theorem
  x >><< z & z <== y implies x >><< y
  proof
    given u such that
A3: x =*=> u & u <=*= z;
    assume
A2: z <== y;
    take u;
    thus x =*=> u by A3;
    thus y =*=> u by A2,A3,Lem5;
  end;
