theorem
  X is push-pop & not emp s1 & not emp s2 &
  pop s1 = pop s2 & top s1 = top s2 implies s1 = s2
  proof
    assume A1: X is push-pop;
    assume not emp s1; then
    s1 = push(top s1, pop s1) by A1;
    hence thesis by A1;
  end;
