(* --------------------------------------- *)
(* Convenience lemmas for working with substitution. *)

Lemma AnnTyping_co_subst_nondep : forall L G D g A1 A2 A3 b B,
AnnDefEq G D g A1 A2 ->
(forall x, x `notin` L -> AnnTyping ([(x,Co (Eq A1 A2 A3))] ++ G) (open_tm_wrt_co b (g_Var_f x)) B) ->
AnnTyping G (open_tm_wrt_co b g) B.