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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.
Abort.
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