proposition: Lemma prev_noroot p a b : {in `](prev_root p a b), b[, noroot p}.
proof: Proof. move=> z; case: prev_rootP; first by rewrite itv_xx. by move=> y np0 py0 hy hp hz; rewrite (negPf (hp _ _)). move=> c np0 ->; case: leP=> hab; last by rewrite itv_xx. by move=> hp hz; rewrite (negPf (hp _ _)). 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)