Section prefix.
Variable A : Type.
Proof using.
intros. induction l; simpl in *; auto.
Qed.
Proof using.
intros. destruct l.
- reflexivity.
- contradiction.
Qed.
Proof using.
simpl. intuition.
Qed.

Lemma Prefix_in :
forall (l l' : list A),
Prefix l' l ->
forall x, In x l' -> In x l.