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+Set Universe Polymorphism.
+Set Inductive Cumulativity.
+Set Printing Universes.
+
+Inductive List (A: Type) := nil | cons : A -> List A -> List A.
+
+Section ListLift.
+  Universe i j.
+
+  Constraint i < j.
+
+  Definition LiftL {A} : List@{i} A -> List@{j} A := fun x => x.
+
+End ListLift.
+
+Lemma LiftL_Lem A (l : List A) : l = LiftL l.
+Proof. reflexivity. Qed.
+
+Section ListLower.
+  Universe i j.
+
+  Constraint i < j.
+
+  Definition LowerL {A : Type@{i}} : List@{j} A -> List@{i} A := fun x => x.
+
+End ListLower.
+
+Lemma LowerL_Lem@{i j} (A : Type@{j}) (l : List@{i} A) : l = LowerL l.
+Proof. reflexivity. Qed.
+
+Inductive Tp := tp : Type -> Tp.
+
+Section TpLift.
+  Universe i j.
+
+  Constraint i < j.
+
+  Definition LiftTp : Tp@{i} -> Tp@{j} := fun x => x.
+
+End TpLift.
+
+Lemma LiftC_Lem (t : Tp) : LiftTp t = t.
+Proof. reflexivity. Qed.
+
+Section TpLower.
+  Universe i j.
+
+  Constraint i < j.
+
+  Fail Definition LowerTp : Tp@{j} -> Tp@{i} := fun x => x.
+
+End TpLower.
+
+
+Section subtyping_test.
+  Universe i j.
+  Constraint i < j.
+
+  Inductive TP2 := tp2 : Type@{i} -> Type@{j} -> TP2.
+
+End subtyping_test.
+\ No newline at end of file