revert n; induction m; intros.
- destruct n. repeat redL. repeat redL.
- destruct n.
+ repeat redL.
+ transitivity (EqN (enc m) (enc n)). repeat redL. now rewrite IHm.
Qed.
(** *** Substitution *)
Definition Subst := rho (.\ "Subst", "s", "k", "u"; "s" (.\"n"; !EqN "n" "k" "u" (!Var "n"))
(.\"s1", "s2"; !App ("Subst" "s1" "k" "u") ("Subst" "s2" "k" "u"))
(.\"s1"; !Lam ("Subst" "s1" (!Succ "k") "u")) ).
Hint Unfold Subst : cbv.

Lemma Subst_correct s k u :
Subst (tenc s) (enc k) (tenc u) ≡ tenc (subst s k u).