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+
+(* First a simplification of the bug *)
+
+Set Printing Universes.
+
+Inductive enc (A:Type (*1*)) (* : Type.1 *) := C : A -> enc A.
+
+Definition id (X:Type(*5*)) (x:X) := x.
+
+Lemma test : let S := Type(*6 : 7*) in enc S -> S.
+simpl; intros.
+apply enc.
+apply id.
+apply Prop.
+Defined.
+
+(* Then the original bug *)
+
+Require Import List.
+
+Inductive a : Set := (* some dummy inductive *)
+b : (list a) -> a.   (* i don't know if this *)
+                     (* happens for smaller  *)
+                     (* ones                 *)
+
+Inductive sg : Type := Sg. (* single *)
+
+Definition ipl2 (P : a -> Type) :=   (* in Prop, that means P is true forall *)
+fold_right (fun x => prod (P x)) sg. (* the elements of a given list         *)
+
+Definition ind
+     : forall S : a -> Type,
+       (forall ls : list a, ipl2 S ls -> S (b ls)) -> forall s : a, S s :=
+fun (S : a -> Type)
+  (X : forall ls : list a, ipl2 S ls -> S (b ls)) =>
+fix ind2 (s : a) :=
+match s as a return (S a) with
+| b l =>
+    X l
+      (list_rect (fun l0 : list a => ipl2 S l0) Sg
+         (fun (a0 : a) (l0 : list a) (IHl : ipl2 S l0) =>
+          pair (ind2 a0) IHl) l)
+end. (* some induction principle *)
+
+Implicit Arguments ind [S].
+
+Lemma k : a -> Type. (* some ininteresting lemma *)
+intro;pattern H;apply ind;intros.
+  assert (K : Type).
+    induction ls.
+      exact sg.
+      exact sg.
+  exact (prod K sg).
+Defined.
+
+Lemma k' : a -> Type. (* same lemma but with our bug *)
+intro;pattern H;apply ind;intros.
+  apply prod.
+    induction ls.
+      exact sg.
+      exact sg.
+    exact sg. (* Proof complete *)
+Defined. (* bug *)