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+Require Import ProofIrrelevance.
+
+Lemma proof_irrelevance_set : forall (P : Set) (p1 p2 : P), p1 = p2.
+ exact proof_irrelevance.
+Qed.
+
+Lemma paradox : False.
+ assert (H : 0 <> 1) by discriminate.
+ apply H.
+ Fail apply proof_irrelevance. (* inlined version is rejected *)
+ apply proof_irrelevance_set.
+Qed.