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+Set Printing Universes.
+
+Module unidecls.
+  Universes a b.
+End unidecls.
+
+Universe a.
+
+Constraint a < unidecls.a.
+
+Print Universes.
+
+(** These are different universes *)
+Check Type@{a}.
+Check Type@{unidecls.a}.
+
+Check Type@{unidecls.b}.
+
+Fail Check Type@{unidecls.c}.
+
+Fail Check Type@{i}.
+Universe foo.
+Module Foo.
+  (** Already declared globaly: but universe names are scoped at the module level  *)
+  Universe foo.
+  Universe bar.
+
+  Check Type@{Foo.foo}.
+  Definition bar := 0.
+End Foo.
+
+(** Already declared in the module *)
+Universe bar.
+
+(** Accessible outside the module: universe declarations are global *)
+Check Type@{bar}.
+Check Type@{Foo.bar}.
+
+Check Type@{Foo.foo}.
+(** The same *)
+Check Type@{foo}.
+Check Type@{Top.foo}.
+
+Universe secfoo.
+Section Foo'.
+  Fail Universe secfoo.
+  Universe secfoo2.
+  Check Type@{Foo'.secfoo2}.
+  Constraint secfoo2 < a.
+End Foo'.
+
+Check Type@{secfoo2}.
+Fail Check Type@{Foo'.secfoo2}.
+Fail Check eq_refl : Type@{secfoo2} = Type@{a}.
+
+(** Below, u and v are global, fixed universes *)
+Module Type Arg.
+  Universe u.
+  Parameter T: Type@{u}.
+End Arg.
+
+Module Fn(A : Arg).
+  Universes v.
+
+  Check Type@{A.u}.
+  Constraint A.u < v.
+
+  Definition foo : Type@{v} := nat.
+  Definition bar : Type@{A.u} := nat.
+
+  Fail Definition foo(A : Type@{v}) : Type@{A.u} := A.
+End Fn.
+
+Module ArgImpl : Arg.
+  Definition T := nat.
+End ArgImpl.
+
+Module ArgImpl2 : Arg.
+  Definition T := bool.
+End ArgImpl2.
+
+(** Two applications of the functor result in the exact same universes *)
+Module FnApp := Fn(ArgImpl).
+
+Check Type@{FnApp.v}.
+Check FnApp.foo.
+Check FnApp.bar.
+
+Check (eq_refl : Type@{ArgImpl.u} = Type@{ArgImpl2.u}).
+
+Module FnApp2 := Fn(ArgImpl).
+Check Type@{FnApp2.v}.
+Check FnApp2.foo.
+Check FnApp2.bar.
+
+Import ArgImpl2.
+(** Now u refers to ArgImpl.u and ArgImpl2.u *)
+Check FnApp2.bar.
+
+(** It can be shadowed *)
+Universe u.
+
+(** This refers to the qualified name *)
+Check FnApp2.bar.
+
+Constraint u = ArgImpl.u.
+Print Universes.
+
+Set Universe Polymorphism.
+
+Section PS.
+  Universe poly.
+
+  Definition id (A : Type@{poly}) (a : A) : A := a.
+End PS.
+(** The universe is polymorphic and discharged, does not persist *)
+Fail Check Type@{poly}.
+
+Print Universes.
+Check id nat.
+Check id@{Set}.