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

Lemma Prefix_cons :
forall (l l' : list A) a,
Prefix l' l ->
Prefix (a :: l') (a :: l).