Proof using.
intros.
rewrite inputs_m_app in *.
rewrite inputs_m_inr_singleton in *.
rewrite app_nil_r in *.
auto.
Qed.

(* Specifications: *)
Lemma inputs_m_primary_inl :
forall i l,
inputs_m ((Primary, inl (Request i)) :: l) = i :: inputs_m l.