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

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