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 Th2: for I being (S,U)-interpreter-like Function holds
I|(OwnSymbolsOf S) in U-InterpretersOf S
proof
let I be (S,U)-interpreter-like Function;
set O=OwnSymbolsOf S, C=PFuncs(U*,U\/BOOLEAN);
dom (I|O) c= O & rng (I|O) c= C;
then I|O is Function of O,C by RELSET_1:4; then
I|O is (S,U)-interpreter-like & I|O is Element of Funcs(O,C)
by FUNCT_2:8; hence thesis;
end;
