Definition lift (p : {poly F}) := map GRing.Const p.

(* Specifications: *)
Lemma eval_lift (e : seq F) (p : {poly F}) : eval_poly e (lift p) = p.
Lemma lead_coefT_qf (p : polyF) : rpoly p -> qf_cps (@rterm _) (lead_coefT p).
Lemma ramulXnT: forall a n, rterm a -> rpoly (amulXnT a n).
Lemma eval_sumpT (p q : polyF) (e : seq F) : eval_poly e (sumpT p q) = (eval_poly e p) + (eval_poly e q).
Lemma rsumpT (p q : polyF) : rpoly p -> rpoly q -> rpoly (sumpT p q).
Lemma eval_mulpT (p q : polyF) (e : seq F) : eval_poly e (mulpT p q) = (eval_poly e p) * (eval_poly e q).
Lemma rmulpT (p q : polyF) : rpoly p -> rpoly q -> rpoly (mulpT p q).