(** * Functions P, P', Y and I as defined by Bellantoni and Cook

  - arities of P: (1, 1)

  - arities of P': (2, 0)

  - arities of Y: (2, 1)

  - arities of I: (2, 1)
*)

Definition P (x:bs)(y:bs) : bs := skipn (length x) y.

Lemma P_nil : forall x, P x nil = nil.