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

theorem Th1726:  :: Theorem 1.7. (2) => (6)
  x "/\" (y "\/" x) = x implies x "\/" y = y "\/" x
  proof
    assume
A0: x "/\" (y "\/" x) = x;
    x "\/" y = (x "/\" (y "\/" x)) "\/" (y "/\" (y "\/" x)) by Ze,A0
            .= (x "\/" y) "/\" (y "\/" x) by DefD
            .= ((x "\/" y) "/\" y) "\/" ((x "\/" y) "/\" x) by LATTICES:def 11
            .= y "\/" ((x "\/" y) "/\" x) by DefA1
            .= y "\/" x by DefA2;
    hence thesis;
  end;
