proposition: Lemma gtr_hornerW : {in `[a, b] &, {homo horner p : x y /~ x < y}}.
proof: Proof. by move=> x y axb ayb yx; rewrite -ltr_opp2 -!hornerN (ltr_hornerW dern_pos). 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)