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

Lemma sqrt2_spec : forall x y,
wB/ 4 <= φ x ->
let (s,r) := sqrt2 x y in
Φ (WW x y) = φ s ^ 2 + [+|r|] /\
[+|r|] <= 2 * φ s.