(* Sqrt *)
(* Direct transcription of an old proof of a fortran program in boyer-moore *)

Lemma diveucl_21_spec_aux : forall a1 a2 b,
wB/2 <= φ b ->
φ a1 < φ b ->
let (q,r) := diveucl_21 a1 a2 b in
φ a1 *wB+ φ a2 = φ q * φ b + φ r /\
0 <= φ r < φ b.