Definition rcv_transI := @ReceiveTrans _ CohI _ msg_wfI _ r_step_cohI.(* The client has to provide instances of the following 
   two structures along with the proofs of Hs and Hr. *)

Structure SendInv := SI {
  st : send_trans coh;
  st_inv : S_inv st;
}.(* The client has to provide instances of the following 
   two structures along with the proofs of Hs and Hr. *)

Structure SendInv := SI {
  st : send_trans coh;
  st_inv : S_inv st;
}.(* The client has to provide instances of the following 
   two structures along with the proofs of Hs and Hr. *)

Structure SendInv := SI {
  st : send_trans coh;
  st_inv : S_inv st;
}.(* The client has to provide instances of the following 
   two structures along with the proofs of Hs and Hr. *)

Structure SendInv := SI {
  st : send_trans coh;
  st_inv : S_inv st;
}.Structure ReceiveInv := RI {
  rt : receive_trans coh;
  rt_inv : R_inv rt;
}.Structure ReceiveInv := RI {
  rt : receive_trans coh;
  rt_inv : R_inv rt;
}.Structure ReceiveInv := RI {
  rt : receive_trans coh;
  rt_inv : R_inv rt;
}.Structure ReceiveInv := RI {
  rt : receive_trans coh;
  rt_inv : R_inv rt;
}.Structure InductiveInv := II {
  sts : seq SendInv;
  rts : seq ReceiveInv;
  _ : map st sts = snd_trans p;
  _ : map rt rts = rcv_trans p
}.Structure InductiveInv := II {
  sts : seq SendInv;
  rts : seq ReceiveInv;
  _ : map st sts = snd_trans p;
  _ : map rt rts = rcv_trans p
}.Structure InductiveInv := II {
  sts : seq SendInv;
  rts : seq ReceiveInv;
  _ : map st sts = snd_trans p;
  _ : map rt rts = rcv_trans p
}.Structure InductiveInv := II {
  sts : seq SendInv;
  rts : seq ReceiveInv;
  _ : map st sts = snd_trans p;
  _ : map rt rts = rcv_trans p
}.(* Obtain new send/receive transitions *)
Definition stsI sts := map (fun stt =>
                          @snd_transI (st stt) (@st_inv stt)) sts.Definition rtsI rts := map (fun rtt =>
                          @rcv_transI (rt rtt) (@rt_inv rtt)) rts.

(* Specifications: *)
Lemma us : uniq (map (@t_snd _ _) (stsI (sts ii))).
Lemma ur : uniq (map (@t_rcv _ _) (rtsI (rts ii))).