
theorem Th12:
  for T,S being non empty Poset, f being Function of T,T st f
  is_a_retraction_of T,S holds Image f = the RelStr of S
proof
  let T,S be non empty Poset, f be Function of T,T;
A1: the carrier of Image f = rng f by YELLOW_0:def 15;
  assume
A2: f is_a_retraction_of T,S;
  thus thesis by A2,A1,Th9,YELLOW_0:57;
end;
