proposition: Lemma poly_alg_initial : pf =1 horner_alg (pf 'X).
proof: Proof. apply: poly_ind => [|p a IHp]; first by rewrite !rmorph0. rewrite !rmorphD !rmorphM /= -{}IHp horner_algC ?horner_algX. by rewrite -alg_polyC rmorph_alg. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype bigop finset tuple) mathcomp(div ssralg countalg binomial)