Definition addcarryc_def x y :=
let r := addcarry x y in
if leb r x then C1 r else C0 r.

Axiom diveucl_21_spec : forall a1 a2 b,
let (q,r) := diveucl_21 a1 a2 b in
let (q',r') := Z.div_eucl (to_Z a1 * wB + to_Z a2) (to_Z b) in
to_Z a1 < to_Z b -> to_Z q = q' /\ to_Z r = r'.