
theorem Th6:
  for S being reflexive RelStr, T being reflexive transitive RelStr
  , f being Function of S, T, X being Subset of S holds downarrow (f.:X) c=
  downarrow (f.:downarrow X)
proof
  let S be reflexive RelStr, T be reflexive transitive RelStr, f be Function
  of S, T, X be Subset of S;
  f.:X c= f.:downarrow X by RELAT_1:123,WAYBEL_0:16;
  hence thesis by YELLOW_3:6;
end;
