Definition send_stepI: send_step_t (send_safeI) :=
  fun this to d msg S => (@send_step _ _ st this to d msg (proj1 S)).

(* Specifications: *)
Lemma s_safe_defI this to d msg : send_safeI this to d msg <-> exists b pf, @send_stepI this to d msg pf = Some b.
Lemma s_step_cohI : s_step_coh_t CohI (t_snd st) send_stepI.