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+Set Implicit Arguments.
+
+Definition pred_le A (P Q : A->Prop) :=
+ forall x, P x -> Q x.
+
+Lemma pred_le_refl : forall A (P:A->Prop),
+ pred_le P P.
+Proof. unfold pred_le. auto. Qed.
+
+Hint Resolve pred_le_refl.
+
+Lemma test :
+ forall (P1 P2:nat->Prop),
+ (forall Q, pred_le (fun a => P1 a /\ P2 a) Q -> True) ->
+ True.
+Proof. intros. eapply H. eauto. (* used to work *)
+ apply pred_le_refl. Qed.