#[local]
Hint Extern 5 => change 0 with (min 0 0) : core.
Local Hint Resolve poly_add_valid_compat poly_mul_valid_compat : core.
Local Hint Constructors valid : core.
#[local]
Hint Extern 5 => lia : core.
(* Compatibility with validity *)

(* Specifications: *)
Lemma poly_of_formula_valid_compat : forall f, exists n, valid n (poly_of_formula f).
(* The soundness lemma ; alas not complete! *)
Lemma poly_of_formula_sound : forall fl fr var,
poly_of_formula fl = poly_of_formula fr -> formula_eval var fl = formula_eval var fr.