(* Substitution preserves regularity *)

(* Specifications: *)
Lemma lift_rec_preserve_regular :
forall U : redexes,
regular U -> forall n m : nat, regular (lift_rec_r U m n).
Lemma subst_rec_preserve_regular :
forall U V : redexes,
regular U -> regular V -> forall n : nat, regular (subst_rec_r U V n).
Lemma subst_preserve_regular :
forall U V : redexes, regular U -> regular V -> regular (subst_r U V).