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+Variable Ack : nat -> nat -> nat.
+
+Axiom Ack0 : forall m : nat, Ack 0 m = S m.
+Axiom Ack1 : forall n : nat, Ack (S n) 0 = Ack n 1.
+Axiom Ack2 : forall n m : nat, Ack (S n) (S m) = Ack n (Ack (S n) m).
+
+Hint Rewrite Ack0 Ack1 Ack2 : base0.
+
+Lemma ResAck0 : (Ack 2 2 = 7 -> False) -> False.
+Proof.
+  intros.
+  autorewrite with base0 in H using try (apply H; reflexivity).
+Qed.
+
+Lemma ResAck1 : forall H:(Ack 2 2 = 7 -> False), True -> False.
+Proof.
+  intros.
+  autorewrite with base0 in *.
+    apply H;reflexivity.
+Qed.
+
+(* Check autorewrite does not solve existing evars *)
+(* See discussion started by A. Chargueraud in Oct 2010 on coqdev *)
+
+Hint Rewrite <- plus_n_O : base1.
+Goal forall y, exists x, y+x = y.
+eexists. autorewrite with base1.
+Fail reflexivity.
+