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+Fail Check Prop : Prop. (* Prop:Prop
+ : Prop *)
+Fail Check Set : Prop. (* Set:Prop
+ : Prop *)
+Fail Check ((bool -> Prop) : Prop). (* bool -> Prop:Prop
+ : Prop *)
+Axiom proof_irrelevance : forall (P : Prop) (p1 p2 : P), p1 = p2.
+Check ((True : Prop) : Set). (* (True:Prop):Set
+ : Set *)
+Goal (forall (v : Type) (f1 f0 : v -> Prop),
+ @eq (v -> Prop) f0 f1).
+intros.
+Fail apply proof_irrelevance.
+admit.
+Defined. (* Unnamed_thm is defined *)
+Set Printing Universes.
+Check ((True : Prop) : Set). (* Toplevel input, characters 0-28:
+Error: Universe inconsistency (cannot enforce Prop <= Set because Set
+< Prop). *)