proposition: Theorem approximates_ext f g xi t : (forall x, f x = g x) -> approximates xi t f -> approximates xi t g.
proof: Proof. move=> Hfg Hmain. case: t Hmain =>[c| |tm] Hmain Hne. destruct Hmain as [H|Hmain] =>//. now left. right. exact: is_const_ext_weak Hmain. by move=> *; rewrite -Hfg; apply: Hmain. move/(_ Hne): Hmain. exact: TM_fun_eq. Qed.
imports: Coq(Reals ZArith Psatz) mathcomp.ssreflect(ssreflect ssrbool ssrfun eqtype ssrnat seq bigop) Interval Xreal Basic Interval_compl Datatypes Taylor_model_sharp Bound Bound_quad Univariate_sig