proposition: Theorem round_round_sqrt_FLT : forall choice1 choice2, (emin <= 0)%Z -> ((emin' <= emin - prec - 2)%Z \/ (2 * emin' <= emin - 4 * prec - 2)%Z) -> (2 * prec + 2 <= prec')%Z -> forall x, FLT_format beta emin prec x -> round_round_eq (FLT_exp emin prec) (FLT_exp emin' prec') choice1 choice2 (sqrt x).
proof: Proof. intros choice1 choice2 Hemin Heminprec Hprec x Fx. apply round_round_sqrt. - now apply FLT_exp_valid. - now apply FLT_exp_valid. - now apply FLT_round_round_sqrt_hyp. - now apply generic_format_FLT. Qed.
imports: Coq(ZArith Reals Psatz) Core FTZ