 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 3.9. (1) <=> (5)
  x "/\" y = y "/\" x iff ex_glb_of x,y & y "/\" x = glb (x,y)
  proof
    thus x "/\" y = y "/\" x implies ex_glb_of x,y & y "/\" x = glb (x,y)
    proof
      assume x "/\" y = y "/\" x; then
      y "/\" x [= y by LATTICES:def 8;
      hence thesis by Th3956;
    end;
    assume ex_glb_of x,y & y "/\" x = glb (x,y);
    hence thesis by Th391i4,Th3965;
  end;
