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+Require Import Coq.Arith.Arith.
+
+Module A.
+
+ Fixpoint foo (n:nat) :=
+ match n with
+ | 0 => 0
+ | S n => bar n
+ end
+
+ with bar (n:nat) :=
+ match n with
+ | 0 => 0
+ | S n => foo n
+ end.
+
+ Lemma using_foo:
+ forall (n:nat), foo n = 0 /\ bar n = 0.
+ Proof.
+ induction n ; split ; auto ;
+ destruct IHn ; auto.
+ Qed.
+
+End A.
+
+
+Module B.
+
+ Module A := A.
+ Import A.
+
+End B.
+
+Module E.
+
+ Module B := B.
+ Import B.A.
+
+ (* Bug 1 *)
+ Lemma test_1:
+ forall (n:nat), foo n = 0.
+ Proof.
+ intros ; destruct n.
+ reflexivity.
+ specialize (A.using_foo (S n)) ; intros.
+ simpl in H.
+ simpl.
+ destruct H.
+ assumption.
+ Qed.
+
+End E. \ No newline at end of file