proposition: Lemma ders0r : p.[a] = 0 -> {in `]a, b], forall x, sgr p.[x] = sp'c}.
proof: Proof. move=> pa0 x hx; rewrite hsgp // (le_lt_trans _ (derq0r _)) //. by rewrite hornerZ pa0 mulr0. Qed.
imports: mathcomp.ssreflect.ssreflect mathcomp(ssrfun ssrbool eqtype ssrnat seq choice fintype) mathcomp(bigop order ssralg poly polydiv ssrnum zmodp) mathcomp(polyorder path interval ssrint)