
theorem
  for a being non empty Ordinal, n being non zero Nat
  st omega -exponent last CantorNF a <> 0
  holds CantorNF(a +^ n) = CantorNF a ^ <% n %>
proof
  let a be non empty Ordinal, n be non zero Nat;
  assume omega -exponent last CantorNF a <> 0;
  then 0 c< omega -exponent last CantorNF a by XBOOLE_1:2, XBOOLE_0:def 8;
  then A1: 0 in omega -exponent last CantorNF a by ORDINAL1:11;
  thus CantorNF(a +^ n) = CantorNF(a +^ n*^1) by ORDINAL2:39
    .= CantorNF(a +^ (n*^exp(omega, 0 qua Ordinal))) by ORDINAL2:43
    .= CantorNF a ^ <% n*^exp(omega,0 qua Ordinal) %> by A1, Th73
    .= CantorNF a ^ <% n*^1 %> by ORDINAL2:43
    .= CantorNF a ^ <% n %> by ORDINAL2:39;
end;
