Ltac jump_simpl :=
  repeat
    match goal with
      | |- context [jump xH] => rewrite (jump_simpl xH)
      | |- context [jump (xO ?p)] => rewrite (jump_simpl (xO p))
      | |- context [jump (xI ?p)] => rewrite (jump_simpl (xI p))
    end.

Lemma nth_jump p l : nth p (tail l) = hd (jump p l).