
theorem Th1:
  for f,g being Function st g in product f holds rng g c= Union f
proof
  let f,g be Function;
  assume
A1: g in product f;
  let y be object;
  assume y in rng g;
  then consider x being object such that
A2: x in dom g and
A3: y = g.x by FUNCT_1:def 3;
A4: dom g = dom f by A1,CARD_3:9;
  then y in f.x by A1,A2,A3,CARD_3:9;
  hence thesis by A4,A2,CARD_5:2;
end;
