
theorem Th11:
  for S,T being non empty Poset, f being Function st f
  is_a_retraction_of T,S holds f is idempotent Function of T,T
proof
  let S,T be non empty Poset, f be Function;
  assume
A1: f is_a_retraction_of T,S;
  then
A2: f is Function of T,S;
A3: S is SubRelStr of T by A1;
  f*incl(S,T) = id S by A1,Th7;
  hence thesis by A2,A3,Th6;
end;
