reserve
  a,b,c,d,e for Ordinal,
  m,n for Nat,
  f for Ordinal-Sequence,
  x for object;
reserve S,S1,S2 for Sequence;

theorem
  a |^|^ 3 = exp(a,exp(a, a))
  proof
    3 = succ 2;
    hence a |^|^ 3 = exp(a, a|^|^2) by Th14 .= exp(a,exp(a, a)) by Th18;
  end;
