
theorem
  for A being non empty Cantor-normal-form Ordinal-Sequence
  for b being Ordinal, n being non zero Nat
  st omega -exponent last A <> 0 holds A ^ <% n %> is Cantor-normal-form
proof
  let A be non empty Cantor-normal-form Ordinal-Sequence;
  let b be Ordinal, n be non zero Nat;
  assume omega -exponent last A <> 0;
  then 0 c< omega -exponent last A by XBOOLE_1:2, XBOOLE_0:def 8;
  then A1: 0 in omega -exponent last A by ORDINAL1:11;
  A ^ <% n*^exp(omega,0 qua Ordinal) %> = A ^ <% n*^1 %> by ORDINAL2:43
    .= A ^ <% n %> by ORDINAL2:39;
  hence thesis by A1, Th37;
end;
