decide equality.
apply input_eq_dec.
Qed.
Inductive PB_input :=
| Request : input -> PB_input
| Read : PB_input.
Inductive PB_output :=
| RequestResponse : input -> output -> PB_output
| ReadResponse : data -> PB_output.
Record PB_data :=
{
queue : list input;
state : data
}.
Definition all_nodes : list name := [Primary; Backup].

Lemma all_nodes_all :
forall x,
In x all_nodes.