Lemma not_true_eq_false : forall (b:bool), b <> true -> b = false. Proof. destruct b;intros;trivial. elim H. exact (refl_equal true). Qed. Section BUG. Variable b : bool. Hypothesis H : b <> true. Hypothesis H0 : b = true. Hypothesis H1 : b <> true. Goal False. rewrite (not_true_eq_false _ H) in * |-. contradiction. Qed. End BUG.