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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.
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