
theorem Th42:
  for a, b being Ordinal, n being Nat st a in exp(omega,b)
  holds n *^ a in exp(omega,b)
proof
  let a, b be Ordinal, n be Nat;
  assume a in exp(omega,b);
  then for c be Ordinal st c in dom(n --> a) holds
    (n --> a).c in exp(omega,b) by FUNCOP_1:7;
  then Sum^(n --> a) in exp(omega,b) by Th41;
  hence thesis by Th26;
end;
