End Double_round_sqrt_FLT.
Section Double_round_sqrt_FTZ.
Variable emin prec : Z.
Variable emin' prec' : Z.
Context { prec_gt_0_ : Prec_gt_0 prec }.
Context { prec_gt_0_' : Prec_gt_0 prec' }.

Lemma FTZ_double_round_sqrt_hyp :
(2 * (emin' + prec') <= emin + prec <= 1)%Z ->
(2 * prec + 2 <= prec')%Z ->
double_round_sqrt_hyp (FTZ_exp emin prec) (FTZ_exp emin' prec').