Class BaseParamsPartialMap (P0 : BaseParams) (P1 : BaseParams) := 
  {
    pt_map_data : @data P0 -> @data P1 ;
    pt_map_input : @input P0 -> option (@input P1) ;
    pt_map_output : @output P0 -> option (@output P1)
  }.Class BaseParamsPartialMap (P0 : BaseParams) (P1 : BaseParams) := 
  {
    pt_map_data : @data P0 -> @data P1 ;
    pt_map_input : @input P0 -> option (@input P1) ;
    pt_map_output : @output P0 -> option (@output P1)
  }.Class BaseParamsPartialMap (P0 : BaseParams) (P1 : BaseParams) := 
  {
    pt_map_data : @data P0 -> @data P1 ;
    pt_map_input : @input P0 -> option (@input P1) ;
    pt_map_output : @output P0 -> option (@output P1)
  }.Class BaseParamsPartialMap (P0 : BaseParams) (P1 : BaseParams) := 
  {
    pt_map_data : @data P0 -> @data P1 ;
    pt_map_input : @input P0 -> option (@input P1) ;
    pt_map_output : @output P0 -> option (@output P1)
  }.Class MultiParamsMsgPartialMap
 (B0 : BaseParams) (B1 : BaseParams)
 (P0 : MultiParams B0) (P1 : MultiParams B1) :=
  {
    pt_map_msg : @msg B0 P0 -> option (@msg B1 P1)
  }.Class MultiParamsMsgPartialMap
 (B0 : BaseParams) (B1 : BaseParams)
 (P0 : MultiParams B0) (P1 : MultiParams B1) :=
  {
    pt_map_msg : @msg B0 P0 -> option (@msg B1 P1)
  }.Definition pt_map_name_msg nm :=
  match pt_map_msg (snd nm) with
  | Some m => Some (tot_map_name (fst nm), m)
  | None => None
  end.Definition pt_mapped_net_handlers me src m st :=
  let '(out, st', ps) := net_handlers me src m st in
  (filterMap pt_map_output out, pt_map_data st', filterMap pt_map_name_msg ps).Definition pt_mapped_input_handlers me inp st :=
  let '(out, st', ps) := input_handlers me inp st in
  (filterMap pt_map_output out, pt_map_data st', filterMap pt_map_name_msg ps).Class FailureParamsPartialMapCongruency
  (B0 : BaseParams) (B1 : BaseParams)
  (P0 : MultiParams B0) (P1 : MultiParams B1)
  (F0 : FailureParams P0) (F1 : FailureParams P1)
  (B : BaseParamsPartialMap B0 B1) : Prop :=
  {
    pt_reboot_eq : forall d, pt_map_data (reboot d) = reboot (pt_map_data d)
  }.Class FailureParamsPartialMapCongruency
  (B0 : BaseParams) (B1 : BaseParams)
  (P0 : MultiParams B0) (P1 : MultiParams B1)
  (F0 : FailureParams P0) (F1 : FailureParams P1)
  (B : BaseParamsPartialMap B0 B1) : Prop :=
  {
    pt_reboot_eq : forall d, pt_map_data (reboot d) = reboot (pt_map_data d)
  }.Class FailMsgParamsPartialMapCongruency 
  (B0 : BaseParams) (B1 : BaseParams)
  (P0 : MultiParams B0) (P1 : MultiParams B1)
  (F0 : FailMsgParams P0) (F1 : FailMsgParams P1)
  (P : MultiParamsMsgPartialMap P0 P1) : Prop :=
  {
    pt_fail_msg_fst_snd : pt_map_msg msg_fail = Some msg_fail
  }.Class FailMsgParamsPartialMapCongruency 
  (B0 : BaseParams) (B1 : BaseParams)
  (P0 : MultiParams B0) (P1 : MultiParams B1)
  (F0 : FailMsgParams P0) (F1 : FailMsgParams P1)
  (P : MultiParamsMsgPartialMap P0 P1) : Prop :=
  {
    pt_fail_msg_fst_snd : pt_map_msg msg_fail = Some msg_fail
  }.Class NewMsgParamsPartialMapCongruency
  (B0 : BaseParams) (B1 : BaseParams)
  (P0 : MultiParams B0) (P1 : MultiParams B1)
  (N0 : NewMsgParams P0) (N1 : NewMsgParams P1)
  (P : MultiParamsMsgPartialMap P0 P1) : Prop :=
  {
    pt_new_msg_fst_snd : pt_map_msg msg_new = Some msg_new
  }.Class NewMsgParamsPartialMapCongruency
  (B0 : BaseParams) (B1 : BaseParams)
  (P0 : MultiParams B0) (P1 : MultiParams B1)
  (N0 : NewMsgParams P0) (N1 : NewMsgParams P1)
  (P : MultiParamsMsgPartialMap P0 P1) : Prop :=
  {
    pt_new_msg_fst_snd : pt_map_msg msg_new = Some msg_new
  }.Definition pt_map_trace_occ (e : @name _ multi_fst * (@input base_fst + list (@output base_fst))) :
 option (@name _ multi_snd * (@input base_snd + list (@output base_snd))) :=
match e with
| (n, inl io) => 
  match pt_map_input io with
  | Some io' => Some (tot_map_name n, inl io')
  | None => None
  end
| (n, inr out) => Some (tot_map_name n, inr (filterMap pt_map_output out))
end.Definition pt_map_packet (p : @packet _ multi_fst)  :=
match p with
| mkPacket src dst m =>
  match pt_map_msg m with
  | Some m' => Some (mkPacket (tot_map_name src) (tot_map_name dst) m')
  | None => None
  end
end.Definition pt_map_net (net : @network _ multi_fst) : @network _ multi_snd :=
  {| nwPackets := filterMap pt_map_packet net.(nwPackets) ;
     nwState := fun n => pt_map_data (net.(nwState) (tot_map_name_inv n)) |}.

Lemma pt_map_update_eq_some : forall net d p p', pt_map_packet p = Some p' -> (fun n : name => pt_map_data (update name_eq_dec (nwState net) (pDst p) d (tot_map_name_inv n))) = update name_eq_dec (fun n : name => pt_map_data (nwState net (tot_map_name_inv n))) (pDst p') (pt_map_data d).