Section Double_round_sqrt.
Definition double_round_sqrt_hyp fexp1 fexp2 :=
(forall ex, (2 * fexp1 ex <= fexp1 (2 * ex))%Z)
/\ (forall ex, (2 * fexp1 ex <= fexp1 (2 * ex - 1))%Z)
/\ (forall ex, (fexp1 (2 * ex) < 2 * ex)%Z ->
(fexp2 ex + ex <= 2 * fexp1 ex - 2)%Z).

Lemma double_round_sqrt :
forall fexp1 fexp2 : Z -> Z,
Valid_exp fexp1 -> Valid_exp fexp2 ->
forall (choice1 choice2 : Z -> bool),
double_round_sqrt_hyp fexp1 fexp2 ->
forall x,
generic_format beta fexp1 x ->
double_round_eq fexp1 fexp2 choice1 choice2 (sqrt x).