theorem
  for B, Z, p, q st p in dom B & B.p = 1 & q in Z holds p^q in Z
proof
  let B, Z, p, q;
  assume that A1: p in dom B & B.p = 1 and A2: q in Z;
  A3: q in Z^^1 by A2;
  Z is B-closed;
  hence p^q in Z by A1, A3;
end;
