(* Build a polynomial from an infinite sequence of coefficients and a bound. *)
Fact poly_key : unit. Proof. by []. Qed.
Definition poly := locked_with poly_key poly_expanded_def.
Canonical poly_unlockable := [unlockable fun poly].
Local Notation "\poly_ ( i < n ) E" := (poly n (fun i : nat => E)).

Lemma polyseq_poly n E :
E n.-1 != 0 -> \poly_(i < n) E i = mkseq [eta E] n :> seq R.