 reserve a,b for object;
 reserve k,l,m,n for Nat;
 reserve p,q,r,s for FinSequence;
 reserve P for non empty FinSequence-membered set;
 reserve S,T for Polish-language;
 reserve V for Polish-language of T;
 reserve K for non trivial Polish-language;
 reserve E for Polish-arity-function of K;
 reserve B for Polish-arity-function;
 reserve A for Polish-arity-function of T;
 reserve C for Extension of B;
 reserve Z for B-closed Polish-language;

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;
