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;
