Inductive Name := primary | backup.Inductive Name := primary | backup.Inductive Name := primary | backup.Definition Name_eq_dec : forall x y : Name, {x = y} + {x <> y}.Inductive Msg := inc | ack.Inductive Msg := inc | ack.Inductive Msg := inc | ack.Definition Msg_eq_dec : forall x y : Msg, {x = y} + {x <> y}.Inductive Input := request_inc.Inductive Input := request_inc.Definition Input_eq_dec : forall x y : Input, {x = y} + {x <> y}.Inductive Output := inc_executed.Inductive Output := inc_executed.Definition Output_eq_dec : forall x y : Output, {x = y} + {x <> y}.Definition Data := nat.Definition init_Data := 0.Definition Handler (S : Type) := GenHandler (Name * Msg) S Output unit.Definition PrimaryNetHandler (m : Msg) : Handler Data :=
  match m with
  | ack => write_output inc_executed
  | _ => nop
  end.Definition BackupInputHandler (i : Input) : Handler Data := nop.Definition NetHandler (me : Name) (m : Msg) : Handler Data :=
  match me with
  | primary => PrimaryNetHandler m
  | backup => BackupNetHandler m
  end.Definition InputHandler (me : Name) (i : Input) : Handler Data :=
  match me with
  | primary => PrimaryInputHandler i
  | backup => BackupInputHandler i
  end.Instance Counter_BaseParams : BaseParams :=
  {
    data := Data;
    input := Input;
    output := Output
  }.

Lemma all_Names_Nodes : forall n, In n Nodes.