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diff --git a/test-suite/success/vm_univ_poly.v b/test-suite/success/vm_univ_poly.v
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+(* Basic tests *)
+Polymorphic Definition pid {T : Type} (x : T) : T := x.
+(*
+Definition _1 : pid true = true :=
+  @eq_refl _ true <: pid true = true.
+
+Polymorphic Definition a_type := Type.
+
+Definition _2 : a_type@{i} = Type@{i} :=
+  @eq_refl _ Type@{i} <: a_type@{i} = Type@{i}.
+
+Polymorphic Definition FORALL (T : Type) (P : T -> Prop) : Prop :=
+  forall x : T, P x.
+
+Polymorphic Axiom todo : forall {T:Type}, T -> T.
+
+Polymorphic Definition todo' (T : Type) := @todo T.
+
+Definition _3 : @todo'@{Set} = @todo@{Set} :=
+  @eq_refl _ (@todo@{Set}) <: @todo'@{Set} = @todo@{Set}.
+*)
+
+(* Inductive Types *)
+Inductive sumbool (A B : Prop) : Set :=
+| left : A -> sumbool A B
+| right : B -> sumbool A B.
+
+Definition x : sumbool True False := left _ _ I.
+
+Definition sumbool_copy {A B : Prop} (H : sumbool A B) : sumbool A B :=
+  match H with
+  | left _ _ x => left _ _ x
+  | right _ _ x => right _ _ x
+  end.
+
+Definition _4 : sumbool_copy x = x :=
+  @eq_refl _ x <: sumbool_copy x = x.
+
+(* Polymorphic Inductive Types *)
+Polymorphic Inductive poption@{i} (T : Type@{i}) : Type@{i} :=
+| PSome : T -> poption@{i} T
+| PNone : poption@{i} T.
+
+Polymorphic Definition poption_default@{i} {T : Type@{i}} (p : poption@{i} T) (x : T) : T :=
+  match p with
+  | @PSome _ y => y
+  | @PNone _ => x
+  end.
+
+Polymorphic Inductive plist@{i} (T : Type@{i}) : Type@{i} :=
+| pnil
+| pcons : T -> plist@{i} T -> plist@{i} T.
+
+Arguments pnil {_}.
+Arguments pcons {_} _ _.
+
+Polymorphic Definition pmap@{i j}
+            {T : Type@{i}} {U : Type@{j}} (f : T -> U) :=
+  fix pmap (ls : plist@{i} T) : plist@{j} U :=
+    match ls with
+    | @pnil _ => @pnil _
+    | @pcons _ l ls => @pcons@{j} U (f l) (pmap@{i j} ls)
+    end.
+
+Universe Ubool.
+Inductive tbool : Type@{Ubool} := ttrue | tfalse.
+
+
+Eval vm_compute in pmap pid (pcons true (pcons false pnil)).
+Eval vm_compute in pmap (fun x => match x with
+                                  | pnil => true
+                                  | pcons _ _ => false
+                                  end) (pcons pnil (pcons (pcons false pnil) pnil)).
+Eval vm_compute in pmap (fun x => x -> Type) (pcons tbool (pcons (plist tbool) pnil)).
+
+Polymorphic Inductive Tree@{i} (T : Type@{i}) : Type@{i} :=
+| Empty
+| Branch : plist@{i} (Tree@{i} T) -> Tree@{i} T.
+
+Polymorphic Definition pfold@{i u}
+            {T : Type@{i}} {U : Type@{u}} (f : T -> U -> U) :=
+  fix pfold (acc : U) (ls : plist@{i} T) : U :=
+    match ls with
+    | pnil => acc
+    | pcons a b => pfold (f a acc) b
+    end.
+
+Polymorphic Inductive nat@{i} : Type@{i} :=
+| O
+| S : nat -> nat.
+
+Polymorphic Fixpoint nat_max@{i} (a b : nat@{i}) : nat@{i} :=
+  match a , b with
+  | O , b => b
+  | a , O => a
+  | S a , S b => S (nat_max a b)
+  end.
+
+Polymorphic Fixpoint height@{i} {T : Type@{i}} (t : Tree@{i} T) : nat@{i} :=
+  match t return nat@{i} with
+  | Empty _ => O
+  | Branch _ ls => S@{i} (pfold@{i i} nat_max O (pmap height ls))
+  end.
+
+Polymorphic Fixpoint repeat@{i} {T : Type@{i}} (n : nat@{i}) (v : T) : plist@{i} T :=
+  match n return plist@{i} T with
+  | O => pnil
+  | S n => pcons@{i} v (repeat n v)
+  end.
+
+Polymorphic Fixpoint big_tree@{i} (n : nat@{i}) : Tree@{i} nat@{i} :=
+  match n with
+  | O => @Empty nat@{i}
+  | S n' => Branch@{i} nat@{i} (repeat@{i} n' (big_tree@{i} n'))
+  end.
+
+Eval compute in height (big_tree (S (S (S O)))).
+
+Let big := S (S (S (S (S O)))).
+Polymorphic Definition really_big@{i} := (S@{i} (S (S (S (S (S (S (S (S (S O)))))))))).
+
+Time Definition _5 : height (@Empty nat) = O :=
+  @eq_refl nat O <: height (@Empty nat) = O.
+
+Time Definition _6 : height@{Set} (@Branch nat pnil) = S O :=
+  @eq_refl nat@{Set} (S@{Set} O@{Set}) <: @eq nat@{Set} (height@{Set} (@Branch@{Set} nat@{Set} (@pnil@{Set} (Tree@{Set} nat@{Set})))) (S@{Set} O@{Set}).
+
+Time Definition _7 : height (big_tree big) = big :=
+  @eq_refl nat big <: height (big_tree big) = big.
+
+Time Definition _8 : height (big_tree really_big) = really_big :=
+ @eq_refl nat@{Set} (S@{Set}
+        (S@{Set}
+           (S@{Set}
+              (S@{Set}
+                 (S@{Set}
+                    (S@{Set} (S@{Set} (S@{Set} (S@{Set} (S@{Set} O@{Set}))))))))))
+ <:
+ @eq nat@{Set}
+   (@height nat@{Set} (big_tree really_big@{Set}))
+   really_big@{Set}.