Section BasicOperations.
Local Notation "{ k ~> u } t" := (open_rec k u t) (at level 67).
(** The first property we would like to show is the analogue to [subst_fresh]: index substitution has no effect for closed terms.  Here is an initial attempt at the proof. *)

Lemma open_rec_lc_0 : forall k u e,
lc e ->
e = {k ~> u} e.