
theorem Th2:
  for R being Relation, X being set holds (R|X)~ = X|`(R~) & (X|`R)~ = (R~)|X
proof
  let R be Relation, X be set;
  thus (R|X)~ = X|`(R~) by Lm1;
  ((R~)|X)~ = X|`((R~)~) by Lm1;
  hence thesis;
end;
