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+(* Check that "dependent inversion" behaves correctly w.r.t to universes *)
+
+Require Import Eqdep.
+
+Set Implicit Arguments.
+
+Inductive illist(A:Type) : nat -> Type :=
+  illistn : illist A 0
+| illistc : forall n:nat, A -> illist A n -> illist A (S n).
+
+Inductive isig (A:Type)(P:A -> Type) : Type :=
+  iexists : forall x : A, P x -> isig P.
+
+Lemma inv : forall (A:Type)(n n':nat)(ts':illist A n'), n' = S n ->
+  isig (fun t => isig (fun ts =>
+    eq_dep nat (fun n => illist A n) n' ts' (S n) (illistc t ts))).
+Proof.
+intros.
+dependent inversion ts'.