theorem Th11:
  for P, p, q, m, n st p in P^^m & q in P^^n holds p^q in P^^(m+n)
proof
  let P, p, q, m, n;
  assume p in P^^m & q in P^^n;
  then p^q in (P^^m)^(P^^n) by Def2;
  hence thesis by Th10;
end;
