set D = DTConMSA X;
set OU = [:the carrier' of S,{the carrier of S}:] \/ (Union (coprod X));
consider p being FinSequence such that
A2:
t ==> p
by A1;
A3:
[t,p] in the Rules of (DTConMSA X)
by A2, LANG1:def 1;
reconsider a = t as Element of [:the carrier' of S,{the carrier of S}:] \/ (Union (coprod X)) ;
reconsider p = p as Element of ([:the carrier' of S,{the carrier of S}:] \/ (Union (coprod X))) * by A3, ZFMISC_1:106;
[a,p] in REL X
by A2, LANG1:def 1;
then
a in [:the carrier' of S,{the carrier of S}:]
by Def9;
then consider o being OperSymbol of S, x2 being Element of {the carrier of S} such that
A4:
a = [o,x2]
by DOMAIN_1:9;
take
o
; :: thesis: [o,the carrier of S] = t
thus
[o,the carrier of S] = t
by A4, TARSKI:def 1; :: thesis: verum