theorem
  x [= z & y [= z implies (x "\/" y) "\/" z = x "\/" (y "\/" z)
  proof
    assume
AA: x [= z & y [= z; then
A0: x "\/" z = z & y "\/" z = z by LATTICES:def 3;
    x "/\" z = x & y "/\" z = y by LATTICES:4,AA;
    hence thesis by A0,DefW33;
  end;
