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+Axiom P : nat -> Prop.
+Axiom admit : forall n : nat, P n -> P n -> n = S n.
+Axiom foo : forall n, P n.
+
+Create HintDb bar.
+Hint Extern 3 => symmetry : bar.
+Hint Resolve admit : bar.
+Hint Immediate foo : bar.
+
+Lemma qux : forall n : nat, n = S n.
+Proof.
+intros n.
+eauto with bar.
+Defined.
+
+Goal True.
+pose (e := eq_refl (qux 0)); unfold qux in e.
+match type of e with context [eq_sym] => fail 1 | _ => idtac end.