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

theorem  :: Theorem 1.7. (1) => (5)
  (x "/\" y) "\/" x = x implies x "/\" y = y "/\" x
  proof
    assume (x "/\" y) "\/" x = x; then
    y "/\" x = (y "/\" (x "/\" y)) "\/" (y "/\" x) by LATTICES:def 11
            .= (x "/\" y) "\/" (y "/\" x) by Lem36c
            .= (x "/\" y) "\/" (x "/\" (y "/\" x)) by Lem36c
            .= x "/\" (y "\/" (y "/\" x)) by LATTICES:def 11
            .= x "/\" y by ROBBINS3:def 3;
    hence thesis;
  end;
