proposition: Fact derq_pos x : x \in `]a, b[ -> (q^`()).[x] > 0.
proof: Proof. move=> hx; rewrite derivZ hornerZ -sgr_cp0 sgr_smul mulr_sg_eq1 derp_neq0 //. exact/eqP/(@polyrN0_itv `]a, b[). 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)