Local Notation "'N'" := Int.modulus (at level 0).

Lemma addlength_aux2: forall len n, 0 <= len < Int.modulus -> Int.unsigned (Int.repr (n + len * 8)) < Int.unsigned (lo_part n) -> Int.unsigned (hi_part n) + (Int.unsigned (lo_part n) + (len * 8) mod Int.modulus - (Int.unsigned (lo_part n) + len * 8) mod Int.modulus) / Int.modulus = Int.unsigned (hi_part n) + 1.