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

Axiom invert_a_Fam : forall G F A,
Typing G (a_Fam F) A ->
exists a B, DefEq G (dom G) A B a_Star /\
binds F (Ax a B) toplevel /\ Typing nil B a_Star.