(** Demo: We will need the next two properties later in the tutorial, so we show that even though there are many cases to consider, [default_simp] can find these proofs. *)

(* Specifications: *)
Lemma fv_nom_swap : forall z y n,
z `notin` fv_nom n ->
y `notin` fv_nom (swap y z n).
Lemma shuffle_swap : forall w y n z,
w <> z -> y <> z ->
(swap w y (swap y z n)) = (swap w z (swap w y n)).