(* Lemma co_subst_fresh : forall G phi a0 x s, AnnPropWff G phi -> AnnCtx ((x ~ s) ++ G) -> tm_subst_tm_constraint a0 x phi = phi. *)

(* Specifications: *)
Lemma co_subst_fresh_1 :
forall G a A g c s,
AnnTyping G a A -> AnnCtx ((c ~ s) ++ G) -> co_subst_co_tm g c A = A.
Lemma co_subst_fresh_2 :
forall G a A g c s,
AnnTyping G a A -> AnnCtx ((c ~ s) ++ G) -> co_subst_co_tm g c a = a.