proposition: Lemma derspr : sgr p.[a] = sp'c -> {in `[a, b], forall x, sgr p.[x] = sp'c}.
proof: Proof. move=> spa x hx; rewrite hsgp // (lt_le_trans _ (derqpr _)) //. by rewrite -sgr_cp0 hornerZ sgr_smul spa -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)