(* ---------------------------------------------- *)

Lemma An_CAbs_exists2
: ∀ (c : atom) (G : context) (phi : constraint) (a B : tm),
c `notin` union (dom G) (union (fv_co_co_tm a) (fv_co_co_tm B))
→ AnnTyping ([(c, Co phi)] ++ G) (open_tm_wrt_co a (g_Var_f c)) (open_tm_wrt_co B (g_Var_f c))
→ AnnTyping G (a_CAbs phi a) (a_CPi phi B).