theorem Th20:
  (push(e,s) in coset s1 implies s in coset s1) &
  (not emp s & pop s in coset s1 implies s in coset s1)
  proof
    pop push(e,s) = s & not emp push(e,s) by Def11,Def12;
    hence push(e,s) in coset s1 implies s in coset s1 by Def17;
    assume not emp s; then
    push(top s, pop s) = s by Def9;
    hence thesis by Def17;
  end;
