reserve U1,U2,U3 for Universal_Algebra,
  n,m for Nat,
  o1 for operation of U1,
  o2 for operation of U2,
  o3 for operation of U3,
  x,y for set;
reserve a for FinSequence of U1,
  f for Function of U1,U2;

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;
