(* Take-home exercise:  Finally we can show that all of the relations only include locally-closed terms through very straightforward proofs. *)

(* Specifications: *)
Lemma value_to_lc : forall e,
value e -> lc e.
Lemma eval_to_lc : forall e1 e2,
eval e1 e2 -> lc e1 /\ lc e2.
Lemma typing_to_lc : forall E e T,
typing E e T -> lc e.