
theorem Th10:
  for S,T being complete LATTICE for f being idempotent Function
  of T,T for h being Function of S, Image f holds f*h = h
proof
  let S,T be complete LATTICE;
  let f be idempotent Function of T,T;
  let h be Function of S, Image f;
  rng h c= the carrier of Image f;
  then
A1: rng h c= rng f by YELLOW_0:def 15;
  f*f = f by QUANTAL1:def 9;
  then rng f c= dom f by FUNCT_1:15;
  then rng h c= dom f by A1;
  hence thesis by A1,YELLOW16:4;
end;
