theorem
  for h be Function of U1,U2 st h is_homomorphism holds rng h =
  the carrier of Image h
proof
  let h be Function of U1,U2;
  dom h = the carrier of U1 by FUNCT_2:def 1;
  then
A1: rng h = h.:(the carrier of U1) by RELAT_1:113;
  assume h is_homomorphism;
  hence thesis by A1,Def6;
end;
