Proof using.
intros P Q eP eQ s1 s2 e. destruct e; simpl. unfold or_tl. intuition.
- left; apply eP with (Cons x s1); [constructor; assumption | assumption].
- right; apply eQ with (Cons x s1); [constructor; assumption | assumption].
Qed.

Lemma extensional_impl_tl :
forall (P Q: infseq T -> Prop),
extensional P -> extensional Q -> extensional (P ->_ Q).