+ Definition updateITE_ {Γ:TypeEnv}{TV:Kind->Type}{κ}{n}(tv:TV κ)(ite:InstantiatedTypeEnv TV Γ)
+ : InstantiatedTypeEnv TV (list_ins n κ Γ).
+ rewrite list_ins_app.
+ rewrite <- (list_take_drop _ Γ n) in ite.
+ apply ilist_app.
+ apply ilist_chop in ite; auto.
+ apply ICons.
+ apply tv.
+ apply ilist_chop' in ite.
+ apply ite.
+ Defined.
+