Use projections in the instance of Timeless for pairs

algebra/cofe.v

@@ -323,9 +323,9 @@ Section product.
       apply (conv_compl n (chain_map snd c)).
   Qed.
   Canonical Structure prodC : cofeT := CofeT (A * B) prod_cofe_mixin.
-  Global Instance pair_timeless (x : A) (y : B) :
-    Timeless x → Timeless y → Timeless (x,y).
-  Proof. by intros ?? [x' y'] [??]; split; apply (timeless _). Qed.
+  Global Instance prod_timeless (x : A * B) :
+    Timeless (x.1) → Timeless (x.2) → Timeless x.
+  Proof. by intros ???[??]; split; apply (timeless _). Qed.
   Global Instance prod_discrete_cofe : Discrete A → Discrete B → Discrete prodC.
   Proof. intros ?? [??]; apply _. Qed.
 End product.

program_logic/boxes.v

@@ -57,11 +57,6 @@ Proof. solve_proper. Qed.
 Global Instance slice_persistent γ P : PersistentP (slice N γ P).
 Proof. apply _. Qed.
 
-(* This should go automatic *)
-Instance box_own_auth_timeless γ
-  (a : auth (option (excl bool))) : TimelessP (box_own_auth γ a).
-Proof. apply own_timeless, pair_timeless; apply _. Qed.
-
 Lemma box_own_auth_agree γ b1 b2 :
   box_own_auth γ (● Excl' b1) ★ box_own_auth γ (◯ Excl' b2) ⊢ b1 = b2.
 Proof.