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(** ** Local closure and relations                                       *)
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(** All of our semantics only hold for locally closed terms, and we can prove that.  Sometimes, the proofs are straightforward; sometimes a little work is needed. *)

(* Specifications: *)
Lemma step_lc_exp1 : forall e1 e2, step e1 e2 -> lc_exp e1.
(* /ADMITTED *)
(** *** Exercise [step_lc_exp2]  Use properties such as [subst_exp_intro] and [subst_exp_lc_exp] to show that the result of a step is _also_ locally closed. *)
Lemma step_lc_exp2 : forall e1 e2, step e1 e2 -> lc_exp e2.