
theorem Lemma12b:
  for X being non empty set,
      R being (Relation of X),
      x,y being Element of X holds
    not [x,y] in R` implies [x,y] in R
  proof
    let X be non empty set,
        R be (Relation of X),
        x,y be Element of X;
    assume
A2: not [x,y] in R`;
    R \/ R` = [#][:X, X:] by SUBSET_1:10;
    hence thesis by A2, XBOOLE_0:def 3;
  end;
