 reserve L for non empty LattStr;
 reserve v100,v102,v2,v1,v0,v3,v101 for Element of L;
 reserve L for WA_Lattice;
 reserve x,y,z,u for Element of L;

theorem
  z [= x & z [= y implies (x "/\" y) "/\" z = x "/\" (y "/\" z)
  proof
    assume
AA: z [= x & z [= y; then
A0: z "\/" x = x & z "\/" y = y by LATTICES:def 3;
    z "/\" x = z & z "/\" y = z by LATTICES:4,AA;
    hence thesis by A0,DefW3;
  end;
