#[local]
Hint Resolve Pos.le_max_r Pos.le_max_l : core.
#[local]
Hint Constructors valid linear : core.
(* Compatibility of validity w.r.t algebraic operations *)

Lemma poly_add_valid_compat : forall kl kr pl pr, valid kl pl -> valid kr pr ->
valid (Pos.max kl kr) (poly_add pl pr).