proposition: Lemma TM_div_mixed_r_correct_strong M (b : I.type) (x0 : R) (X : interval) f g : i_validTM x0 X M f -> is_const g X (I.convert b) -> i_validTM x0 X (TM_div_mixed_r M b) (fun x => Xdiv (f x) (g x)).
proof: Proof. move=> Hf [[|y] Hy1 Hy2]. - apply TM_div_mixed_r_nai with (2 := Hf). now apply contains_Xnan. - apply: (@TM_fun_eq (fun x => f x / Xreal y)%XR). by move=> x Hx /=; rewrite Hy2. exact: TM_div_mixed_r_correct. Qed.
imports: Coq(ZArith Psatz Reals) Flocq(Raux) Coquelicot(Coquelicot) mathcomp.ssreflect(ssreflect ssrfun ssrbool eqtype ssrnat seq fintype bigop) Stdlib MathComp Coquelicot Xreal Interval Basic Xreal_derive Interval_compl Datatypes Taylor_poly Basic_rec Bound