(* ** BPCP reduces to iBPCP *)
Definition f (P : stack bool) (A : stack bool) := omap (fun x => pos card_eq x P) A.
Definition g (P : stack bool) (A : list nat) := map (fun n => nth n P ( [], [] )) A.

Lemma PCPb_iff_iPCPb P : PCPb P <-> iPCPb P.