theorem :: (17)
  X <> {} implies R.:^X c= R.:X
proof
  assume
A1: X <> {};
  let y be object;
  assume
A2: y in R.:^X;
  consider x being object such that
A3: x in X by A1,XBOOLE_0:def 1;
  y in Im(R,x) by A2,A3,Th24;
  then [x,y] in R by Th9;
  hence thesis by A3,RELAT_1:def 13;
end;
