proposition: Lemma roots_on_comp p a b s : roots_on (p \Po (-'X)) `](-b), (-a)[ (map (-%R) s) <-> roots_on p `]a, b[ s.
proof: Proof. split=> /= hs x; rewrite ?root_comp ?hornerE. move: (hs (- x)); rewrite (mem_map oppr_inj). by rewrite root_comp ?hornerE oppr_itv !opprK. by rewrite -[x]opprK oppr_itv /= (mem_map oppr_inj) -(hs (- x)) !opprK. 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)