(* --------------------------------------------------------------------- *)
(* This is the place for "smart constructors" and "smart inversion" lemmas. They are especialy useful for constructing derivations from a particular variable and avoiding the co-finite quantification stuff.  *)
(* In a locally nameless development, these should be stated and immediately proven after substitution. *)

Lemma An_CAbs_inversion : ∀ (G : context) (phi : constraint) (a A : tm),
AnnTyping G (a_CAbs phi a) A
-> exists B, A = (a_CPi phi B) /\
forall c, c  `notin` dom G
->   AnnPropWff G phi /\
AnnTyping ([(c, Co phi)] ++ G) (open_tm_wrt_co a (g_Var_f c))
(open_tm_wrt_co B (g_Var_f c)).