proposition: Lemma poly_ivt (p : {poly R}) (a b : R) : a <= b -> 0 \in `[p.[a], p.[b]] -> { x : R | x \in `[a, b] & root p x }.
proof: Proof. by move=> leab root_p_ab; apply/sig2W/poly_ivt. 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)