proposition: Lemma nth_lift n p k : nth (lift n p) k = if k < n then 0%R else nth p (k - n).
proof: Proof. Proof (nth_ncons 0%R n 0%R p k). Lemma horner_polyC c x : horner tt (polyC c) x = c. Proof. rewrite !hornerE polyCE size_polyCons size_polyNil big_nat1 nth_polyCons. by rewrite pow_O Rmult_1_r. 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