(* --------------------------------------------------------------------- *)
(* 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_CPi_inversion :
∀ (G:context) (phi : constraint) (B T : tm),
AnnTyping G (a_CPi phi B) T ->
T = a_Star /\
AnnPropWff G phi /\
∀ c, c \notin dom G
-> AnnTyping ([(c, Co phi)] ++ G) (open_tm_wrt_co B (g_Var_f c)) a_Star.