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.

Lemma in_remove_iff (A : Type) `(EQ_DEC : hasEqDec A) (x1 : A) (xs2 : list A)
: forall z, In z (remove Prelude.eq_dec x1 xs2) <-> (In z xs2 /\ z <> x1).