proposition: Lemma set_nth_correct pi p n ai a : pi >:: p -> ai >: a -> set_nth pi n ai >:: PolR.set_nth p n a.
proof: Proof. move=> Hp Ha k; rewrite /nth /PolR.nth. exact: (MathComp.set_nth_correct (Rel := fun v t => t >: v)). 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