Proof using.
destruct h; auto.
Qed.

(* Specifications: *)
Lemma outputs_m_inr_nil_singleton :
forall h,
outputs_m [(h,inr [])] = [].
Lemma outputs_m_inr_primary_singleton :
forall h i l,
h = Primary ->
outputs_m [(h, inr [RequestResponse i l])] = [l].
Lemma inputs_1_singleton :
forall l i,
inputs_1 l = [i] ->
exists os,
l = [(i, os)].