
theorem Th88:
  for a being Ordinal, n being Nat holds a (+) n = a +^ n
proof
  let a be Ordinal, n be Nat;
  A1: 0 c= omega -exponent last CantorNF a;
  thus a (+) n = a (+) (n*^1) by ORDINAL2:39
    .= a (+) (n*^exp(omega,0 qua Ordinal)) by ORDINAL2:43
    .= a +^ (n*^exp(omega,0 qua Ordinal)) by A1, Th86
    .= a +^ (n*^1) by ORDINAL2:43
    .= a +^ n by ORDINAL2:39;
end;
