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

Axiom invert_a_Pi: forall G rho A0 A B0,
Typing G (a_Pi rho A0 B0) A ->
DefEq G (dom G) A a_Star a_Star /\ (exists L, forall x, x `notin` L -> Typing ([(x, Tm A0)] ++ G) (open_tm_wrt_tm B0 (a_Var_f x)) a_Star) /\ Typing G A0 a_Star.