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

Axiom invert_a_App_Irrel : forall G a b C,
Typing G (a_App a Irrel b) C ->
exists A B b0, Typing G a (a_Pi Irrel A B) /\
Typing G b0 A /\
DefEq G (dom G) C (open_tm_wrt_tm B b0) a_Star.