63 tc_Int_Oint, Z, Y ), X ) }.
% 1.12/1.63 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.12/1.63 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 1.12/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 1.12/1.63 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 1.12/1.63 ) }.
% 1.12/1.63 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.12/1.63 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 1.12/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) =
% 1.12/1.63 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 1.12/1.63 ) }.
% 1.12/1.63 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.12/1.63 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Z, Y ),
% 1.12/1.63 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 1.12/1.63 ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.12/1.63 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.12/1.63 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Y, Z ),
% 1.12/1.63 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 1.12/1.63 ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.12/1.63 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.12/1.63 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 1.12/1.63 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 1.12/1.63 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.12/1.63 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.12/1.63 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 1.12/1.63 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.12/1.63 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) = Z }.
% 1.12/1.63 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.12/1.63 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = Z }.
% 1.12/1.63 { ! class_Divides_Osemiring__div( X ), ! T = c_Groups_Ozero__class_Ozero( X
% 1.12/1.63 ), c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.12/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.12/1.63 { ! class_Divides_Osemiring__div( X ), T = c_Groups_Ozero__class_Ozero( X )
% 1.12/1.63 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.12/1.63 c_Divides_Odiv__class_Odiv( X, Z, Y ) }.
% 1.12/1.63 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.12/1.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, X ) =
% 1.12/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.12/1.63 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.12/1.63 , c_Divides_Odiv__class_Odiv( X, Y, Y ) = c_Groups_Oone__class_Oone( X )
% 1.12/1.63 }.
% 1.12/1.63 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.12/1.63 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.12/1.63 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.12/1.63 }.
% 1.12/1.63 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.12/1.63 tc_Int_Oint, X, Y ) ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.12/1.63 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.12/1.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.12/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.12/1.63 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.12/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.12/1.63 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.12/1.63 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.12/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.12/1.63 tc_Int_Oint ), Y ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.12/1.63 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.12/1.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.12/1.63 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.12/1.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.12/1.63 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 1.12/1.63 c_Groups_Oone__class_Oone( X ) ) = Y }.
% 1.12/1.63 { ! T = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), alpha50( X,
% 1.12/1.63 Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), Z =
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.12/1.63 tc_Int_Oint, T, Z ) = Y }.
% 1.12/1.63 { ! T = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), alpha50( X,
% 1.12/1.63 Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z =
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.12/1.63 tc_Int_Oint, T, Z ) = Y }.
% 1.12/1.63 { ! alpha50( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 1.12/1.63 { ! alpha50( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.12/1.63 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha50( X, Y ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.12/1.63 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y )
% 1.12/1.63 , alpha50( X, Y ) }.
% 1.12/1.63 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 1.12/1.63 alpha15( X, Z ) }.
% 1.12/1.63 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 1.12/1.63 alpha30( X, Y, Z ) }.
% 1.12/1.63 { ! alpha15( X, Z ), ! alpha30( X, Y, Z ), hBOOL( hAPP( Z,
% 1.12/1.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ) }.
% 1.12/1.63 { ! alpha30( X, Y, Z ), alpha35( X, Y, Z ) }.
% 1.12/1.63 { ! alpha30( X, Y, Z ), alpha39( X, Y, Z ) }.
% 1.12/1.63 { ! alpha35( X, Y, Z ), ! alpha39( X, Y, Z ), alpha30( X, Y, Z ) }.
% 1.12/1.63 { ! alpha39( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha43( X, Y, Z ) }.
% 1.12/1.63 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha39( X, Y, Z ) }.
% 1.12/1.63 { ! alpha43( X, Y, Z ), alpha39( X, Y, Z ) }.
% 1.12/1.63 { ! alpha43( X, Y, Z ), ! alpha45( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 1.12/1.63 { ! hBOOL( hAPP( Z, skol53( T, U, Z ) ) ), alpha43( X, Y, Z ) }.
% 1.12/1.63 { alpha45( X, Y, skol53( X, Y, Z ) ), alpha43( X, Y, Z ) }.
% 1.12/1.63 { ! alpha45( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.12/1.63 skol54( X, T, U ) ) }.
% 1.12/1.63 { ! alpha45( X, Y, Z ), alpha47( X, Y, Z, skol54( X, Y, Z ) ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T ), ! alpha47( X, Y, Z
% 1.12/1.63 , T ), alpha45( X, Y, Z ) }.
% 1.12/1.63 { ! alpha47( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.63 T, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.12/1.63 { ! alpha47( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.12/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 1.12/1.63 .
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 1.12/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha47( X,
% 1.12/1.63 Y, Z, T ) }.
% 1.12/1.63 { ! alpha35( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha40( X, Y, Z ) }.
% 1.12/1.63 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.12/1.63 tc_Int_Oint ), X ), alpha35( X, Y, Z ) }.
% 1.12/1.63 { ! alpha40( X, Y, Z ), alpha35( X, Y, Z ) }.
% 1.12/1.63 { ! alpha40( X, Y, Z ), ! alpha44( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 1.12/1.63 { ! hBOOL( hAPP( Z, skol55( T, U, Z ) ) ), alpha40( X, Y, Z ) }.
% 1.12/1.63 { alpha44( X, Y, skol55( X, Y, Z ) ), alpha40( X, Y, Z ) }.
% 1.12/1.63 { ! alpha44( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), skol56( T, U, W ) ) }.
% 1.12/1.63 { ! alpha44( X, Y, Z ), alpha46( X, Y, Z, skol56( X, Y, Z ) ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! alpha46( X, Y, Z, T )
% 1.12/1.63 , alpha44( X, Y, Z ) }.
% 1.12/1.63 { ! alpha46( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X
% 1.12/1.63 ) }.
% 1.12/1.63 { ! alpha46( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.12/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 1.12/1.63 .
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X ), ! Y =
% 1.12/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha46( X,
% 1.12/1.63 Y, Z, T ) }.
% 1.12/1.63 { ! alpha15( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.12/1.63 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.12/1.63 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha15( X, Y ) }.
% 1.12/1.63 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), alpha15
% 1.12/1.63 ( X, Y ) }.
% 1.12/1.63 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ),
% 1.12/1.63 c_Complex_Orcis( Z, Y ) ), X ) = c_Complex_Orcis( hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( c_RealDef_Oreal
% 1.12/1.63 ( tc_Nat_Onat ), X ) ), Y ) ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.12/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol57( Z, T ) ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol57( X, Y ) ), X ) =
% 1.12/1.63 Y }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), ! hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), X ) = Y, Z =
% 1.12/1.63 skol57( X, Y ) }.
% 1.12/1.63 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.12/1.63 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.12/1.63 { Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.12/1.63 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 1.12/1.63 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 1.12/1.63 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 1.12/1.63 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 1.12/1.63 tc_Nat_Onat, Z, Y ), X ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.12/1.63 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.12/1.63 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) = X }.
% 1.12/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.12/1.63 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ), Y ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.12/1.63 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, Z ),
% 1.12/1.63 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, Z ) ) }.
% 1.12/1.63 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP(
% 1.12/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ), hAPP(
% 1.12/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) = hAPP(
% 1.12/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ),
% 1.12/1.63 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) }.
% 1.12/1.63 { hAPP( c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ),
% 1.12/1.63 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) =
% 1.12/1.63 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP(
% 1.12/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), Y ), hAPP(
% 1.12/1.63 c_Nat_Osemiring__1__class_Oof__nat( tc_Int_Oint ), X ) ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 1.12/1.63 tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 1.12/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 1.12/1.63 tc_Nat_Onat, Y, X ), Y ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.63 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 1.12/1.63 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) =
% 1.12/1.63 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.63 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 1.12/1.63 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) = Y }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.63 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 1.12/1.63 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) = Y }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X
% 1.12/1.63 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.12/1.63 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ),
% 1.12/1.63 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, X ) ) }.
% 1.12/1.63 { c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, c_Complex_Orcis( Y
% 1.12/1.63 , X ) ) = c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ) }.
% 1.12/1.63 { c_Complex_Orcis( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) =
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.12/1.63 { c_Complex_Ocis( X ) = c_Complex_Orcis( c_Groups_Oone__class_Oone(
% 1.12/1.63 tc_RealDef_Oreal ), X ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 1.12/1.63 ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.63 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 1.12/1.63 , c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.12/1.63 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.12/1.63 tc_Nat_Onat, Y, X ), X ) ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.63 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 1.12/1.63 , c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.12/1.63 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.12/1.63 tc_Nat_Onat, Y, X ), X ) ) }.
% 1.12/1.63 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 1.12/1.63 alpha16( X, Z ) }.
% 1.12/1.63 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 1.12/1.63 alpha31( X, Y, Z ) }.
% 1.12/1.63 { ! alpha16( X, Z ), ! alpha31( X, Y, Z ), hBOOL( hAPP( Z,
% 1.12/1.63 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ) }.
% 1.12/1.63 { ! alpha31( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.12/1.63 alpha36( X, Y, Z ) }.
% 1.12/1.63 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha31( X, Y, Z ) }.
% 1.12/1.63 { ! alpha36( X, Y, Z ), alpha31( X, Y, Z ) }.
% 1.12/1.63 { ! alpha36( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, X
% 1.12/1.63 ), alpha41( X, Y, Z, T ) }.
% 1.12/1.63 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol58( X, T, U ), X ),
% 1.12/1.63 alpha36( X, Y, Z ) }.
% 1.12/1.63 { ! alpha41( X, Y, Z, skol58( X, Y, Z ) ), alpha36( X, Y, Z ) }.
% 1.12/1.63 { ! alpha41( X, Y, Z, T ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.12/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 1.12/1.63 hBOOL( hAPP( Z, U ) ) }.
% 1.12/1.63 { ! hBOOL( hAPP( Z, skol59( U, W, Z, V0 ) ) ), alpha41( X, Y, Z, T ) }.
% 1.12/1.63 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol59( X, Y, Z, T ) )
% 1.12/1.63 , T ), alpha41( X, Y, Z, T ) }.
% 1.12/1.63 { ! alpha16( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.12/1.63 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.12/1.63 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha16( X, Y ) }.
% 1.12/1.63 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha16
% 1.12/1.63 ( X, Y ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.12/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), Y ),
% 1.12/1.63 ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc( Z ) ) ), Z
% 1.12/1.63 = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.63 ( tc_Nat_Onat ), X ), ! Z = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X
% 1.12/1.63 ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), Y ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.63 ( tc_Nat_Onat ), X ), ! Z = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X
% 1.12/1.63 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc( Z ) ) ) }
% 1.12/1.63 .
% 1.12/1.63 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 1.12/1.63 alpha17( X, Z ), alpha32( X, Y, Z ) }.
% 1.12/1.63 { ! alpha17( X, Z ), hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 1.12/1.63 tc_Nat_Onat, Y, X ) ) ) }.
% 1.12/1.63 { ! alpha32( X, Y, Z ), hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 1.12/1.63 tc_Nat_Onat, Y, X ) ) ) }.
% 1.12/1.63 { ! alpha32( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.12/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol60( X
% 1.12/1.63 , Y, T ) ), Y ) }.
% 1.12/1.63 { ! alpha32( X, Y, Z ), alpha37( X, Y, Z, skol60( X, Y, Z ) ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), T ), Y ), ! alpha37( X
% 1.12/1.63 , Y, Z, T ), alpha32( X, Y, Z ) }.
% 1.12/1.63 { ! alpha37( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.12/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc
% 1.12/1.63 ( T ) ) ) }.
% 1.12/1.63 { ! alpha37( X, Y, Z, T ), hBOOL( hAPP( Z, T ) ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.12/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc( T ) ) ), !
% 1.12/1.63 hBOOL( hAPP( Z, T ) ), alpha37( X, Y, Z, T ) }.
% 1.12/1.63 { ! alpha17( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.12/1.63 { ! alpha17( X, Y ), hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero(
% 1.12/1.63 tc_Nat_Onat ) ) ) }.
% 1.12/1.63 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( Y,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha17( X, Y ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X
% 1.12/1.63 , Y ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.12/1.63 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.12/1.63 tc_Nat_Onat, Y, X ), X ) ) }.
% 1.12/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.12/1.63 c_Complex_Orcis( T, Z ) ), c_Complex_Orcis( Y, X ) ) = c_Complex_Orcis(
% 1.12/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), T ), Y ),
% 1.12/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.12/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol61( Z, T ) ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.12/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.12/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol61( X, Y ) ), X ) =
% 1.12/1.63 Y }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.12/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ), !
% 1.12/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.12/1.63 tc_Nat_Onat ), Y ), c_RComplete_Onatfloor(
% 1.12/1.63 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X, hAPP(
% 1.12/1.63 c_RealDef_Oreal( tc_Nat_Onat ), Y ) ) ) = c_Divides_Odiv__class_Odiv(
% 1.12/1.63 tc_Nat_Onat, c_RComplete_Onatfloor( X ), Y ) }.
% 1.12/1.63 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 1.12/1.63 c_RealDef_Oreal( tc_Nat_Onat ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat,
% 1.12/1.63 Y, X ) ), c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, hAPP(
% 1.12/1.63 c_RealDef_Oreal( tc_Nat_Onat ), Y ), hAPP( c_RealDef_Oreal( tc_Nat_Onat )
% 1.12/1.63 , X ) ) ) }.
% 1.12/1.63 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.12/1.63 hAPP( c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide
% 1.12/1.63 ( X, T, Y ) ), Z ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.12/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.12/1.63 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 1.12/1.63 .
% 1.12/1.63 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.12/1.63 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 1.12/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 1.12/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 1.12/1.63 { class_Groups_Ocancel__comm__monoid__add( tc_Complex_Ocomplex ) }.
% 1.12/1.63 { class_Rings_Ocomm__semiring__0( tc_Complex_Ocomplex ) }.
% 1.12/1.63 { class_Rings_Ocomm__ring( tc_Complex_Ocomplex ) }.
% 1.12/1.63 { class_Rings_Oidom( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Groups_Ocancel__comm__monoid__add( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Rings_Ocomm__semiring__0( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Rings_Ocomm__ring( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 1.12/1.63 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 1.12/1.63 { class_Rings_Oidom( tc_Int_Oint ) }.
% 1.12/1.63 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 1.12/1.63 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 1.12/1.63 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 1.12/1.63 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 1.12/1.63 ) ) }.
% 1.12/1.63 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 1.12/1.63 .
% 1.12/1.63 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 1.12/1.63 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.12/1.63 tc_Int_Oint ) }.
% 1.12/1.63 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.12/1.63 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 1.12/1.63 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 1.12/1.63 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 1.12/1.63 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 1.12/1.63 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 1.12/1.63 { class_Groups_Oordered__ab__group__add__abs( tc_Int_Oint ) }.
% 1.12/1.63 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 1.12/1.63 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 1.12/1.63 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.12/1.63 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 1.12/1.63 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 1.12/1.63 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 1.12/1.63 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 1.12/1.63 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 1.12/1.63 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 1.12/1.63 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 1.12/1.63 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 1.12/1.63 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 1.12/1.63 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 1.12/1.63 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 1.12/1.63 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 1.12/1.63 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 1.12/1.63 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 1.12/1.63 { class_Rings_Oordered__ring__abs( tc_Int_Oint ) }.
% 1.12/1.63 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 1.12/1.63 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 1.12/1.63 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 1.12/1.63 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 1.12/1.63 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 1.12/1.63 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 1.12/1.63 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 1.12/1.63 { class_Nat_Osemiring__char__0( tc_Int_Oint ) }.
% 1.12/1.63 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 1.12/1.63 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 1.12/1.63 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 1.12/1.63 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 1.12/1.63 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 1.12/1.63 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 1.12/1.63 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 1.12/1.63 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 1.12/1.63 { class_Rings_Osemiring__1( tc_Int_Oint ) }.
% 1.12/1.63 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 1.12/1.63 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 1.12/1.63 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 1.12/1.63 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 1.12/1.63 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 1.12/1.63 { class_Int_Onumber__ring( tc_Int_Oint ) }.
% 1.12/1.63 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 1.12/1.63 { class_Orderings_Oord( tc_Int_Oint ) }.
% 1.12/1.63 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 1.12/1.63 { class_Power_Opower( tc_Int_Oint ) }.
% 1.12/1.63 { class_Groups_Ozero( tc_Int_Oint ) }.
% 1.12/1.63 { class_Rings_Oring( tc_Int_Oint ) }.
% 1.12/1.63 { class_Int_Onumber( tc_Int_Oint ) }.
% 1.12/1.63 { class_Groups_Oone( tc_Int_Oint ) }.
% 1.12/1.63 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.12/1.63 tc_Nat_Onat ) }.
% 1.12/1.63 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.12/1.63 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 1.12/1.63 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 1.12/1.63 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 1.12/1.63 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.12/1.63 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 1.12/1.63 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.12/1.63 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 1.12/1.63 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 1.12/1.63 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 1.12/1.63 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 1.12/1.63 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 1.12/1.63 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 1.12/1.63 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 1.12/1.63 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 1.12/1.63 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 1.12/1.63 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 1.12/1.63 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 1.12/1.63 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 1.12/1.63 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 1.12/1.63 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 1.12/1.63 { class_Nat_Osemiring__char__0( tc_Nat_Onat ) }.
% 1.12/1.63 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 1.12/1.63 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 1.12/1.63 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 1.12/1.63 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 1.12/1.63 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 1.12/1.63 { class_Rings_Osemiring__1( tc_Nat_Onat ) }.
% 1.12/1.63 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 1.12/1.63 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 1.12/1.63 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 1.12/1.63 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 1.12/1.63 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 1.12/1.63 { class_Power_Opower( tc_Nat_Onat ) }.
% 1.12/1.63 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 1.12/1.63 { class_Int_Onumber( tc_Nat_Onat ) }.
% 1.12/1.63 { class_Groups_Oone( tc_Nat_Onat ) }.
% 1.12/1.63 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 1.12/1.63 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 1.12/1.63 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 1.12/1.63 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.12/1.63 tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_RealDef_Oreal ) }
% 1.12/1.63 .
% 1.12/1.63 { class_Rings_Olinordered__comm__semiring__strict( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Rings_Olinordered__semiring__1__strict( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_RealVector_Oreal__normed__div__algebra( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Rings_Olinordered__semiring__strict( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_RealVector_Oreal__normed__algebra__1( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Groups_Oordered__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Groups_Oordered__ab__group__add__abs( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_RealVector_Oreal__normed__algebra( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Groups_Oordered__comm__monoid__add( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Groups_Olinordered__ab__group__add( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Groups_Ocancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Rings_Oring__1__no__zero__divisors( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Rings_Oordered__cancel__semiring( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_RealVector_Oreal__normed__vector( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Rings_Olinordered__ring__strict( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Rings_Oring__no__zero__divisors( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Rings_Oordered__comm__semiring( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Rings_Olinordered__semiring__1( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Groups_Oordered__ab__group__add( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Groups_Ocancel__semigroup__add( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Rings_Olinordered__semiring( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Rings_Olinordered__semidom( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Groups_Oab__semigroup__mult( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Groups_Ocomm__monoid__mult( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Groups_Oab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Rings_Oordered__semiring( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Rings_Oordered__ring__abs( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Rings_Ono__zero__divisors( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Groups_Ocomm__monoid__add( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Rings_Olinordered__ring( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Rings_Olinordered__idom( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Rings_Ocomm__semiring__1( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Rings_Ocomm__semiring( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Nat_Osemiring__char__0( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Groups_Oab__group__add( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Rings_Ozero__neq__one( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Rings_Oordered__ring( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Orderings_Opreorder( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Orderings_Olinorder( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Groups_Omonoid__mult( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Rings_Ocomm__ring__1( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Groups_Omonoid__add( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Rings_Osemiring__1( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Rings_Osemiring__0( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Groups_Ogroup__add( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Rings_Omult__zero( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Orderings_Oorder( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Int_Oring__char__0( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Int_Onumber__ring( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Rings_Osemiring( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Orderings_Oord( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Rings_Oring__1( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Fields_Ofield( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Power_Opower( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Groups_Ozero( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Rings_Oring( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Int_Onumber( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Groups_Oone( tc_RealDef_Oreal ) }.
% 1.12/1.63 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.12/1.63 tc_Complex_Ocomplex ) }.
% 1.12/1.63 { class_RealVector_Oreal__normed__div__algebra( tc_Complex_Ocomplex ) }.
% 1.12/1.63 { class_RealVector_Oreal__normed__algebra__1( tc_Complex_Ocomplex ) }.
% 1.12/1.63 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 1.12/1.63 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.12/1.63 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.12/1.63 { class_RealVector_Oreal__normed__vector( tc_Complex_Ocomplex ) }.
% 1.12/1.63 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.12/1.63 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.12/1.63 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 1.12/1.63 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 1.12/1.63 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.12/1.63 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.12/1.63 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 1.12/1.63 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 1.12/1.63 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 1.12/1.63 { class_Nat_Osemiring__char__0( tc_Complex_Ocomplex ) }.
% 1.12/1.63 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 1.12/1.63 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 1.12/1.63 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 1.12/1.63 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 1.12/1.63 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 1.12/1.63 { class_Rings_Osemiring__1( tc_Complex_Ocomplex ) }.
% 1.12/1.63 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 1.12/1.63 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 1.12/1.63 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 1.12/1.63 { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 1.12/1.63 { class_Int_Onumber__ring( tc_Complex_Ocomplex ) }.
% 1.12/1.63 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 1.12/1.63 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 1.12/1.63 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 1.12/1.63 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 1.12/1.63 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 1.12/1.63 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 1.12/1.63 { class_Int_Onumber( tc_Complex_Ocomplex ) }.
% 1.12/1.63 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 1.12/1.63 { ! class_Rings_Oidom( X ),
% 1.12/1.63 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.12/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.12/1.63 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 1.12/1.63 ) ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.12/1.63 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 1.12/1.63 X ) ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.12/1.63 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 1.12/1.63 ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.12/1.63 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 1.12/1.63 }.
% 1.12/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.12/1.63 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.12/1.63 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.12/1.63 class_Groups_Oordered__ab__group__add__abs( tc_Polynomial_Opoly( X ) ) }
% 1.12/1.63 .
% 1.12/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.12/1.63 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.12/1.63 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.12/1.63 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 1.12/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.12/1.63 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.12/1.63 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 1.12/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.12/1.63 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.12/1.63 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.12/1.63 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.12/1.63 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 1.12/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 1.12/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 1.12/1.63 ( tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 1.12/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 1.12/1.63 ( tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 1.12/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring__abs(
% 1.12/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 1.12/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 1.12/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 1.12/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 1.12/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 1.12/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Fields_Ofield( X ), class_Divides_Osemiring__div(
% 1.12/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 1.12/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__idom( X ), class_Nat_Osemiring__char__0(
% 1.12/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 1.12/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 1.12/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 1.12/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 1.12/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 1.12/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 1.12/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 1.12/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 1.12/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Osemiring__1(
% 1.12/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 1.12/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 1.12/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 1.12/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 1.12/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 1.12/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Rings_Ocomm__ring__1( X ), class_Int_Onumber__ring(
% 1.12/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 1.12/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 1.12/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 1.12/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 1.12/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 1.12/1.63 }.
% 1.12/1.63 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 1.12/1.63 ) ) }.
% 1.12/1.63 { ! class_Rings_Ocomm__ring__1( X ), class_Int_Onumber( tc_Polynomial_Opoly
% 1.12/1.63 ( X ) ) }.
% 1.12/1.63 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 1.12/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.12/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 1.12/1.63 c_RealDef_Oreal( tc_Nat_Onat ), c_Nat_OSuc( c_Groups_Oplus__class_Oplus(
% 1.12/1.63 tc_Nat_Onat, v_N1____, v_N2____ ) ) ), hAPP( c_RealDef_Oreal( tc_Nat_Onat
% 1.12/1.63 ), c_Nat_OSuc( hAPP( v_f____, c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.12/1.63 v_N1____, v_N2____ ) ) ) ) ) }.
% 1.12/1.63
% 1.12/1.63 *** allocated 15000 integers for clauses
% 1.12/1.63 *** allocated 22500 integers for clauses
% 1.12/1.63 *** allocated 33750 integers for clauses
% 1.12/1.63 *** allocated 50625 integers for clauses
% 1.12/1.63 *** allocated 75937 integers for clauses
% 1.12/1.63 *** allocated 113905 integers for clauses
% 1.12/1.63 percentage equality = 0.228342, percentage horn = 0.905083
% 1.12/1.63 This is a problem with some equality
% 1.12/1.63
% 1.12/1.63
% 1.12/1.63
% 1.12/1.63 Options Used:
% 1.12/1.63
% 1.12/1.63 useres = 1
% 1.12/1.63 useparamod = 1
% 1.12/1.63 useeqrefl = 1
% 1.12/1.63 useeqfact = 1
% 1.12/1.63 usefactor = 1
% 1.12/1.63 usesimpsplitting = 0
% 1.12/1.63 usesimpdemod = 5
% 1.12/1.63 usesimpres = 3
% 1.12/1.63
% 1.12/1.63 resimpinuse = 1000
% 1.12/1.63 resimpclauses = 20000
% 1.12/1.63 substype = eqrewr
% 1.12/1.63 backwardsubs = 1
% 1.12/1.63 selectoldest = 5
% 1.12/1.63
% 1.12/1.63 litorderings [0] = split
% 1.12/1.63 litorderings [1] = extend the termordering, first sorting on arguments
% 1.12/1.63
% 1.12/1.63 termordering = kbo
% 1.12/1.63
% 1.12/1.63 litapriori = 0
% 1.12/1.63 termapriori = 1
% 1.12/1.63 litaposteriori = 0
% 1.12/1.63 termaposteriori = 0
% 1.12/1.63 demodaposteriori = 0
% 1.12/1.63 ordereqreflfact = 0
% 1.12/1.63
% 1.12/1.63 litselect = negord
% 1.12/1.63
% 1.12/1.63 maxweight = 15
% 1.12/1.63 maxdepth = 30000
% 1.12/1.63 maxlength = 115
% 1.12/1.63 maxnrvars = 195
% 1.12/1.63 excuselevel = 1
% 1.12/1.63 increasemaxweight = 1
% 1.12/1.63
% 1.12/1.63 maxselected = 10000000
% 1.12/1.63 maxnrclauses = 10000000
% 1.12/1.63
% 1.12/1.63 showgenerated = 0
% 1.12/1.63 showkept = 0
% 1.12/1.63 showselected = 0
% 1.12/1.63 showdeleted = 0
% 1.12/1.63 showresimp = 1
% 1.12/1.63 showstatus = 2000
% 1.12/1.63
% 1.12/1.63 prologoutput = 0
% 1.12/1.63 nrgoals = 5000000
% 1.12/1.63 totalproof = 1
% 1.12/1.63
% 1.12/1.63 Symbols occurring in the translation:
% 1.12/1.63
% 1.12/1.63 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.12/1.63 . [1, 2] (w:1, o:226, a:1, s:1, b:0),
% 1.12/1.63 ! [4, 1] (w:0, o:123, a:1, s:1, b:0),
% 1.12/1.63 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.12/1.63 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.12/1.63 hAPP [38, 2] (w:1, o:250, a:1, s:1, b:0),
% 1.12/1.63 v_f____ [39, 0] (w:1, o:11, a:1, s:1, b:0),
% 1.12/1.63 c_SEQ_Osubseq [40, 1] (w:1, o:131, a:1, s:1, b:0),
% 1.12/1.63 tc_Nat_Onat [41, 0] (w:1, o:14, a:1, s:1, b:0),
% 1.12/1.63 v_N1____ [42, 0] (w:1, o:15, a:1, s:1, b:0),
% 1.12/1.63 v_N2____ [43, 0] (w:1, o:16, a:1, s:1, b:0),
% 1.12/1.63 c_Groups_Oplus__class_Oplus [44, 3] (w:1, o:327, a:1, s:1, b:0),
% 1.12/1.63 c_Orderings_Oord__class_Oless__eq [45, 3] (w:1, o:328, a:1, s:1, b:0)
% 1.12/1.63 ,
% 1.12/1.63 class_Orderings_Opreorder [48, 1] (w:1, o:135, a:1, s:1, b:0),
% 1.12/1.63 c_Nat_OSuc [51, 1] (w:1, o:136, a:1, s:1, b:0),
% 1.12/1.63 class_Groups_Oordered__ab__semigroup__add__imp__le [55, 1] (w:1, o:
% 1.12/1.63 138, a:1, s:1, b:0),
% 1.12/1.63 class_Groups_Oordered__ab__semigroup__add [59, 1] (w:1, o:139, a:1
% 1.12/1.63 , s:1, b:0),
% 1.12/1.63 class_Orderings_Olinorder [70, 1] (w:1, o:140, a:1, s:1, b:0),
% 1.12/1.63 class_Orderings_Oord [73, 1] (w:1, o:133, a:1, s:1, b:0),
% 1.12/1.63 tc_fun [74, 2] (w:1, o:295, a:1, s:1, b:0),
% 1.12/1.63 class_Orderings_Oorder [76, 1] (w:1, o:134, a:1, s:1, b:0),
% 1.12/1.63 class_Groups_Ocancel__semigroup__add [78, 1] (w:1, o:141, a:1, s:1
% 1.12/1.63 , b:0),
% 1.12/1.63 class_Groups_Ocancel__ab__semigroup__add [79, 1] (w:1, o:142, a:1, s:
% 1.12/1.63 1, b:0),
% 1.12/1.63 class_Groups_Oab__semigroup__add [80, 1] (w:1, o:143, a:1, s:1, b:0)
% 1.12/1.63 ,
% 1.12/1.63 tc_RealDef_Oreal [83, 0] (w:1, o:68, a:1, s:1, b:0),
% 1.12/1.63 c_RealDef_Oreal [84, 1] (w:1, o:128, a:1, s:1, b:0),
% 1.12/1.63 c_SEQ_Odecseq [90, 2] (w:1, o:297, a:1, s:1, b:0),
% 1.12/1.63 c_SEQ_Oincseq [92, 2] (w:1, o:298, a:1, s:1, b:0),
% 1.12/1.63 c_SEQ_Omonoseq [93, 2] (w:1, o:299, a:1, s:1, b:0),
% 1.12/1.63 c_Groups_Oone__class_Oone [94, 1] (w:1, o:144, a:1, s:1, b:0),
% 1.12/1.63 class_Rings_Ocomm__semiring__1 [95, 1] (w:1, o:148, a:1, s:1, b:0),
% 1.12/1.63 class_Groups_Oone [96, 1] (w:1, o:149, a:1, s:1, b:0),
% 1.12/1.63 c_Orderings_Oord__class_Oless [97, 3] (w:1, o:329, a:1, s:1, b:0),
% 1.12/1.63 c_Groups_Ozero__class_Ozero [98, 1] (w:1, o:150, a:1, s:1, b:0),
% 1.12/1.63 class_Rings_Osemiring__1 [101, 1] (w:1, o:156, a:1, s:1, b:0),
% 1.12/1.63 c_Nat_Osemiring__1__class_Oof__nat__aux [102, 4] (w:1, o:374, a:1, s:
% 1.12/1.63 1, b:0),
% 1.12/1.63 c_Groups_Ominus__class_Ominus [103, 3] (w:1, o:330, a:1, s:1, b:0),
% 1.12/1.63 class_Groups_Ozero [105, 1] (w:1, o:157, a:1, s:1, b:0),
% 1.12/1.63 class_Groups_Ogroup__add [106, 1] (w:1, o:158, a:1, s:1, b:0),
% 1.12/1.63 class_Groups_Oab__group__add [107, 1] (w:1, o:159, a:1, s:1, b:0),
% 1.12/1.63 class_Groups_Oordered__ab__group__add [108, 1] (w:1, o:160, a:1, s:1
% 1.12/1.63 , b:0),
% 1.12/1.63 hBOOL [113, 1] (w:1, o:161, a:1, s:1, b:0),
% 1.12/1.63 class_Groups_Olinordered__ab__group__add [115, 1] (w:1, o:162, a:1
% 1.12/1.63 , s:1, b:0),
% 1.12/1.63 class_Groups_Oordered__comm__monoid__add [116, 1] (w:1, o:163, a:1
% 1.12/1.63 , s:1, b:0),
% 1.12/1.63 class_Groups_Oordered__cancel__ab__semigroup__add [118, 1] (w:1, o:
% 1.12/1.63 164, a:1, s:1, b:0),
% 1.12/1.63 class_Groups_Omonoid__add [119, 1] (w:1, o:165, a:1, s:1, b:0),
% 1.12/1.63 class_Groups_Ocomm__monoid__add [120, 1] (w:1, o:166, a:1, s:1, b:0)
% 1.12/1.63 ,
% 1.12/1.63 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 1.12/1.63 121, 1] (w:1, o:191, a:1, s:1, b:0),
% 1.12/1.63 class_Rings_Olinordered__semidom [124, 1] (w:1, o:169, a:1, s:1, b:0)
% 1.12/1.63 ,
% 1.12/1.63 class_Rings_Olinordered__idom [125, 1] (w:1, o:170, a:1, s:1, b:0),
% 1.12/1.63 v_d____ [126, 0] (w:1, o:92, a:1, s:1, b:0),
% 1.12/1.63 v_r [127, 0] (w:1, o:93, a:1, s:1, b:0),
% 1.12/1.63 class_Rings_Ozero__neq__one [128, 1] (w:1, o:171, a:1, s:1, b:0),
% 1.12/1.63 c_Groups_Oabs__class_Oabs [130, 2] (w:1, o:301, a:1, s:1, b:0),
% 1.12/1.63 c_RComplete_Onatceiling [131, 1] (w:1, o:129, a:1, s:1, b:0),
% 1.12/1.63 c_Int_Onumber__class_Onumber__of [134, 2] (w:1, o:302, a:1, s:1, b:0)
% 1.12/1.63 ,
% 1.12/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [136, 2] (w:1, o:
% 1.12/1.63 300, a:1, s:1, b:0),
% 1.12/1.63 tc_Polynomial_Opoly [137, 1] (w:1, o:206, a:1, s:1, b:0),
% 1.12/1.63 class_Int_Onumber [139, 1] (w:1, o:207, a:1, s:1, b:0),
% 1.12/1.63 class_Int_Onumber__ring [140, 1] (w:1, o:208, a:1, s:1, b:0),
% 1.12/1.63 class_Int_Oring__char__0 [141, 1] (w:1, o:209, a:1, s:1, b:0),
% 1.12/1.63 class_Groups_Oordered__ab__group__add__abs [142, 1] (w:1, o:210, a:1
% 1.12/1.63 , s:1, b:0),
% 1.12/1.63 tc_Int_Oint [143, 0] (w:1, o:96, a:1, s:1, b:0),
% 1.12/1.63 tc_Complex_Ocomplex [146, 0] (w:1, o:97, a:1, s:1, b:0),
% 1.12/1.63 v_w____ [147, 0] (w:1, o:98, a:1, s:1, b:0),
% 1.12/1.63 c_RealVector_Onorm__class_Onorm [148, 2] (w:1, o:296, a:1, s:1, b:0)
% 1.12/1.63 ,
% 1.12/1.63 c_RComplete_Onatfloor [150, 1] (w:1, o:130, a:1, s:1, b:0),
% 1.12/1.63 v_g____ [152, 1] (w:1, o:211, a:1, s:1, b:0),
% 1.12/1.63 class_RealVector_Oreal__normed__vector [159, 1] (w:1, o:172, a:1, s:1
% 1.12/1.63 , b:0),
% 1.12/1.63 v_z____ [162, 0] (w:1, o:107, a:1, s:1, b:0),
% 1.12/1.63 class_RealVector_Oreal__normed__algebra__1 [163, 1] (w:1, o:173, a:1
% 1.12/1.63 , s:1, b:0),
% 1.12/1.63 c_Nat__Numeral_Oneg [166, 1] (w:1, o:212, a:1, s:1, b:0),
% 1.12/1.63 c_Int_Osucc [170, 1] (w:1, o:213, a:1, s:1, b:0),
% 1.12/1.63 c_Complex_Oii [172, 0] (w:1, o:112, a:1, s:1, b:0),
% 1.12/1.63 c_Nat__Transfer_Otsub [173, 2] (w:1, o:303, a:1, s:1, b:0),
% 1.12/1.63 c_SEQ_OBseq [174, 2] (w:1, o:304, a:1, s:1, b:0),
% 1.12/1.63 c_Int_OPls [176, 0] (w:1, o:114, a:1, s:1, b:0),
% 1.12/1.63 c_Int_Opred [177, 1] (w:1, o:214, a:1, s:1, b:0),
% 1.12/1.63 c_Complex_Oexpi [178, 1] (w:1, o:215, a:1, s:1, b:0),
% 1.12/1.63 c_Groups_Otimes__class_Otimes [179, 1] (w:1, o:216, a:1, s:1, b:0),
% 1.12/1.63 c_Nat_Osemiring__1__class_Oof__nat [180, 1] (w:1, o:217, a:1, s:1, b:
% 1.12/1.63 0),
% 1.12/1.63 class_RealVector_Oreal__normed__algebra [181, 1] (w:1, o:174, a:1, s:
% 1.12/1.63 1, b:0),
% 1.12/1.63 class_Rings_Omult__zero [182, 1] (w:1, o:180, a:1, s:1, b:0),
% 1.12/1.63 class_Rings_Oring__no__zero__divisors [183, 1] (w:1, o:151, a:1, s:1
% 1.12/1.63 , b:0),
% 1.12/1.63 class_Rings_Ono__zero__divisors [184, 1] (w:1, o:181, a:1, s:1, b:0)
% 1.12/1.63 ,
% 1.12/1.63 class_Rings_Osemiring [189, 1] (w:1, o:182, a:1, s:1, b:0),
% 1.12/1.63 class_Rings_Ocomm__semiring [190, 1] (w:1, o:183, a:1, s:1, b:0),
% 1.12/1.63 class_Groups_Oab__semigroup__mult [191, 1] (w:1, o:218, a:1, s:1, b:0
% 1.12/1.63 ),
% 1.12/1.63 class_Nat_Osemiring__char__0 [192, 1] (w:1, o:132, a:1, s:1, b:0),
% 1.12/1.63 class_RealVector_Oreal__normed__div__algebra [197, 1] (w:1, o:184, a:
% 1.12/1.63 1, s:1, b:0),
% 1.12/1.63 class_Groups_Omonoid__mult [198, 1] (w:1, o:219, a:1, s:1, b:0),
% 1.12/1.63 class_Groups_Ocomm__monoid__mult [199, 1] (w:1, o:220, a:1, s:1, b:0)
% 1.12/1.63 ,
% 1.12/1.63 class_Rings_Olinordered__ring [200, 1] (w:1, o:167, a:1, s:1, b:0),
% 1.12/1.63 class_Rings_Olinordered__ring__strict [201, 1] (w:1, o:168, a:1, s:1
% 1.12/1.63 , b:0),
% 1.12/1.63 class_Rings_Oordered__cancel__semiring [202, 1] (w:1, o:185, a:1, s:1
% 1.12/1.63 , b:0),
% 1.12/1.63 class_Rings_Oordered__ring [203, 1] (w:1, o:186, a:1, s:1, b:0),
% 1.12/1.63 class_Rings_Oordered__semiring [204, 1] (w:1, o:188, a:1, s:1, b:0),
% 1.12/1.63
% 1.12/1.63 class_Rings_Oordered__comm__semiring [205, 1] (w:1, o:189, a:1, s:1
% 1.12/1.63 , b:0),
% 1.12/1.63 class_Rings_Olinordered__semiring__strict [206, 1] (w:1, o:175, a:1
% 1.12/1.63 , s:1, b:0),
% 1.12/1.63 class_Rings_Olinordered__comm__semiring__strict [207, 1] (w:1, o:176
% 1.12/1.63 , a:1, s:1, b:0),
% 1.12/1.63 class_Rings_Oring [209, 1] (w:1, o:152, a:1, s:1, b:0),
% 1.12/1.63 class_Rings_Oring__1 [210, 1] (w:1, o:153, a:1, s:1, b:0),
% 1.12/1.63 class_Rings_Olinordered__semiring [211, 1] (w:1, o:177, a:1, s:1, b:0
% 1.12/1.63 ),
% 1.12/1.63 class_Rings_Oordered__ring__abs [212, 1] (w:1, o:187, a:1, s:1, b:0)
% 1.12/1.63 ,
% 1.12/1.63 class_Rings_Olinordered__semiring__1 [214, 1] (w:1, o:178, a:1, s:1
% 1.12/1.63 , b:0),
% 1.12/1.63 class_Rings_Olinordered__semiring__1__strict [215, 1] (w:1, o:179, a:
% 1.12/1.63 1, s:1, b:0),
% 1.12/1.63 c_Power_Opower__class_Opower [222, 1] (w:1, o:221, a:1, s:1, b:0),
% 1.12/1.63 c_Complex_Ocis [223, 1] (w:1, o:222, a:1, s:1, b:0),
% 1.12/1.63 class_Power_Opower [225, 1] (w:1, o:223, a:1, s:1, b:0),
% 1.12/1.63 class_Rings_Osemiring__0 [226, 1] (w:1, o:155, a:1, s:1, b:0),
% 1.12/1.63 class_Rings_Ocomm__ring__1 [227, 1] (w:1, o:145, a:1, s:1, b:0),
% 1.12/1.63 class_Rings_Oring__1__no__zero__divisors [228, 1] (w:1, o:154, a:1
% 1.12/1.63 , s:1, b:0),
% 1.12/1.63 c_Power_Opower_Opower [231, 3] (w:1, o:331, a:1, s:1, b:0),
% 1.12/1.63 c_Divides_Odiv__class_Odiv [234, 3] (w:1, o:332, a:1, s:1, b:0),
% 1.12/1.63 class_Divides_Osemiring__div [235, 1] (w:1, o:224, a:1, s:1, b:0),
% 1.12/1.63 c_Complex_Orcis [239, 2] (w:1, o:305, a:1, s:1, b:0),
% 1.12/1.63 c_Rings_Oinverse__class_Odivide [245, 3] (w:1, o:333, a:1, s:1, b:0)
% 1.12/1.63 ,
% 1.12/1.63 class_Fields_Ofield [246, 1] (w:1, o:137, a:1, s:1, b:0),
% 1.60/1.97 class_Rings_Oidom [248, 1] (w:1, o:190, a:1, s:1, b:0),
% 1.60/1.97 class_Groups_Ocancel__comm__monoid__add [249, 1] (w:1, o:225, a:1, s:
% 1.60/1.97 1, b:0),
% 1.60/1.97 class_Rings_Ocomm__semiring__0 [250, 1] (w:1, o:147, a:1, s:1, b:0),
% 1.60/1.97
% 1.60/1.97 class_Rings_Ocomm__ring [251, 1] (w:1, o:146, a:1, s:1, b:0),
% 1.60/1.97 tc_HOL_Obool [253, 0] (w:1, o:95, a:1, s:1, b:0),
% 1.60/1.97 alpha1 [254, 2] (w:1, o:306, a:1, s:1, b:1),
% 1.60/1.97 alpha2 [255, 2] (w:1, o:312, a:1, s:1, b:1),
% 1.60/1.97 alpha3 [256, 3] (w:1, o:338, a:1, s:1, b:1),
% 1.60/1.97 alpha4 [257, 3] (w:1, o:345, a:1, s:1, b:1),
% 1.60/1.97 alpha5 [258, 2] (w:1, o:315, a:1, s:1, b:1),
% 1.60/1.97 alpha6 [259, 2] (w:1, o:317, a:1, s:1, b:1),
% 1.60/1.97 alpha7 [260, 2] (w:1, o:318, a:1, s:1, b:1),
% 1.60/1.97 alpha8 [261, 2] (w:1, o:319, a:1, s:1, b:1),
% 1.60/1.97 alpha9 [262, 3] (w:1, o:346, a:1, s:1, b:1),
% 1.60/1.97 alpha10 [263, 3] (w:1, o:347, a:1, s:1, b:1),
% 1.60/1.97 alpha11 [264, 4] (w:1, o:375, a:1, s:1, b:1),
% 1.60/1.97 alpha12 [265, 4] (w:1, o:376, a:1, s:1, b:1),
% 1.60/1.97 alpha13 [266, 3] (w:1, o:348, a:1, s:1, b:1),
% 1.60/1.97 alpha14 [267, 2] (w:1, o:307, a:1, s:1, b:1),
% 1.60/1.97 alpha15 [268, 2] (w:1, o:308, a:1, s:1, b:1),
% 1.60/1.97 alpha16 [269, 2] (w:1, o:309, a:1, s:1, b:1),
% 1.60/1.97 alpha17 [270, 2] (w:1, o:310, a:1, s:1, b:1),
% 1.60/1.97 alpha18 [271, 2] (w:1, o:311, a:1, s:1, b:1),
% 1.60/1.97 alpha19 [272, 3] (w:1, o:349, a:1, s:1, b:1),
% 1.60/1.97 alpha20 [273, 3] (w:1, o:334, a:1, s:1, b:1),
% 1.60/1.97 alpha21 [274, 2] (w:1, o:320, a:1, s:1, b:1),
% 1.60/1.97 alpha22 [275, 2] (w:1, o:321, a:1, s:1, b:1),
% 1.60/1.97 alpha23 [276, 2] (w:1, o:322, a:1, s:1, b:1),
% 1.60/1.97 alpha24 [277, 3] (w:1, o:335, a:1, s:1, b:1),
% 1.60/1.97 alpha25 [278, 3] (w:1, o:336, a:1, s:1, b:1),
% 1.60/1.97 alpha26 [279, 4] (w:1, o:377, a:1, s:1, b:1),
% 1.60/1.97 alpha27 [280, 4] (w:1, o:378, a:1, s:1, b:1),
% 1.60/1.97 alpha28 [281, 3] (w:1, o:337, a:1, s:1, b:1),
% 1.60/1.97 alpha29 [282, 2] (w:1, o:323, a:1, s:1, b:1),
% 1.60/1.97 alpha30 [283, 3] (w:1, o:339, a:1, s:1, b:1),
% 1.60/1.97 alpha31 [284, 3] (w:1, o:340, a:1, s:1, b:1),
% 1.60/1.97 alpha32 [285, 3] (w:1, o:341, a:1, s:1, b:1),
% 1.60/1.97 alpha33 [286, 2] (w:1, o:324, a:1, s:1, b:1),
% 1.60/1.97 alpha34 [287, 2] (w:1, o:325, a:1, s:1, b:1),
% 1.60/1.97 alpha35 [288, 3] (w:1, o:342, a:1, s:1, b:1),
% 1.60/1.97 alpha36 [289, 3] (w:1, o:343, a:1, s:1, b:1),
% 1.60/1.97 alpha37 [290, 4] (w:1, o:379, a:1, s:1, b:1),
% 1.60/1.97 alpha38 [291, 2] (w:1, o:326, a:1, s:1, b:1),
% 1.60/1.97 alpha39 [292, 3] (w:1, o:344, a:1, s:1, b:1),
% 1.60/1.97 alpha40 [293, 3] (w:1, o:350, a:1, s:1, b:1),
% 1.60/1.97 alpha41 [294, 4] (w:1, o:380, a:1, s:1, b:1),
% 1.60/1.97 alpha42 [295, 2] (w:1, o:313, a:1, s:1, b:1),
% 1.60/1.97 alpha43 [296, 3] (w:1, o:351, a:1, s:1, b:1),
% 1.60/1.97 alpha44 [297, 3] (w:1, o:352, a:1, s:1, b:1),
% 1.60/1.97 alpha45 [298, 3] (w:1, o:353, a:1, s:1, b:1),
% 1.60/1.97 alpha46 [299, 4] (w:1, o:381, a:1, s:1, b:1),
% 1.60/1.97 alpha47 [300, 4] (w:1, o:382, a:1, s:1, b:1),
% 1.60/1.97 alpha48 [301, 3] (w:1, o:354, a:1, s:1, b:1),
% 1.60/1.97 alpha49 [302, 2] (w:1, o:314, a:1, s:1, b:1),
% 1.60/1.97 alpha50 [303, 2] (w:1, o:316, a:1, s:1, b:1),
% 1.60/1.97 alpha51 [304, 3] (w:1, o:355, a:1, s:1, b:1),
% 1.60/1.97 skol1 [305, 2] (w:1, o:251, a:1, s:1, b:1),
% 1.60/1.97 skol2 [306, 2] (w:1, o:259, a:1, s:1, b:1),
% 1.60/1.97 skol3 [307, 3] (w:1, o:359, a:1, s:1, b:1),
% 1.60/1.97 skol4 [308, 2] (w:1, o:264, a:1, s:1, b:1),
% 1.60/1.97 skol5 [309, 2] (w:1, o:272, a:1, s:1, b:1),
% 1.60/1.97 skol6 [310, 2] (w:1, o:277, a:1, s:1, b:1),
% 1.60/1.97 skol7 [311, 2] (w:1, o:286, a:1, s:1, b:1),
% 1.60/1.97 skol8 [312, 2] (w:1, o:290, a:1, s:1, b:1),
% 1.60/1.97 skol9 [313, 2] (w:1, o:292, a:1, s:1, b:1),
% 1.60/1.97 skol10 [314, 2] (w:1, o:252, a:1, s:1, b:1),
% 1.60/1.97 skol11 [315, 2] (w:1, o:253, a:1, s:1, b:1),
% 1.60/1.97 skol12 [316, 2] (w:1, o:254, a:1, s:1, b:1),
% 1.60/1.97 skol13 [317, 2] (w:1, o:255, a:1, s:1, b:1),
% 1.60/1.97 skol14 [318, 2] (w:1, o:256, a:1, s:1, b:1),
% 1.60/1.97 skol15 [319, 2] (w:1, o:257, a:1, s:1, b:1),
% 1.60/1.97 skol16 [320, 1] (w:1, o:192, a:1, s:1, b:1),
% 1.60/1.97 skol17 [321, 2] (w:1, o:258, a:1, s:1, b:1),
% 1.60/1.97 skol18 [322, 3] (w:1, o:360, a:1, s:1, b:1),
% 1.60/1.97 skol19 [323, 3] (w:1, o:361, a:1, s:1, b:1),
% 1.60/1.97 skol20 [324, 1] (w:1, o:193, a:1, s:1, b:1),
% 8.98/9.31 skol21 [325, 2] (w:1, o:293, a:1, s:1, b:1),
% 8.98/9.31 skol22 [326, 1] (w:1, o:194, a:1, s:1, b:1),
% 8.98/9.31 skol23 [327, 2] (w:1, o:294, a:1, s:1, b:1),
% 8.98/9.31 skol24 [328, 1] (w:1, o:195, a:1, s:1, b:1),
% 8.98/9.31 skol25 [329, 3] (w:1, o:356, a:1, s:1, b:1),
% 8.98/9.31 skol26 [330, 1] (w:1, o:196, a:1, s:1, b:1),
% 8.98/9.31 skol27 [331, 3] (w:1, o:357, a:1, s:1, b:1),
% 8.98/9.31 skol28 [332, 3] (w:1, o:358, a:1, s:1, b:1),
% 8.98/9.31 skol29 [333, 1] (w:1, o:197, a:1, s:1, b:1),
% 8.98/9.31 skol30 [334, 0] (w:1, o:12, a:1, s:1, b:1),
% 8.98/9.31 skol31 [335, 0] (w:1, o:13, a:1, s:1, b:1),
% 8.98/9.31 skol32 [336, 4] (w:1, o:383, a:1, s:1, b:1),
% 8.98/9.31 skol33 [337, 2] (w:1, o:260, a:1, s:1, b:1),
% 8.98/9.31 skol34 [338, 2] (w:1, o:261, a:1, s:1, b:1),
% 8.98/9.31 skol35 [339, 2] (w:1, o:262, a:1, s:1, b:1),
% 8.98/9.31 skol36 [340, 2] (w:1, o:263, a:1, s:1, b:1),
% 8.98/9.31 skol37 [341, 3] (w:1, o:362, a:1, s:1, b:1),
% 8.98/9.31 skol38 [342, 1] (w:1, o:198, a:1, s:1, b:1),
% 8.98/9.31 skol39 [343, 1] (w:1, o:199, a:1, s:1, b:1),
% 8.98/9.31 skol40 [344, 2] (w:1, o:265, a:1, s:1, b:1),
% 8.98/9.31 skol41 [345, 2] (w:1, o:266, a:1, s:1, b:1),
% 8.98/9.31 skol42 [346, 2] (w:1, o:267, a:1, s:1, b:1),
% 8.98/9.31 skol43 [347, 1] (w:1, o:200, a:1, s:1, b:1),
% 8.98/9.31 skol44 [348, 2] (w:1, o:268, a:1, s:1, b:1),
% 8.98/9.31 skol45 [349, 2] (w:1, o:269, a:1, s:1, b:1),
% 8.98/9.31 skol46 [350, 2] (w:1, o:270, a:1, s:1, b:1),
% 8.98/9.31 skol47 [351, 1] (w:1, o:201, a:1, s:1, b:1),
% 8.98/9.31 skol48 [352, 1] (w:1, o:202, a:1, s:1, b:1),
% 8.98/9.31 skol49 [353, 2] (w:1, o:271, a:1, s:1, b:1),
% 8.98/9.31 skol50 [354, 2] (w:1, o:273, a:1, s:1, b:1),
% 8.98/9.31 skol51 [355, 2] (w:1, o:274, a:1, s:1, b:1),
% 8.98/9.31 skol52 [356, 2] (w:1, o:275, a:1, s:1, b:1),
% 8.98/9.31 skol53 [357, 3] (w:1, o:363, a:1, s:1, b:1),
% 8.98/9.31 skol54 [358, 3] (w:1, o:364, a:1, s:1, b:1),
% 8.98/9.31 skol55 [359, 3] (w:1, o:365, a:1, s:1, b:1),
% 8.98/9.31 skol56 [360, 3] (w:1, o:366, a:1, s:1, b:1),
% 8.98/9.31 skol57 [361, 2] (w:1, o:276, a:1, s:1, b:1),
% 8.98/9.31 skol58 [362, 3] (w:1, o:367, a:1, s:1, b:1),
% 8.98/9.31 skol59 [363, 4] (w:1, o:384, a:1, s:1, b:1),
% 8.98/9.31 skol60 [364, 3] (w:1, o:368, a:1, s:1, b:1),
% 8.98/9.31 skol61 [365, 2] (w:1, o:278, a:1, s:1, b:1),
% 8.98/9.31 skol62 [366, 2] (w:1, o:279, a:1, s:1, b:1),
% 8.98/9.31 skol63 [367, 2] (w:1, o:280, a:1, s:1, b:1),
% 8.98/9.31 skol64 [368, 2] (w:1, o:281, a:1, s:1, b:1),
% 8.98/9.31 skol65 [369, 2] (w:1, o:282, a:1, s:1, b:1),
% 8.98/9.31 skol66 [370, 2] (w:1, o:283, a:1, s:1, b:1),
% 8.98/9.31 skol67 [371, 2] (w:1, o:284, a:1, s:1, b:1),
% 8.98/9.31 skol68 [372, 2] (w:1, o:285, a:1, s:1, b:1),
% 8.98/9.31 skol69 [373, 1] (w:1, o:203, a:1, s:1, b:1),
% 8.98/9.31 skol70 [374, 2] (w:1, o:287, a:1, s:1, b:1),
% 8.98/9.31 skol71 [375, 2] (w:1, o:288, a:1, s:1, b:1),
% 8.98/9.31 skol72 [376, 3] (w:1, o:369, a:1, s:1, b:1),
% 8.98/9.31 skol73 [377, 3] (w:1, o:370, a:1, s:1, b:1),
% 8.98/9.31 skol74 [378, 3] (w:1, o:371, a:1, s:1, b:1),
% 8.98/9.31 skol75 [379, 1] (w:1, o:204, a:1, s:1, b:1),
% 8.98/9.31 skol76 [380, 1] (w:1, o:205, a:1, s:1, b:1),
% 8.98/9.31 skol77 [381, 3] (w:1, o:372, a:1, s:1, b:1),
% 8.98/9.31 skol78 [382, 3] (w:1, o:373, a:1, s:1, b:1),
% 8.98/9.31 skol79 [383, 2] (w:1, o:289, a:1, s:1, b:1),
% 8.98/9.31 skol80 [384, 2] (w:1, o:291, a:1, s:1, b:1).
% 8.98/9.31
% 8.98/9.31
% 8.98/9.31 Starting Search:
% 8.98/9.31
% 8.98/9.31 *** allocated 170857 integers for clauses
% 8.98/9.31 Resimplifying inuse:
% 8.98/9.31 Done
% 8.98/9.31
% 8.98/9.31
% 8.98/9.31 Intermediate Status:
% 8.98/9.31 Generated: 2914
% 8.98/9.31 Kept: 2001
% 8.98/9.31 Inuse: 72
% 8.98/9.31 Deleted: 0
% 8.98/9.31 Deletedinuse: 0
% 8.98/9.31
% 8.98/9.31 *** allocated 256285 integers for clauses
% 8.98/9.31 Resimplifying inuse:
% 8.98/9.31 Done
% 8.98/9.31
% 8.98/9.31 *** allocated 170857 integers for termspace/termends
% 8.98/9.31 Resimplifying inuse:
% 8.98/9.31 Done
% 8.98/9.31
% 8.98/9.31
% 8.98/9.31 Intermediate Status:
% 8.98/9.31 Generated: 9791
% 8.98/9.31 Kept: 4285
% 8.98/9.31 Inuse: 260
% 8.98/9.31 Deleted: 1
% 8.98/9.31 Deletedinuse: 0
% 8.98/9.31
% 8.98/9.31 *** allocated 384427 integers for clauses
% 8.98/9.31 Resimplifying inuse:
% 8.98/9.31 Done
% 8.98/9.31
% 8.98/9.31 Resimplifying inuse:
% 8.98/9.31 Done
% 8.98/9.31
% 8.98/9.31 *** allocated 256285 integers for termspace/termends
% 8.98/9.31
% 8.98/9.31 Intermediate Status:
% 8.98/9.31 Generated: 17992
% 8.98/9.31 Kept: 6631
% 8.98/9.31 Inuse: 307
% 8.98/9.31 Deleted: 4
% 8.98/9.31 Deletedinuse: 0
% 8.98/9.31
% 8.98/9.31 Resimplifying inuse:
% 8.98/9.31 Done
% 8.98/9.31
% 8.98/9.31 *** allocated 576640 integers for clauses
% 8.98/9.31 Resimplifying inuse:
% 8.98/9.31 Done
% 8.98/9.31
% 8.98/9.31
% 8.98/9.31 Intermediate Status:
% 8.98/9.31 Generated: 24966
% 8.98/9.31 Kept: 8644
% 8.98/9.31 Inuse: 364
% 8.98/9.31 Deleted: 5
% 8.98/9.31 Deletedinuse: 1
% 8.98/9.31
% 8.98/9.31 Resimplifying inuse:
% 8.98/9.31 Done
% 41.31/41.68
% 41.31/41.68 Resimplifying inuse:
% 41.31/41.68 Done
% 41.31/41.68
% 41.31/41.68
% 41.31/41.68 Intermediate Status:
% 41.31/41.68 Generated: 31162
% 41.31/41.68 Kept: 10644
% 41.31/41.68 Inuse: 412
% 41.31/41.68 Deleted: 5
% 41.31/41.68 Deletedinuse: 1
% 41.31/41.68
% 41.31/41.68 *** allocated 384427 integers for termspace/termends
% 41.31/41.68 *** allocated 864960 integers for clauses
% 41.31/41.68 Resimplifying inuse:
% 41.31/41.68 Done
% 41.31/41.68
% 41.31/41.68 Resimplifying inuse:
% 41.31/41.68 Done
% 41.31/41.68
% 41.31/41.68
% 41.31/41.68 Intermediate Status:
% 41.31/41.68 Generated: 36412
% 41.31/41.68 Kept: 12656
% 41.31/41.68 Inuse: 468
% 41.31/41.68 Deleted: 5
% 41.31/41.68 Deletedinuse: 1
% 41.31/41.68
% 41.31/41.68 Resimplifying inuse:
% 41.31/41.68 Done
% 41.31/41.68
% 41.31/41.68 Resimplifying inuse:
% 41.31/41.68 Done
% 41.31/41.68
% 41.31/41.68
% 41.31/41.68 Intermediate Status:
% 41.31/41.68 Generated: 42938
% 41.31/41.68 Kept: 14681
% 41.31/41.68 Inuse: 526
% 41.31/41.68 Deleted: 7
% 41.31/41.68 Deletedinuse: 1
% 41.31/41.68
% 41.31/41.68 Resimplifying inuse:
% 41.31/41.68 Done
% 41.31/41.68
% 41.31/41.68 Resimplifying inuse:
% 41.31/41.68 Done
% 41.31/41.68
% 41.31/41.68
% 41.31/41.68 Intermediate Status:
% 41.31/41.68 Generated: 49513
% 41.31/41.68 Kept: 16697
% 41.31/41.68 Inuse: 589
% 41.31/41.68 Deleted: 9
% 41.31/41.68 Deletedinuse: 1
% 41.31/41.68
% 41.31/41.68 *** allocated 1297440 integers for clauses
% 41.31/41.68 Resimplifying inuse:
% 41.31/41.68 Done
% 41.31/41.68
% 41.31/41.68 *** allocated 576640 integers for termspace/termends
% 41.31/41.68
% 41.31/41.68 Intermediate Status:
% 41.31/41.68 Generated: 56341
% 41.31/41.68 Kept: 19634
% 41.31/41.68 Inuse: 650
% 41.31/41.68 Deleted: 12
% 41.31/41.68 Deletedinuse: 1
% 41.31/41.68
% 41.31/41.68 Resimplifying inuse:
% 41.31/41.68 Done
% 41.31/41.68
% 41.31/41.68 Resimplifying clauses:
% 41.31/41.68 Done
% 41.31/41.68
% 41.31/41.68
% 41.31/41.68 Intermediate Status:
% 41.31/41.68 Generated: 60272
% 41.31/41.68 Kept: 21640
% 41.31/41.68 Inuse: 685
% 41.31/41.68 Deleted: 263
% 41.31/41.68 Deletedinuse: 2
% 41.31/41.68
% 41.31/41.68 Resimplifying inuse:
% 41.31/41.68 Done
% 41.31/41.68
% 41.31/41.68 Resimplifying inuse:
% 41.31/41.68 Done
% 41.31/41.68
% 41.31/41.68
% 41.31/41.68 Intermediate Status:
% 41.31/41.68 Generated: 69467
% 41.31/41.68 Kept: 24382
% 41.31/41.68 Inuse: 700
% 41.31/41.68 Deleted: 263
% 41.31/41.68 Deletedinuse: 2
% 41.31/41.68
% 41.31/41.68 Resimplifying inuse:
% 41.31/41.68 Done
% 41.31/41.68
% 41.31/41.68 Resimplifying inuse:
% 41.31/41.68 Done
% 41.31/41.68
% 41.31/41.68 *** allocated 1946160 integers for clauses
% 41.31/41.68
% 41.31/41.68 Intermediate Status:
% 41.31/41.68 Generated: 78059
% 41.31/41.68 Kept: 28848
% 41.31/41.68 Inuse: 755
% 41.31/41.68 Deleted: 264
% 41.31/41.68 Deletedinuse: 3
% 41.31/41.68
% 41.31/41.68 Resimplifying inuse:
% 41.31/41.68 Done
% 41.31/41.68
% 41.31/41.68 *** allocated 864960 integers for termspace/termends
% 41.31/41.68
% 41.31/41.68 Intermediate Status:
% 41.31/41.68 Generated: 82927
% 41.31/41.68 Kept: 32174
% 41.31/41.68 Inuse: 769
% 41.31/41.68 Deleted: 265
% 41.31/41.68 Deletedinuse: 3
% 41.31/41.68
% 41.31/41.68 Resimplifying inuse:
% 41.31/41.68 Done
% 41.31/41.68
% 41.31/41.68 Resimplifying inuse:
% 41.31/41.68 Done
% 41.31/41.68
% 41.31/41.68
% 41.31/41.68 Intermediate Status:
% 41.31/41.68 Generated: 88542
% 41.31/41.68 Kept: 34225
% 41.31/41.68 Inuse: 806
% 41.31/41.68 Deleted: 265
% 41.31/41.68 Deletedinuse: 3
% 41.31/41.68
% 41.31/41.68 Resimplifying inuse:
% 41.31/41.68 Done
% 41.31/41.68
% 41.31/41.68 Resimplifying inuse:
% 41.31/41.68 Done
% 41.31/41.68
% 41.31/41.68
% 41.31/41.68 Intermediate Status:
% 41.31/41.68 Generated: 93648
% 41.31/41.68 Kept: 36249
% 41.31/41.68 Inuse: 846
% 41.31/41.68 Deleted: 265
% 41.31/41.68 Deletedinuse: 3
% 41.31/41.68
% 41.31/41.68 Resimplifying inuse:
% 41.31/41.68 Done
% 41.31/41.68
% 41.31/41.68 Resimplifying inuse:
% 41.31/41.68 Done
% 41.31/41.68
% 41.31/41.68
% 41.31/41.68 Intermediate Status:
% 41.31/41.68 Generated: 105882
% 41.31/41.68 Kept: 41362
% 41.31/41.68 Inuse: 874
% 41.31/41.68 Deleted: 268
% 41.31/41.68 Deletedinuse: 6
% 41.31/41.68
% 41.31/41.68 Resimplifying inuse:
% 41.31/41.68 Done
% 41.31/41.68
% 41.31/41.68 Resimplifying clauses:
% 41.31/41.68 Done
% 41.31/41.68
% 41.31/41.68 Resimplifying inuse:
% 41.31/41.68 Done
% 41.31/41.68
% 41.31/41.68 *** allocated 2919240 integers for clauses
% 41.31/41.68
% 41.31/41.68 Intermediate Status:
% 41.31/41.68 Generated: 112218
% 41.31/41.68 Kept: 43408
% 41.31/41.68 Inuse: 910
% 41.31/41.68 Deleted: 490
% 41.31/41.68 Deletedinuse: 6
% 41.31/41.68
% 41.31/41.68 Resimplifying inuse:
% 41.31/41.68 Done
% 41.31/41.68
% 41.31/41.68 Resimplifying inuse:
% 41.31/41.68 Done
% 41.31/41.68
% 41.31/41.68
% 41.31/41.68 Intermediate Status:
% 41.31/41.68 Generated: 118539
% 41.31/41.68 Kept: 45414
% 41.31/41.68 Inuse: 941
% 41.31/41.68 Deleted: 490
% 41.31/41.68 Deletedinuse: 6
% 41.31/41.68
% 41.31/41.68 Resimplifying inuse:
% 41.31/41.68 Done
% 41.31/41.68
% 41.31/41.68 Resimplifying inuse:
% 41.31/41.68 Done
% 41.31/41.68
% 41.31/41.68 *** allocated 1297440 integers for termspace/termends
% 41.31/41.68
% 41.31/41.68 Intermediate Status:
% 41.31/41.68 Generated: 124881
% 41.31/41.68 Kept: 47416
% 41.31/41.68 Inuse: 972
% 41.31/41.68 Deleted: 490
% 41.31/41.68 Deletedinuse: 6
% 41.31/41.68
% 41.31/41.68 Resimplifying inuse:
% 41.31/41.68 Done
% 41.31/41.68
% 41.31/41.68 Resimplifying inuse:
% 41.31/41.68 Done
% 41.31/41.68
% 41.31/41.68
% 41.31/41.68 Intermediate Status:
% 41.31/41.68 Generated: 130741
% 41.31/41.68 Kept: 49426
% 41.31/41.68 Inuse: 1004
% 41.31/41.68 Deleted: 490
% 41.31/41.68 Deletedinuse: 6
% 41.31/41.68
% 41.31/41.68 Resimplifying inuse:
% 41.31/41.68 Done
% 41.31/41.68
% 41.31/41.68 Resimplifying inuse:
% 41.31/41.68 Done
% 41.31/41.68
% 41.31/41.68
% 41.31/41.68 Intermediate Status:
% 41.31/41.68 Generated: 136470
% 41.31/41.68 Kept: 51441
% 41.31/41.68 Inuse: 1039
% 41.31/41.68 Deleted: 490
% 41.31/41.68 Deletedinuse: 6
% 41.31/41.68
% 41.31/41.68 Resimplifying inuse:
% 41.31/41.68 Done
% 41.31/41.68
% 41.31/41.68 Resimplifying inuse:
% 41.31/41.68 Done
% 41.31/41.68
% 41.31/41.68
% 41.31/41.68 Intermediate Status:
% 41.31/41.68 Generated: 142438
% 41.31/41.68 Kept: 53467
% 41.31/41.68 Inuse: 1073
% 41.31/41.68 Deleted: 490
% 41.31/41.68 Deletedinuse: 6
% 41.31/41.68
% 41.31/41.68 Resimplifying inuse:
% 41.31/41.68 Done
% 41.31/41.68
% 41.31/41.68 Resimplifying inuse:
% 41.31/41.68 Done
% 41.31/41.68
% 41.31/41.68
% 41.31/41.68 Intermediate Status:
% 41.31/41.68 Generated: 149392
% 41.31/41.68 Kept: 55472
% 41.31/41.68 Inuse: 1090
% 41.31/41.68 Deleted: 490
% 41.31/41.68 Deletedinuse: 6
% 41.31/41.68
% 41.31/41.68
% 41.31/41.68 Intermediate Status:
% 41.31/41.68 Generated: 158163
% 41.31/41.68 Kept: 57984
% 41.31/41.68 Inuse: 1101
% 41.31/41.68 Deleted: 490
% 41.31/41.68 Deletedinuse: 6
% 41.31/41.68
% 41.31/41.68 Resimplifying inuse:
% 41.31/41.68 Done
% 41.31/41.68
% 41.31/41.68 Resimplifying inuse:
% 41.31/41.68 Done
% 41.31/41.68
% 41.31/41.68
% 41.31/41.68 Intermediate Status:
% 41.31/41.68 Generated: 169074
% 41.31/41.68 Kept: 62968
% 41.31/41.68 Inuse: 1139
% 41.31/41.68 Deleted: 490
% 41.31/41.68 Deletedinuse: 6
% 41.31/41.68
% 41.31/41.68 Resimplifying inuse:
% 41.31/41.68 Done
% 41.31/41.68
% 41.31/41.68 Resimplifying clauses:
% 41.31/41.68 Done
% 41.31/41.68
% 41.31/41.68
% 41.31/41.68 Intermediate Status:
% 41.31/41.68 Generated: 181418
% 41.31/41.68 Kept: 66712
% 41.31/41.68 Inuse: 1145
% 41.31/41.68 Deleted: 690
% 41.31/41.68 Deletedinuse: 6
% 41.31/41.68
% 41.31/41.68 Resimplifying inuse:
% 41.31/41.68 Done
% 41.31/41.68
% 41.31/41.68 *** allocated 4378860 integers for clauses
% 41.31/41.68 Resimplifying inuse:
% 118.83/119.22 Done
% 118.83/119.22
% 118.83/119.22
% 118.83/119.22 Intermediate Status:
% 118.83/119.22 Generated: 187465
% 118.83/119.22 Kept: 68739
% 118.83/119.22 Inuse: 1187
% 118.83/119.22 Deleted: 694
% 118.83/119.22 Deletedinuse: 7
% 118.83/119.22
% 118.83/119.22 Resimplifying inuse:
% 118.83/119.22 Done
% 118.83/119.22
% 118.83/119.22 Resimplifying inuse:
% 118.83/119.22 Done
% 118.83/119.22
% 118.83/119.22
% 118.83/119.22 Intermediate Status:
% 118.83/119.22 Generated: 195756
% 118.83/119.22 Kept: 70880
% 118.83/119.22 Inuse: 1244
% 118.83/119.22 Deleted: 698
% 118.83/119.22 Deletedinuse: 8
% 118.83/119.22
% 118.83/119.22 Resimplifying inuse:
% 118.83/119.22 Done
% 118.83/119.22
% 118.83/119.22 *** allocated 1946160 integers for termspace/termends
% 118.83/119.22
% 118.83/119.22 Intermediate Status:
% 118.83/119.22 Generated: 206079
% 118.83/119.22 Kept: 76319
% 118.83/119.22 Inuse: 1269
% 118.83/119.22 Deleted: 701
% 118.83/119.22 Deletedinuse: 11
% 118.83/119.22
% 118.83/119.22 Resimplifying inuse:
% 118.83/119.22 Done
% 118.83/119.22
% 118.83/119.22
% 118.83/119.22 Intermediate Status:
% 118.83/119.22 Generated: 212622
% 118.83/119.22 Kept: 79035
% 118.83/119.22 Inuse: 1289
% 118.83/119.22 Deleted: 701
% 118.83/119.22 Deletedinuse: 11
% 118.83/119.22
% 118.83/119.22 Resimplifying inuse:
% 118.83/119.22 Done
% 118.83/119.22
% 118.83/119.22
% 118.83/119.22 Intermediate Status:
% 118.83/119.22 Generated: 223131
% 118.83/119.22 Kept: 84935
% 118.83/119.22 Inuse: 1314
% 118.83/119.22 Deleted: 701
% 118.83/119.22 Deletedinuse: 11
% 118.83/119.22
% 118.83/119.22 Resimplifying inuse:
% 118.83/119.22 Done
% 118.83/119.22
% 118.83/119.22 Resimplifying clauses:
% 118.83/119.22 Done
% 118.83/119.22
% 118.83/119.22 Resimplifying inuse:
% 118.83/119.22 Done
% 118.83/119.22
% 118.83/119.22
% 118.83/119.22 Intermediate Status:
% 118.83/119.22 Generated: 231792
% 118.83/119.22 Kept: 86935
% 118.83/119.22 Inuse: 1359
% 118.83/119.22 Deleted: 1456
% 118.83/119.22 Deletedinuse: 12
% 118.83/119.22
% 118.83/119.22 Resimplifying inuse:
% 118.83/119.22 Done
% 118.83/119.22
% 118.83/119.22
% 118.83/119.22 Intermediate Status:
% 118.83/119.22 Generated: 242561
% 118.83/119.22 Kept: 92709
% 118.83/119.22 Inuse: 1379
% 118.83/119.22 Deleted: 1456
% 118.83/119.22 Deletedinuse: 12
% 118.83/119.22
% 118.83/119.22 Resimplifying inuse:
% 118.83/119.22 Done
% 118.83/119.22
% 118.83/119.22
% 118.83/119.22 Intermediate Status:
% 118.83/119.22 Generated: 248952
% 118.83/119.22 Kept: 95763
% 118.83/119.22 Inuse: 1394
% 118.83/119.22 Deleted: 1457
% 118.83/119.22 Deletedinuse: 13
% 118.83/119.22
% 118.83/119.22 Resimplifying inuse:
% 118.83/119.22 Done
% 118.83/119.22
% 118.83/119.22
% 118.83/119.22 Intermediate Status:
% 118.83/119.22 Generated: 252427
% 118.83/119.22 Kept: 98256
% 118.83/119.22 Inuse: 1396
% 118.83/119.22 Deleted: 1457
% 118.83/119.22 Deletedinuse: 13
% 118.83/119.22
% 118.83/119.22 Resimplifying inuse:
% 118.83/119.22 Done
% 118.83/119.22
% 118.83/119.22 *** allocated 6568290 integers for clauses
% 118.83/119.22
% 118.83/119.22 Intermediate Status:
% 118.83/119.22 Generated: 258993
% 118.83/119.22 Kept: 102074
% 118.83/119.22 Inuse: 1424
% 118.83/119.22 Deleted: 1457
% 118.83/119.22 Deletedinuse: 13
% 118.83/119.22
% 118.83/119.22 Resimplifying inuse:
% 118.83/119.22 Done
% 118.83/119.22
% 118.83/119.22
% 118.83/119.22 Intermediate Status:
% 118.83/119.22 Generated: 265173
% 118.83/119.22 Kept: 105605
% 118.83/119.22 Inuse: 1444
% 118.83/119.22 Deleted: 1457
% 118.83/119.22 Deletedinuse: 13
% 118.83/119.22
% 118.83/119.22 Resimplifying inuse:
% 118.83/119.22 Done
% 118.83/119.22
% 118.83/119.22 Resimplifying clauses:
% 118.83/119.22 Done
% 118.83/119.22
% 118.83/119.22
% 118.83/119.22 Intermediate Status:
% 118.83/119.22 Generated: 269344
% 118.83/119.22 Kept: 108555
% 118.83/119.22 Inuse: 1449
% 118.83/119.22 Deleted: 1604
% 118.83/119.22 Deletedinuse: 13
% 118.83/119.22
% 118.83/119.22 Resimplifying inuse:
% 118.83/119.22 Done
% 118.83/119.22
% 118.83/119.22 *** allocated 2919240 integers for termspace/termends
% 118.83/119.22
% 118.83/119.22 Intermediate Status:
% 118.83/119.22 Generated: 273426
% 118.83/119.22 Kept: 111448
% 118.83/119.22 Inuse: 1454
% 118.83/119.22 Deleted: 1604
% 118.83/119.22 Deletedinuse: 13
% 118.83/119.22
% 118.83/119.22 Resimplifying inuse:
% 118.83/119.22 Done
% 118.83/119.22
% 118.83/119.22
% 118.83/119.22 Intermediate Status:
% 118.83/119.22 Generated: 277581
% 118.83/119.22 Kept: 114305
% 118.83/119.22 Inuse: 1459
% 118.83/119.22 Deleted: 1604
% 118.83/119.22 Deletedinuse: 13
% 118.83/119.22
% 118.83/119.22 Resimplifying inuse:
% 118.83/119.22 Done
% 118.83/119.22
% 118.83/119.22 Resimplifying inuse:
% 118.83/119.22 Done
% 118.83/119.22
% 118.83/119.22
% 118.83/119.22 Intermediate Status:
% 118.83/119.22 Generated: 281595
% 118.83/119.22 Kept: 116329
% 118.83/119.22 Inuse: 1485
% 118.83/119.22 Deleted: 1604
% 118.83/119.22 Deletedinuse: 13
% 118.83/119.22
% 118.83/119.22 Resimplifying inuse:
% 118.83/119.22 Done
% 118.83/119.22
% 118.83/119.22 Resimplifying inuse:
% 118.83/119.22 Done
% 118.83/119.22
% 118.83/119.22
% 118.83/119.22 Intermediate Status:
% 118.83/119.22 Generated: 286999
% 118.83/119.22 Kept: 118425
% 118.83/119.22 Inuse: 1519
% 118.83/119.22 Deleted: 1604
% 118.83/119.22 Deletedinuse: 13
% 118.83/119.22
% 118.83/119.22 Resimplifying inuse:
% 118.83/119.22 Done
% 118.83/119.22
% 118.83/119.22
% 118.83/119.22 Intermediate Status:
% 118.83/119.22 Generated: 295258
% 118.83/119.22 Kept: 123554
% 118.83/119.22 Inuse: 1524
% 118.83/119.22 Deleted: 1605
% 118.83/119.22 Deletedinuse: 14
% 118.83/119.22
% 118.83/119.22 Resimplifying inuse:
% 118.83/119.22 Done
% 118.83/119.22
% 118.83/119.22 Resimplifying inuse:
% 118.83/119.22 Done
% 118.83/119.22
% 118.83/119.22
% 118.83/119.22 Intermediate Status:
% 118.83/119.22 Generated: 300310
% 118.83/119.22 Kept: 125710
% 118.83/119.22 Inuse: 1559
% 118.83/119.22 Deleted: 1605
% 118.83/119.22 Deletedinuse: 14
% 118.83/119.22
% 118.83/119.22 Resimplifying inuse:
% 118.83/119.22 Done
% 118.83/119.22
% 118.83/119.22 Resimplifying clauses:
% 118.83/119.22 Done
% 118.83/119.22
% 118.83/119.22 Resimplifying inuse:
% 118.83/119.22 Done
% 118.83/119.22
% 118.83/119.22
% 118.83/119.22 Intermediate Status:
% 118.83/119.22 Generated: 311757
% 118.83/119.22 Kept: 128187
% 118.83/119.22 Inuse: 1569
% 118.83/119.22 Deleted: 1746
% 118.83/119.22 Deletedinuse: 14
% 118.83/119.22
% 118.83/119.22 Resimplifying inuse:
% 118.83/119.22 Done
% 118.83/119.22
% 118.83/119.22 Resimplifying inuse:
% 118.83/119.22 Done
% 118.83/119.22
% 118.83/119.22
% 118.83/119.22 Intermediate Status:
% 118.83/119.22 Generated: 318826
% 118.83/119.22 Kept: 130233
% 118.83/119.22 Inuse: 1599
% 118.83/119.22 Deleted: 1746
% 118.83/119.22 Deletedinuse: 14
% 118.83/119.22
% 118.83/119.22 Resimplifying inuse:
% 118.83/119.22 Done
% 118.83/119.22
% 118.83/119.22
% 118.83/119.22 Intermediate Status:
% 118.83/119.22 Generated: 325592
% 118.83/119.22 Kept: 134324
% 118.83/119.22 Inuse: 1624
% 118.83/119.22 Deleted: 1746
% 118.83/119.22 Deletedinuse: 14
% 118.83/119.22
% 118.83/119.22 Resimplifying inuse:
% 118.83/119.22 Done
% 118.83/119.22
% 118.83/119.22
% 118.83/119.22 Intermediate Status:
% 118.83/119.22 Generated: 329479
% 118.83/119.22 Kept: 137007
% 118.83/119.22 Inuse: 1629
% 118.83/119.22 Deleted: 1746
% 118.83/119.22 Deletedinuse: 14
% 118.83/119.22
% 118.83/119.22 Resimplifying inuse:
% 118.83/119.22 Done
% 118.83/119.22
% 118.83/119.22
% 118.83/119.22 Intermediate Status:
% 118.83/119.22 Generated: 334198
% 118.83/119.22 Kept: 139976
% 118.83/119.22 Inuse: 1639
% 118.83/119.22 Deleted: 1746
% 118.83/119.22 Deletedinuse: 14
% 118.83/119.22
% 118.83/119.22 Resimplifying inuse:
% 118.83/119.22 Done
% 118.83/119.22
% 118.83/119.22
% 118.83/119.22 Intermediate Status:
% 118.83/119.22 Generated: 338422
% 118.83/119.22 Kept: 143124
% 118.83/119.22 Inuse: 1644
% 118.83/119.22 Deleted: 1746
% 118.83/119.22 Deletedinuse: 14
% 118.83/119.22
% 118.83/119.22 Resimplifying inuse:
% 118.83/119.22 Done
% 118.83/119.22
% 118.83/119.22 Resimplifying inuse:
% 118.83/119.22 Done
% 118.83/119.22
% 118.83/119.22
% 118.83/119.22 Intermediate Status:
% 118.83/119.22 Generated: 345238
% 118.83/119.22 Kept: 147170
% 118.83/119.22 Inuse: 1669
% 118.83/119.22 Deleted: 1746
% 118.83/119.22 Deletedinuse: 14
% 217.30/217.72
% 217.30/217.72 Resimplifying inuse:
% 217.30/217.72 Done
% 217.30/217.72
% 217.30/217.72 Resimplifying clauses:
% 217.30/217.72 Done
% 217.30/217.72
% 217.30/217.72
% 217.30/217.72 Intermediate Status:
% 217.30/217.72 Generated: 349270
% 217.30/217.72 Kept: 149920
% 217.30/217.72 Inuse: 1674
% 217.30/217.72 Deleted: 1954
% 217.30/217.72 Deletedinuse: 14
% 217.30/217.72
% 217.30/217.72 Resimplifying inuse:
% 217.30/217.72 Done
% 217.30/217.72
% 217.30/217.72
% 217.30/217.72 Intermediate Status:
% 217.30/217.72 Generated: 353818
% 217.30/217.72 Kept: 152805
% 217.30/217.72 Inuse: 1684
% 217.30/217.72 Deleted: 1954
% 217.30/217.72 Deletedinuse: 14
% 217.30/217.72
% 217.30/217.72 Resimplifying inuse:
% 217.30/217.72 Done
% 217.30/217.72
% 217.30/217.72
% 217.30/217.72 Intermediate Status:
% 217.30/217.72 Generated: 357882
% 217.30/217.72 Kept: 155874
% 217.30/217.72 Inuse: 1689
% 217.30/217.72 Deleted: 1954
% 217.30/217.72 Deletedinuse: 14
% 217.30/217.72
% 217.30/217.72 Resimplifying inuse:
% 217.30/217.72 Done
% 217.30/217.72
% 217.30/217.72
% 217.30/217.72 Intermediate Status:
% 217.30/217.72 Generated: 367608
% 217.30/217.72 Kept: 158228
% 217.30/217.72 Inuse: 1714
% 217.30/217.72 Deleted: 1954
% 217.30/217.72 Deletedinuse: 14
% 217.30/217.72
% 217.30/217.72 Resimplifying inuse:
% 217.30/217.72 Done
% 217.30/217.72
% 217.30/217.72 Resimplifying inuse:
% 217.30/217.72 Done
% 217.30/217.72
% 217.30/217.72 *** allocated 9852435 integers for clauses
% 217.30/217.72
% 217.30/217.72 Intermediate Status:
% 217.30/217.72 Generated: 372884
% 217.30/217.72 Kept: 160297
% 217.30/217.72 Inuse: 1748
% 217.30/217.72 Deleted: 1954
% 217.30/217.72 Deletedinuse: 14
% 217.30/217.72
% 217.30/217.72 Resimplifying inuse:
% 217.30/217.72 Done
% 217.30/217.72
% 217.30/217.72 Resimplifying inuse:
% 217.30/217.72 Done
% 217.30/217.72
% 217.30/217.72
% 217.30/217.72 Intermediate Status:
% 217.30/217.72 Generated: 378703
% 217.30/217.72 Kept: 162377
% 217.30/217.72 Inuse: 1774
% 217.30/217.72 Deleted: 1954
% 217.30/217.72 Deletedinuse: 14
% 217.30/217.72
% 217.30/217.72 Resimplifying inuse:
% 217.30/217.72 Done
% 217.30/217.72
% 217.30/217.72 Resimplifying inuse:
% 217.30/217.72 Done
% 217.30/217.72
% 217.30/217.72
% 217.30/217.72 Intermediate Status:
% 217.30/217.72 Generated: 386992
% 217.30/217.72 Kept: 166883
% 217.30/217.72 Inuse: 1794
% 217.30/217.72 Deleted: 1954
% 217.30/217.72 Deletedinuse: 14
% 217.30/217.72
% 217.30/217.72 Resimplifying inuse:
% 217.30/217.72 Done
% 217.30/217.72
% 217.30/217.72 Resimplifying clauses:
% 217.30/217.72 Done
% 217.30/217.72
% 217.30/217.72 Resimplifying inuse:
% 217.30/217.72 Done
% 217.30/217.72
% 217.30/217.72
% 217.30/217.72 Intermediate Status:
% 217.30/217.72 Generated: 400508
% 217.30/217.72 Kept: 170436
% 217.30/217.72 Inuse: 1809
% 217.30/217.72 Deleted: 2127
% 217.30/217.72 Deletedinuse: 14
% 217.30/217.72
% 217.30/217.72 Resimplifying inuse:
% 217.30/217.72 Done
% 217.30/217.72
% 217.30/217.72 *** allocated 4378860 integers for termspace/termends
% 217.30/217.72
% 217.30/217.72 Intermediate Status:
% 217.30/217.72 Generated: 405800
% 217.30/217.72 Kept: 173921
% 217.30/217.72 Inuse: 1814
% 217.30/217.72 Deleted: 2127
% 217.30/217.72 Deletedinuse: 14
% 217.30/217.72
% 217.30/217.72 Resimplifying inuse:
% 217.30/217.72 Done
% 217.30/217.72
% 217.30/217.72 Resimplifying inuse:
% 217.30/217.72 Done
% 217.30/217.72
% 217.30/217.72
% 217.30/217.72 Intermediate Status:
% 217.30/217.72 Generated: 411447
% 217.30/217.72 Kept: 176020
% 217.30/217.72 Inuse: 1835
% 217.30/217.72 Deleted: 2128
% 217.30/217.72 Deletedinuse: 15
% 217.30/217.72
% 217.30/217.72 Resimplifying inuse:
% 217.30/217.72 Done
% 217.30/217.72
% 217.30/217.72 Resimplifying inuse:
% 217.30/217.72 Done
% 217.30/217.72
% 217.30/217.72
% 217.30/217.72 Intermediate Status:
% 217.30/217.72 Generated: 419123
% 217.30/217.72 Kept: 178026
% 217.30/217.72 Inuse: 1857
% 217.30/217.72 Deleted: 2128
% 217.30/217.72 Deletedinuse: 15
% 217.30/217.72
% 217.30/217.72
% 217.30/217.72 Intermediate Status:
% 217.30/217.72 Generated: 423838
% 217.30/217.72 Kept: 181466
% 217.30/217.72 Inuse: 1859
% 217.30/217.72 Deleted: 2128
% 217.30/217.72 Deletedinuse: 15
% 217.30/217.72
% 217.30/217.72 Resimplifying inuse:
% 217.30/217.72 Done
% 217.30/217.72
% 217.30/217.72 Resimplifying inuse:
% 217.30/217.72 Done
% 217.30/217.72
% 217.30/217.72
% 217.30/217.72 Intermediate Status:
% 217.30/217.72 Generated: 428098
% 217.30/217.72 Kept: 183522
% 217.30/217.72 Inuse: 1877
% 217.30/217.72 Deleted: 2128
% 217.30/217.72 Deletedinuse: 15
% 217.30/217.72
% 217.30/217.72 Resimplifying inuse:
% 217.30/217.72 Done
% 217.30/217.72
% 217.30/217.72
% 217.30/217.72 Intermediate Status:
% 217.30/217.72 Generated: 438545
% 217.30/217.72 Kept: 185935
% 217.30/217.72 Inuse: 1879
% 217.30/217.72 Deleted: 2128
% 217.30/217.72 Deletedinuse: 15
% 217.30/217.72
% 217.30/217.72 Resimplifying inuse:
% 217.30/217.72 Done
% 217.30/217.72
% 217.30/217.72 Resimplifying inuse:
% 217.30/217.72 Done
% 217.30/217.72
% 217.30/217.72 Resimplifying clauses:
% 217.30/217.72 Done
% 217.30/217.72
% 217.30/217.72
% 217.30/217.72 Intermediate Status:
% 217.30/217.72 Generated: 447065
% 217.30/217.72 Kept: 191025
% 217.30/217.72 Inuse: 1894
% 217.30/217.72 Deleted: 2248
% 217.30/217.72 Deletedinuse: 15
% 217.30/217.72
% 217.30/217.72 Resimplifying inuse:
% 217.30/217.72 Done
% 217.30/217.72
% 217.30/217.72 Resimplifying inuse:
% 217.30/217.72 Done
% 217.30/217.72
% 217.30/217.72
% 217.30/217.72 Intermediate Status:
% 217.30/217.72 Generated: 452696
% 217.30/217.72 Kept: 193082
% 217.30/217.72 Inuse: 1918
% 217.30/217.72 Deleted: 2248
% 217.30/217.72 Deletedinuse: 15
% 217.30/217.72
% 217.30/217.72 Resimplifying inuse:
% 217.30/217.72 Done
% 217.30/217.72
% 217.30/217.72 Resimplifying inuse:
% 217.30/217.72 Done
% 217.30/217.72
% 217.30/217.72
% 217.30/217.72 Intermediate Status:
% 217.30/217.72 Generated: 458011
% 217.30/217.72 Kept: 195204
% 217.30/217.72 Inuse: 1939
% 217.30/217.72 Deleted: 2248
% 217.30/217.72 Deletedinuse: 15
% 217.30/217.72
% 217.30/217.72 Resimplifying inuse:
% 217.30/217.72 Done
% 217.30/217.72
% 217.30/217.72 Resimplifying inuse:
% 217.30/217.72 Done
% 217.30/217.72
% 217.30/217.72
% 217.30/217.72 Intermediate Status:
% 217.30/217.72 Generated: 463086
% 217.30/217.72 Kept: 197326
% 217.30/217.72 Inuse: 1959
% 217.30/217.72 Deleted: 2248
% 217.30/217.72 Deletedinuse: 15
% 217.30/217.72
% 217.30/217.72 Resimplifying inuse:
% 217.30/217.72 Done
% 217.30/217.72
% 217.30/217.72 Resimplifying inuse:
% 217.30/217.72 Done
% 217.30/217.72
% 217.30/217.72
% 217.30/217.72 Intermediate Status:
% 217.30/217.72 Generated: 468138
% 217.30/217.72 Kept: 199351
% 217.30/217.72 Inuse: 1978
% 217.30/217.72 Deleted: 2248
% 217.30/217.72 Deletedinuse: 15
% 217.30/217.72
% 217.30/217.72 Resimplifying inuse:
% 217.30/217.72 Done
% 217.30/217.72
% 217.30/217.72 Resimplifying inuse:
% 217.30/217.72 Done
% 217.30/217.72
% 217.30/217.72
% 217.30/217.72 Intermediate Status:
% 217.30/217.72 Generated: 476672
% 217.30/217.72 Kept: 204283
% 217.30/217.72 Inuse: 1994
% 217.30/217.72 Deleted: 2248
% 217.30/217.72 Deletedinuse: 15
% 217.30/217.72
% 217.30/217.72 Resimplifying inuse:
% 217.30/217.72 Done
% 217.30/217.72
% 217.30/217.72
% 217.30/217.72 Intermediate Status:
% 217.30/217.72 Generated: 484415
% 217.30/217.72 Kept: 208707
% 217.30/217.72 Inuse: 2006
% 217.30/217.72 Deleted: 2251
% 217.30/217.72 Deletedinuse: 15
% 217.30/217.72
% 217.30/217.72 Resimplifying inuse:
% 217.30/217.72 Done
% 217.30/217.72
% 217.30/217.72 Resimplifying clauses:
% 217.30/217.72 Done
% 217.30/217.72
% 217.30/217.72 Resimplifying inuse:
% 217.30/217.72 Done
% 217.30/217.72
% 217.30/217.72
% 217.30/217.72 Intermediate Status:
% 217.30/217.72 Generated: 489707
% 217.30/217.72 Kept: 210832
% 217.30/217.72 Inuse: 2026
% 217.30/217.72 Deleted: 2847
% 217.30/217.72 Deletedinuse: 16
% 217.30/217.72
% 217.30/217.72 Resimplifying inuse:
% 217.30/217.72 Done
% 217.30/217.72
% 217.30/217.72 Resimplifying inuse:
% 217.30/217.72 Done
% 217.30/217.72
% 217.30/217.72
% 217.30/217.72 Intermediate Status:
% 217.30/217.72 Generated: 494599
% 217.30/217.72 Kept: 212855
% 217.30/217.72 Inuse: 2044
% 217.30/217.72 Deleted: 2847
% 217.30/217.72 Deletedinuse: 16
% 217.30/217.72
% 217.30/217.72 Resimplifying inuse:
% 217.30/217.72 Done
% 217.30/217.72
% 217.30/217.72 Resimplifying inuse:
% 217.30/217.72 Done
% 217.30/217.72
% 217.30/217.72
% 217.30/217.72 Intermediate Status:
% 217.30/217.72 Generated: 500644
% 217.30/217.72 Kept: 215168
% 217.30/217.72 InuseCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------