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

theorem  :: Theorem 3.7. (1) <=> (4)
  (x "/\" y) "\/" x = x iff y "/\" (x "\/" y) = y
  proof
    thus (x "/\" y) "\/" x = x implies y "/\" (x "\/" y) = y
    proof
      assume (x "/\" y) "\/" x = x; then
      (y "/\" x) "\/" y = y by Th3713;
      hence thesis by Th3712;
    end;
    assume y "/\" (x "\/" y) = y; then
    (y "/\" x) "\/" y = y by Th3712;
    hence thesis by Th3713;
  end;
