Prove that `is_lock` is contractive.

theories/heap_lang/lib/lock.v

@@ -13,7 +13,7 @@ Structure lock Σ `{!heapG Σ} := Lock {
   is_lock (N: namespace) (γ: name) (lock: val) (R: iProp Σ) : iProp Σ;
   locked (γ: name) : iProp Σ;
   (* -- general properties -- *)
-  is_lock_ne N γ lk : NonExpansive (is_lock N γ lk);
+  is_lock_ne N γ lk : Contractive (is_lock N γ lk);
   is_lock_persistent N γ lk R : Persistent (is_lock N γ lk R);
   locked_timeless γ : Timeless (locked γ);
   locked_exclusive γ : locked γ -∗ locked γ -∗ False;

theories/heap_lang/lib/spin_lock.v

@@ -36,8 +36,8 @@ Section proof.
 
   Global Instance lock_inv_ne γ l : NonExpansive (lock_inv γ l).
   Proof. solve_proper. Qed.
-  Global Instance is_lock_ne γ l : NonExpansive (is_lock γ l).
-  Proof. solve_proper. Qed.
+  Global Instance is_lock_contractive γ l : Contractive (is_lock γ l).
+  Proof. solve_contractive. Qed.
 
   (** The main proofs. *)
   Global Instance is_lock_persistent γ l R : Persistent (is_lock γ l R).

theories/heap_lang/lib/ticket_lock.v

@@ -54,11 +54,10 @@ Section proof.
 
   Definition locked (γ : gname) : iProp Σ := (∃ o, own γ (◯ (Excl' o, GSet ∅)))%I.
 
-  Global Instance lock_inv_ne γ lo ln :
-    NonExpansive (lock_inv γ lo ln).
-  Proof. solve_proper. Qed.
-  Global Instance is_lock_ne γ lk : NonExpansive (is_lock γ lk).
+  Global Instance lock_inv_ne γ lo ln : NonExpansive (lock_inv γ lo ln).
   Proof. solve_proper. Qed.
+  Global Instance is_lock_contractive γ lk : Contractive (is_lock γ lk).
+  Proof. solve_contractive. Qed.
   Global Instance is_lock_persistent γ lk R : Persistent (is_lock γ lk R).
   Proof. apply _. Qed.
   Global Instance locked_timeless γ : Timeless (locked γ).