proposition: Lemma eval_Rgcd e p q k k' : (forall p, qf_eval e (k p) = k' (eval_poly e p)) -> qf_eval e (Rgcd p q k) = k' (rgcdp (eval_poly e p) (eval_poly e q)).
proof: Proof. move=> Pk; rewrite /Rgcd /LtSize !eval_Size /rgcdp. case: ltnP=> _; rewrite !eval_Isnull; case: eqP=> // _; by rewrite eval_Size; apply: eval_Rgcd_loop. Qed.
imports: mathcomp.ssreflect.ssreflect mathcomp(ssrfun ssrbool eqtype ssrnat seq choice fintype) mathcomp(finfun path matrix) mathcomp(bigop order ssralg poly polydiv ssrnum zmodp div ssrint) mathcomp(polyorder polyrcf interval polyXY) mathcomp(qe_rcf_th ordered_qelim mxtens)