proposition: Lemma size_TM_any (c X : I.type) n : Pol.size (approx (TM_any c X n)) = n.+1.
proof: Proof. rewrite /TM_any /=. case: n =>[|n] /=. by rewrite !sizes. by rewrite Pol.size_set_nth !sizes maxnSS maxn0. 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