(* Assemble a new send-transition for the rich coherence *)
Definition snd_transI := SendTrans s_safe_cohI s_safe_inI s_safe_defI s_step_cohI.Definition receive_stepI: receive_step_t CohI :=
  fun this from m d C pf => receive_step rt from m (proj1 C) pf.Notation msg_wfI := (fun d (C : CohI d) => msg_wf rt (proj1 C)).

Lemma r_step_cohI : r_step_coh_t msg_wfI (t_rcv rt) receive_stepI.