
theorem Th23:
  for f being Function, g being rng-retract of f holds rng g c= dom f
proof
  let f,g be Function;
  assume that
A1: dom g = rng f and
A2: f*g = id rng f;
  dom g = dom (f*g) by A1,A2;
  hence thesis by FUNCT_1:15;
end;
