theorem
  (for n holds s.n in Y) implies rng s c= Y
proof
  assume
A1: for n holds s.n in Y;
  let y be object;
  assume y in rng s;
  then consider x being object such that
A2: x in dom s and
A3: y = s.x by FUNCT_1:def 3;
  x in NAT by A2,FUNCT_2:def 1;
  hence thesis by A1,A3;
end;
