Section list_util.
Variables A B C : Type.
Hypothesis A_eq_dec : forall x y : A, {x = y} + {x <> y}.
Proof using.
intros l x H.
symmetry in H.
induction l;
now inversion H.
Qed.

Lemma remove_preserve :
forall (x y : A) xs,
x <> y ->
In y xs ->
In y (remove A_eq_dec x xs).