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

Lemma AnnTyping_tm_subst : forall G x A b B (H : AnnTyping ((x ~ Tm A) ++ G) b B),
forall a, AnnTyping G a A ->
AnnTyping G (tm_subst_tm_tm a x b) (tm_subst_tm_tm a x B).