(* -----  inversion lemmas for some typing judgments (with maximal co-finite quantification) ----------- *)

Axiom 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.