(** In an addition, there will be no carries iff there is no common bits in the numbers to add *)

(* Specifications: *)
Lemma nocarry_equiv : forall a b c,
c/2 == lnextcarry a b c -> c.[0] = false ->
(c == 0 <-> land a b == 0).
Lemma nocarry_equiv : forall a b c,
c/2 == lnextcarry a b c -> c.[0] = false ->
(c == 0 <-> land a b == 0).