Module Type ext_invert_sig.
Include ext_subst_sig.
(* ---------- inversion lemmas ---------------- *)

Axiom invert_a_CApp : forall G a g A,
Typing G (a_CApp a g) A ->
g = g_Triv /\
exists a1 b1 A1 B, Typing G a (a_CPi (Eq a1 b1 A1) B) /\
DefEq G (dom G) a1 b1 A1 /\
DefEq G (dom G) A (open_tm_wrt_co B g_Triv) a_Star.