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

Lemma lead_coefTP (k : tF -> fF) :
(forall x e, qf_eval e (k x) = qf_eval e (k (eval e x)%:T%T)) ->
forall (p : polyF) (e : seq F),
qf_eval e (lead_coefT p k) = qf_eval e (k (lead_coef (eval_poly e p))%:T%T).