 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 Th31141: :: Theorem 3.11. (4) <=> (1)
  L is join-commutative iff L is Lattice-like distributive
  proof
    thus L is join-commutative implies L is Lattice-like distributive
    proof
      assume
T0:   L is join-commutative; then
      L is join-associative by Th14;
      hence thesis by T0,Th31145;
    end;
    thus thesis;
  end;
