Local Open Scope logic.

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.