theorem
  for B, Z, p, q, r st p in dom B & B.p = 2 & q in Z & r in Z
    holds p^(q^r) in Z
proof
  let B, Z, p, q, r;
  assume that A1: p in dom B & B.p = 2 and A2: q in Z & r in Z;
  Z^^2 = Z^^(1+1) .= (Z^^1)^Z by POLNOT_1:6 .= Z^Z;
  then A3: q^r in Z^^2 by A2, POLNOT_1:def 2;
  Z is B-closed;
  hence p^(q^r) in Z by A1, A3;
end;
