Instance Counter_MultiParams : MultiParams Counter_BaseParams :=
  {
    name := Name;
    name_eq_dec := Name_eq_dec;
    msg := Msg;
    msg_eq_dec := Msg_eq_dec;
    nodes := Nodes;
    all_names_nodes := all_Names_Nodes;
    no_dup_nodes := NoDup_Nodes;
    init_handlers := fun _ => init_Data;
    net_handlers := fun dst src msg s =>
                      runGenHandler_ignore s (NetHandler dst msg);
    input_handlers := fun nm i s =>
                      runGenHandler_ignore s (InputHandler nm i)
  }.

Lemma input_handlers_InputHandlers : forall h i d os d' ms, input_handlers h i d = (os, d', ms) -> InputHandler h i d = (tt, os, d', ms).