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

theorem Hehe1:  :: Lemma 2.3. (13)
  (ex z being Element of L st x [= z & y [= z) implies
     x "\/" y = y "\/" x
  proof
    assume
A0: ex z being Element of L st x [= z & y [= z;
    y "/\" (x "\/" y) = y
    proof
      consider z being Element of L such that
A1:   x [= z & y [= z by A0;
      thus y "/\" (x "\/" y) = (y "/\" x) "\/" (y "/\" y) by LATTICES:def 11
                       .= (y "/\" x) "\/" y by IMeet
                       .= (y "/\" x) "\/" (y "/\" z) by A1,Lem232
                       .= y "/\" (x "\/" z) by LATTICES:def 11
                       .= y by A1,Lem232;
    end;
    hence thesis by Th1726;
  end;
