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+Set Universe Polymorphism.
+Inductive paths {A : Type} (a : A) : A -> Type := idpath : paths a a where "x = y" := (@paths _ x y) : type_scope.
+Class Contr_internal (A : Type) := BuildContr { center : A ; contr : (forall y : A, center = y) }.
+Inductive trunc_index : Type := minus_two | trunc_S (x : trunc_index).
+Bind Scope trunc_scope with trunc_index.
+Fixpoint IsTrunc_internal (n : trunc_index) (A : Type) : Type :=
+  match n with
+    | minus_two => Contr_internal A
+    | trunc_S n' => forall (x y : A), IsTrunc_internal n' (x = y)
+  end.
+Notation minus_one:=(trunc_S minus_two).
+Notation "0" := (trunc_S minus_one) : trunc_scope.
+Class IsTrunc (n : trunc_index) (A : Type) : Type := Trunc_is_trunc : IsTrunc_internal n A.
+Notation IsHProp := (IsTrunc minus_one).
+Notation IsHSet := (IsTrunc 0).
+Goal forall (A : Type) (a b : A) (H' : IsHSet A), { x : Type & IsHProp x }.
+Proof.
+intros.
+eexists.
+(* exact (H' a b). *)
+(* Undo. *)
+Fail apply (H' a b).
+exact (H' a b).
+Qed.