Definition Nadd n p :=
  match n with
  | N0 => p
  | Npos p0 => (p0+p)%positive
  end.

Lemma of_lu_double_gen d : of_lu (Little.double d) = N.double (of_lu d) /\ of_lu (Little.succ_double d) = N.succ_double (of_lu d).