reserve L for Lattice,
  p,p1,q,q1,r,r1 for Element of L;
reserve x,y,z,X,Y,Z,X1,X2 for set;
reserve H,F for Filter of L;
reserve D for non empty Subset of L;
reserve D1,D2 for non empty Subset of L;
reserve I for I_Lattice,
  i,j,k for Element of I;
reserve B for B_Lattice,
  FB,HB for Filter of B;
reserve I for I_Lattice,
  i,j,k for Element of I,
  DI for non empty Subset of I,
  FI for Filter of I;

theorem Th33:
  D1 "/\" D2 = D2 "/\" D1
proof
  now
    let D1,D2;
    thus D1 "/\" D2 c= D2 "/\" D1
    proof
      let x be object;
      assume x in D1 "/\" D2;
      then ex p,q st x = p"/\"q & p in D1 & q in D2;
      hence thesis;
    end;
  end;
  hence D1 "/\" D2 c= D2 "/\" D1 & D2 "/\" D1 c= D1 "/\" D2;
end;
