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

theorem Th1712: :: Theorem 1.7. (1) <=> (2)
  (x "/\" y) "\/" x = x iff x "/\" (y "\/" x) = x
  proof
    hereby
      assume
A1:   (x "/\" y) "\/" x = x;
      x "/\" (y "\/" x) = (x "/\" y) "\/" (x "/\" x) by LATTICES:def 11
                       .= x by A1,IMeet;
      hence x "/\" (y "\/" x) = x;
    end;
    assume
A1: x "/\" (y "\/" x) = x;
    (x "/\" y) "\/" x = (x "/\" y) "\/" (x "/\" x) by IMeet
                     .= x "/\" (y "\/" x) by LATTICES:def 11;
    hence thesis by A1;
  end;
