diff --git a/theories/logrel/subtyping_rules.v b/theories/logrel/subtyping_rules.v
index 679bc3132e82ae43c4b53b56f546ce9b1044bf7b..2715f374499420f08a5ef2a7e22ca8c34e573b12 100644
--- a/theories/logrel/subtyping_rules.v
+++ b/theories/logrel/subtyping_rules.v
@@ -171,7 +171,7 @@ Section subtyping_rules.
   Qed.
 
   Lemma lty_le_exist C1 C2 :
-    (∀ A, C1 A <: C2 A) -∗
+    ▷ (∀ A, C1 A <: C2 A) -∗
     (∃ A, C1 A) <: (∃ A, C2 A).
   Proof.
     iIntros "#Hle" (v) "!>". iDestruct 1 as (A) "H". iExists A. by iApply "Hle".
diff --git a/theories/logrel/term_types.v b/theories/logrel/term_types.v
index c28e957848503fcf6f28b4c7f92a7f798da1d4b4..b69d653d7f06c18f548b41d1b3c2641084f48170 100644
--- a/theories/logrel/term_types.v
+++ b/theories/logrel/term_types.v
@@ -27,7 +27,7 @@ Definition lty_sum {Σ} (A1 A2 : ltty Σ) : ltty Σ := Ltty (λ w,
 Definition lty_forall `{heapG Σ} {k} (C : lty Σ k → ltty Σ) : ltty Σ :=
   Ltty (λ w, ∀ A, WP w #() {{ ltty_car (C A) }})%I.
 Definition lty_exist {Σ k} (C : lty Σ k → ltty Σ) : ltty Σ :=
-  Ltty (λ w, ∃ A, ltty_car (C A) w)%I.
+  Ltty (λ w, ∃ A, ▷ ltty_car (C A) w)%I.
 
 Definition lty_ref_mut `{heapG Σ} (A : ltty Σ) : ltty Σ := Ltty (λ w,
   ∃ (l : loc) (v : val), ⌜w = #l⌝ ∗ l ↦ v ∗ ▷ ltty_car A v)%I.
@@ -115,6 +115,9 @@ Section term_types.
   Global Instance lty_forall_ne `{heapG Σ} k n :
     Proper (pointwise_relation _ (dist n) ==> dist n) (@lty_forall Σ _ k).
   Proof. solve_proper. Qed.
+  Global Instance lty_exist_contractive k n :
+    Proper (pointwise_relation _ (dist_later n) ==> dist n) (@lty_exist Σ k).
+  Proof. solve_contractive. Qed.
   Global Instance lty_exist_ne k n :
     Proper (pointwise_relation _ (dist n) ==> dist n) (@lty_exist Σ k).
   Proof. solve_proper. Qed.
diff --git a/theories/logrel/term_typing_rules.v b/theories/logrel/term_typing_rules.v
index 605ee561c2f24f079838438af97b1bebb72a522c..383be7e69ef5db2d8d4607f4069a7339769f0aa5 100644
--- a/theories/logrel/term_typing_rules.v
+++ b/theories/logrel/term_typing_rules.v
@@ -240,19 +240,22 @@ Section properties.
     wp_apply (wp_wand with "(He [HΓ //])"); iIntros (w) "[HB $]". by iExists M.
   Qed.
 
-  Lemma ltyped_unpack {k} Γ1 Γ2 Γ3 (x : string) e (C : lty Σ k → ltty Σ) A :
-    Γ1 !! x = Some (lty_exist C) →
-    (∀ X, <![x:=C X]!> Γ1 ⊨ e : A ⫤ Γ2) -∗
-    (Γ1 ⊨ e : A ⫤ Γ2).
+  Lemma ltyped_unpack {k} Γ1 Γ2 Γ3 x e1 e2 (C : lty Σ k → ltty Σ) B :
+    (Γ1 ⊨ e1 : ∃ M, C M ⫤ Γ2) -∗
+    (∀ Y, <![x:=C Y]!> Γ2 ⊨ e2 : B ⫤ Γ3) -∗
+    Γ1 ⊨ (let: x := e1 in e2) : B ⫤ binder_delete x Γ3.
   Proof.
-    iIntros (Hx) "#He". iIntros (vs) "!> HΓ".
-    iDestruct (env_ltyped_lookup with "HΓ") as (v Hv) "[HB HΓ]"; first done.
-    iDestruct ("HB") as (B) "HB".
-    iDestruct (env_ltyped_insert _ _ x with "HB HΓ") as "HΓ".
-    rewrite /binder_insert insert_delete (insert_id _ _ _ Hv).
-    iApply (wp_wand with "(He HΓ)"). eauto.
+    iIntros "#He1 #He2 !>". iIntros (vs) "HΓ1"=> /=.
+    wp_apply (wp_wand with "(He1 HΓ1)"); iIntros (v) "[HC HΓ2]".
+    iDestruct "HC" as (X) "HX". wp_pures.
+    iDestruct (env_ltyped_insert _ _ x with "HX HΓ2") as "HΓ2".
+    iDestruct ("He2" with "HΓ2") as "He2'".
+    destruct x as [|x]; rewrite /= -?subst_map_insert //.
+    wp_apply (wp_wand with "He2'").
+    iIntros (w) "[$ HΓ3]". by iApply env_ltyped_delete.
   Qed.
 
+
   (** Mutable Reference properties *)
   Lemma ltyped_alloc Γ1 Γ2 e A :
     (Γ1 ⊨ e : A ⫤ Γ2) -∗
@@ -304,7 +307,7 @@ Section properties.
     iFrame "HΓ'".
   Qed.
 
-  (** Weak Reference properties *)
+  (** Shared Reference properties *)
   Lemma ltyped_upgrade_shared  Γ Γ' e A :
     (Γ ⊨ e : ref_mut (copy A) ⫤ Γ') -∗
     Γ ⊨ e : ref_shr A ⫤ Γ'.