proposition: Lemma map_correct fi f pi p : (f 0%R = 0%R) -> (forall xi x, xi >: x -> fi xi >: f x) -> pi >:: p -> map fi pi >:: PolR.map f p.
proof: Proof. move=> H0 Hf Hp k; rewrite /map /PolR.map /nth /PolR.nth. apply (@map_correct R I.type) =>//. - exact: J.zero_correct. - by move=> ? /J.contains_only_0 ->; rewrite H0; apply: J.zero_correct. - by move=> *; rewrite -(H0); apply: Hf. - move=> *; exact: Hf. Qed.
imports: Coq(ZArith Reals) Coquelicot(Coquelicot) mathcomp.ssreflect(ssreflect ssrfun ssrbool eqtype ssrnat seq fintype bigop) Flocq(Core) Stdlib MathComp Interval Xreal Basic_rec