Proof using.
intros.
find_apply_lem_hyp refl_trans_1n_n1_trace.
invc H.
- destruct tr; discriminate.
- invc H4. exists x'.
find_apply_lem_hyp app_inj_tail.
intuition. subst.
+ apply refl_trans_n1_1n_trace. auto.
+ subst. constructor. auto.
Qed.

Lemma outputs_m_read_response_singleton  :
forall h o,
outputs_m [(h, inr [ReadResponse o])] = [].