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

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