Fixpoint jump (p:positive) (l:list A) {struct p} : list A :=
  match p with
  | xH => tl l
  | xO p => jump p (jump p l)
  | xI p  => jump p (jump p (tl l))
  end.Fixpoint nth (p:positive) (l:list A) {struct p} : A:=
  match p with
  | xH => hd default l
  | xO p => nth p (jump p l)
  | xI p => nth p (jump p (tl l))
  end.

Lemma jump_tl : forall j l, tl (jump j l) = jump j (tl l).