 reserve L for AD_Lattice;
 reserve x,y,z for Element of L;

theorem Lem232:   :: Lemma 2.3 (2)
  x "\/" y = y iff x "/\" y = x
  proof
    hereby
      assume x "\/" y = y; then
      x "/\" y = (x "/\" x) "\/" (x "/\" y) by LATTICES:def 11
              .= x "\/" (x "/\" y) by IMeet
              .= x by ROBBINS3:def 3;
      hence x "/\" y = x;
    end;
    assume x "/\" y = x;
    hence thesis by LemXX;
  end;
