reserve P,Q,X,Y,Z for set, p,x,x9,x1,x2,y,z for object;

theorem
  for f being Function of X,Y for g being Function of Y,X st f*g = id Y
  holds rng f = Y
proof
  let f be (Function of X,Y),g be Function of Y,X;
  assume f*g = id Y;
  then rng(f*g) = Y;
  then Y c= rng f by RELAT_1:26;
  hence thesis;
end;
