(* ------------------------------------- *)
(* TODO: move elsewhere?  ext_consist for the first two? *)

(* Specifications: *)
Lemma erased_constraint_erase :
forall G a b A, AnnPropWff G (Eq a b A) -> erased_tm (erase a) /\ erased_tm (erase b)
/\ erased_tm (erase A).
Lemma erased_context_erase :
forall G, AnnCtx G -> erased_context (erase_context G).
Lemma AnnGood_add_tm :
forall G x A,  x `notin` dom G -> AnnTyping G A a_Star -> AnnGood G (dom G) -> AnnGood (x ~ Tm A ++ G) (dom (x ~ Tm A ++ G)).