Module L.
Include Coq.Lists.List.
Definition null {A : Type} (l : list A) : bool :=
match l with
| L.nil => true
| L.cons _ _ => false
end.
#[global] Hint Rewrite null_spec in_map_iff in_app_iff : simplication_hints.
#[global] Hint Rewrite in_remove_iff : simplication_hints.

Lemma last_cons {A : Type} (x0 : A) (x1 : A) (xs : list A)
: last (x0 :: xs) x1 = last xs x0.