reserve k,m,n for Nat, kk,mm,nn for Element of NAT, A,B,X,Y,Z,x,y,z for set,
S, S1, S2 for Language, s for (Element of S), w,w1,w2 for (string of S),
U,U1,U2 for non empty set, f,g for Function, p,p1,p2 for FinSequence;

theorem for t0 being 0-termal string of S holds t0=<*S-firstChar.t0*>
proof
let t0 be 0-termal string of S;
reconsider e=(S-multiCat).(SubTerms(t0)) as empty set;
t0 = <*S-firstChar.t0*> ^ e by FOMODEL1:def 37 .= <*S-firstChar.t0*>;
hence thesis;
end;
