proposition: Lemma coprimepP (p q : {poly F}): reflect (forall x, root p x -> q.[x] != 0) (coprimep p q).
proof: Proof. by apply: (iffP idP)=> [/coprimep_root|/root_coprimep]. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(fintype bigop ssralg poly)