proposition: Lemma sqrt_UP_correct : forall p x, valid_ub (sqrt_UP p x) = true /\ le_upper (Xsqrt (toX x)) (toX (sqrt_UP p x)).
proof: Proof. intros p x; split; [easy|]. unfold sqrt_UP. rewrite (@Fsqrt_correct radix). unfold toX. case FtoX; [easy|intro rx]. unfold Xsqrt, Xsqrt_nan, Xsqrt', Xsqrt_nan'. case is_negative_spec; [easy|intros _]. now apply Generic_fmt.round_UP_pt, FLX.FLX_exp_valid. Qed.
imports: Coq(ZArith Reals Psatz) Flocq(Zaux Raux) Xreal Basic Generic Generic_proof Sig