
theorem
  for a being non empty Ordinal, b being Ordinal, n being non zero Nat
  st omega -exponent((CantorNF a).0) in b
  holds CantorNF((n*^exp(omega, b)) +^ a) = <% n*^exp(omega,b) %> ^ CantorNF a
proof
  let a be non empty Ordinal, b be Ordinal, n be non zero Nat;
  assume omega -exponent((CantorNF a).0) in b;
  then A1: <% n*^exp(omega,b) %> ^ CantorNF a is Cantor-normal-form by Th39;
  set A = <% n*^exp(omega,b) %>, B = CantorNF a;
  Sum^(A^B) = (n*^exp(omega, b)) +^ Sum^ B by ORDINAL5:55
    .= (n*^exp(omega, b)) +^ a;
  hence thesis by A1;
end;
