proposition: Lemma derspl : sgr p.[b] = -sp'c -> {in `[a, b], forall x, sgr p.[x] = -sp'c}.
proof: Proof. move=> spb x hx; rewrite hsgpN // (le_lt_trans (derqnl _)) //. by rewrite -sgr_cp0 hornerZ sgr_smul spb mulrN -expr2 sqr_sg derp_neq0. 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)