#[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_mul_mon_valid_compat : forall k i p,
valid k p -> valid (Pos.max (Pos.succ i) k) (poly_mul_mon i p).