Make own_valid_[n] and own_update_[n] curried.

base_logic/lib/auth.v

@@ -117,12 +117,12 @@ Section auth.
       ■ (a ≼ f t) ∗ ▷ φ t ∗ ∀ u b,
       ■ ((f t, a) ~l~> (f u, b)) ∗ ▷ φ u ={E}=∗ ▷ auth_inv γ f φ ∗ auth_own γ b.
   Proof.
-    iIntros "(Hinv & Hγf)". rewrite /auth_inv /auth_own.
+    iIntros "[Hinv Hγf]". rewrite /auth_inv /auth_own.
     iDestruct "Hinv" as (t) "[>Hγa Hφ]".
     iModIntro. iExists t.
-    iDestruct (own_valid_2 with "[$Hγa $Hγf]") as % [? ?]%auth_valid_discrete_2.
+    iDestruct (own_valid_2 with "Hγa Hγf") as % [? ?]%auth_valid_discrete_2.
     iSplit; first done. iFrame. iIntros (u b) "[% Hφ]".
-    iMod (own_update_2 with "[$Hγa $Hγf]") as "[Hγa Hγf]".
+    iMod (own_update_2 with "Hγa Hγf") as "[Hγa Hγf]".
     { eapply auth_update; eassumption. }
     iModIntro. iFrame. iExists u. iFrame.
   Qed.

base_logic/lib/boxes.v

@@ -57,7 +57,7 @@ Proof. 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.
-  rewrite /box_own_prop own_valid_2 prod_validI /= and_elim_l.
+  rewrite /box_own_prop -own_op own_valid prod_validI /= and_elim_l.
   by iDestruct 1 as % [[[] [=]%leibniz_equiv] ?]%auth_valid_discrete.
 Qed.
 
@@ -72,7 +72,7 @@ Qed.
 Lemma box_own_agree γ Q1 Q2 :
   (box_own_prop γ Q1 ∗ box_own_prop γ Q2) ⊢ ▷ (Q1 ≡ Q2).
 Proof.
-  rewrite /box_own_prop own_valid_2 prod_validI /= and_elim_r.
+  rewrite /box_own_prop -own_op own_valid prod_validI /= and_elim_r.
   rewrite option_validI /= agree_validI agree_equivI later_equivI /=.
   iIntros "#HQ". iNext. rewrite -{2}(iProp_fold_unfold Q1).
   iRewrite "HQ". by rewrite iProp_fold_unfold.

base_logic/lib/cancelable_invariants.v

@@ -39,7 +39,7 @@ Section proofs.
   Proof. by rewrite cinv_own_op Qp_div_2. Qed.
 
   Lemma cinv_own_valid γ q1 q2 : cinv_own γ q1 ∗ cinv_own γ q2 ⊢ ✓ (q1 + q2)%Qp.
-  Proof. rewrite /cinv_own own_valid_2. by iIntros "% !%". Qed.
+  Proof. rewrite /cinv_own -own_op own_valid. by iIntros "% !%". Qed.
 
   Lemma cinv_own_1_l γ q : cinv_own γ 1 ∗ cinv_own γ q ⊢ False.
   Proof. rewrite cinv_own_valid. by iIntros (?%(exclusive_l 1%Qp)). Qed.

base_logic/lib/own.v

@@ -68,11 +68,10 @@ Proof.
   (* implicit arguments differ a bit *)
   by trans (✓ cmra_transport inG_prf a : iProp Σ)%I; last destruct inG_prf.
 Qed.
-Lemma own_valid_2 γ a1 a2 : own γ a1 ∗ own γ a2 ⊢ ✓ (a1 ⋅ a2).
-Proof. by rewrite -own_op own_valid. Qed.
-Lemma own_valid_3 γ a1 a2 a3 : own γ a1 ∗ own γ a2 ∗ own γ a3 ⊢ ✓ (a1 ⋅ a2 ⋅ a3).
-Proof. by rewrite -!own_op assoc own_valid. Qed.
-
+Lemma own_valid_2 γ a1 a2 : own γ a1 ⊢ own γ a2 -∗ ✓ (a1 ⋅ a2).
+Proof. apply wand_intro_r. by rewrite -own_op own_valid. Qed.
+Lemma own_valid_3 γ a1 a2 a3 : own γ a1 ⊢ own γ a2 -∗ own γ a3 -∗ ✓ (a1 ⋅ a2 ⋅ a3).
+Proof. do 2 apply wand_intro_r. by rewrite -!own_op own_valid. Qed.
 Lemma own_valid_r γ a : own γ a ⊢ own γ a ∗ ✓ a.
 Proof. apply (uPred.always_entails_r _ _). apply own_valid. Qed.
 Lemma own_valid_l γ a : own γ a ⊢ ✓ a ∗ own γ a.
@@ -122,11 +121,11 @@ Proof.
   by apply bupd_mono, exist_elim=> a''; apply pure_elim_l=> ->.
 Qed.
 Lemma own_update_2 γ a1 a2 a' :
-  a1 ⋅ a2 ~~> a' → own γ a1 ∗ own γ a2 ==∗ own γ a'.
-Proof. intros. rewrite -own_op. by apply own_update. Qed.
+  a1 ⋅ a2 ~~> a' → own γ a1 ⊢ own γ a2 ==∗ own γ a'.
+Proof. intros. apply wand_intro_r. rewrite -own_op. by apply own_update. Qed.
 Lemma own_update_3 γ a1 a2 a3 a' :
-  a1 ⋅ a2 ⋅ a3 ~~> a' → own γ a1 ∗ own γ a2 ∗ own γ a3 ==∗ own γ a'.
-Proof. intros. rewrite -!own_op assoc. by apply own_update. Qed.
+  a1 ⋅ a2 ⋅ a3 ~~> a' → own γ a1 ⊢ own γ a2 -∗ own γ a3 ==∗ own γ a'.
+Proof. intros. do 2 apply wand_intro_r. rewrite -!own_op. by apply own_update. Qed.
 End global.
 
 Arguments own_valid {_ _} [_] _ _.

base_logic/lib/saved_prop.v

@@ -35,7 +35,7 @@ Section saved_prop.
   Lemma saved_prop_agree γ x y :
     saved_prop_own γ x ∗ saved_prop_own γ y ⊢ ▷ (x ≡ y).
   Proof.
-    rewrite own_valid_2 agree_validI agree_equivI later_equivI.
+    rewrite -own_op own_valid agree_validI agree_equivI later_equivI.
     set (G1 := cFunctor_map F (iProp_fold, iProp_unfold)).
     set (G2 := cFunctor_map F (@iProp_unfold Σ, @iProp_fold Σ)).
     assert (∀ z, G2 (G1 z) ≡ z) as help.

base_logic/lib/wsat.v

@@ -57,7 +57,7 @@ Proof. by rewrite (own_empty (coPset_disjUR) enabled_name). Qed.
 Lemma ownE_op E1 E2 : E1 ⊥ E2 → ownE (E1 ∪ E2) ⊣⊢ ownE E1 ∗ ownE E2.
 Proof. intros. by rewrite /ownE -own_op coPset_disj_union. Qed.
 Lemma ownE_disjoint E1 E2 : ownE E1 ∗ ownE E2 ⊢ E1 ⊥ E2.
-Proof. rewrite /ownE own_valid_2. by iIntros (?%coPset_disj_valid_op). Qed.
+Proof. rewrite /ownE -own_op own_valid. by iIntros (?%coPset_disj_valid_op). Qed.
 Lemma ownE_op' E1 E2 : E1 ⊥ E2 ∧ ownE (E1 ∪ E2) ⊣⊢ ownE E1 ∗ ownE E2.
 Proof.
   iSplit; [iIntros "[% ?]"; by iApply ownE_op|].
@@ -72,7 +72,7 @@ Proof. by rewrite (own_empty (gset_disjUR positive) disabled_name). Qed.
 Lemma ownD_op E1 E2 : E1 ⊥ E2 → ownD (E1 ∪ E2) ⊣⊢ ownD E1 ∗ ownD E2.
 Proof. intros. by rewrite /ownD -own_op gset_disj_union. Qed.
 Lemma ownD_disjoint E1 E2 : ownD E1 ∗ ownD E2 ⊢ E1 ⊥ E2.
-Proof. rewrite /ownD own_valid_2. by iIntros (?%gset_disj_valid_op). Qed.
+Proof. rewrite /ownD -own_op own_valid. by iIntros (?%gset_disj_valid_op). Qed.
 Lemma ownD_op' E1 E2 : E1 ⊥ E2 ∧ ownD (E1 ∪ E2) ⊣⊢ ownD E1 ∗ ownD E2.
 Proof.
   iSplit; [iIntros "[% ?]"; by iApply ownD_op|].
@@ -87,7 +87,7 @@ Lemma invariant_lookup (I : gmap positive (iProp Σ)) i P :
   own invariant_name (◯ {[i := invariant_unfold P]}) ⊢
   ∃ Q, I !! i = Some Q ∗ ▷ (Q ≡ P).
 Proof.
-  rewrite own_valid_2 auth_validI /=. iIntros "[#HI #HvI]".
+  rewrite -own_op own_valid auth_validI /=. iIntros "[#HI #HvI]".
   iDestruct "HI" as (I') "HI". rewrite gmap_equivI gmap_validI.
   iSpecialize ("HI" $! i). iSpecialize ("HvI" $! i).
   rewrite left_id_L lookup_fmap lookup_op lookup_singleton uPred.option_equivI.

heap_lang/lib/counter.v

@@ -54,9 +54,9 @@ Section mono_proof.
     iModIntro. wp_let. wp_op.
     wp_bind (CAS _ _ _). iInv N as (c') ">[Hγ Hl]" "Hclose".
     destruct (decide (c' = c)) as [->|].
-    - iDestruct (own_valid_2 with "[$Hγ $Hγf]")
+    - iDestruct (own_valid_2 with "Hγ Hγf")
         as %[?%mnat_included _]%auth_valid_discrete_2.
-      iMod (own_update_2 with "[$Hγ $Hγf]") as "[Hγ Hγf]".
+      iMod (own_update_2 with "Hγ Hγf") as "[Hγ Hγf]".
       { apply auth_update, (mnat_local_update _ _ (S c)); auto. } 
       wp_cas_suc. iMod ("Hclose" with "[Hl Hγ]") as "_".
       { iNext. iExists (S c). rewrite Nat2Z.inj_succ Z.add_1_l. by iFrame. }
@@ -74,9 +74,9 @@ Section mono_proof.
   Proof.
     iIntros (ϕ) "Hc HΦ". iDestruct "Hc" as (γ) "(% & #? & #Hinv & Hγf)".
     rewrite /read /=. wp_let. iInv N as (c) ">[Hγ Hl]" "Hclose". wp_load.
-    iDestruct (own_valid_2 with "[$Hγ $Hγf]")
+    iDestruct (own_valid_2 with "Hγ Hγf")
       as %[?%mnat_included _]%auth_valid_discrete_2.
-    iMod (own_update_2 with "[$Hγ $Hγf]") as "[Hγ Hγf]".
+    iMod (own_update_2 with "Hγ Hγf") as "[Hγ Hγf]".
     { apply auth_update, (mnat_local_update _ _ c); auto. }
     iMod ("Hclose" with "[Hl Hγ]") as "_"; [iNext; iExists c; by iFrame|].
     iApply ("HΦ" with "[-]"). rewrite /mcounter; eauto 10.
@@ -132,7 +132,7 @@ Section contrib_spec.
     iModIntro. wp_let. wp_op.
     wp_bind (CAS _ _ _). iInv N as (c') ">[Hγ Hl]" "Hclose".
     destruct (decide (c' = c)) as [->|].
-    - iMod (own_update_2 with "[$Hγ $Hγf]") as "[Hγ Hγf]".
+    - iMod (own_update_2 with "Hγ Hγf") as "[Hγ Hγf]".
       { apply auth_update, option_local_update, prod_local_update_2.
         apply (nat_local_update _ _ (S c) (S n)); omega. }
       wp_cas_suc. iMod ("Hclose" with "[Hl Hγ]") as "_".
@@ -149,7 +149,7 @@ Section contrib_spec.
   Proof.
     iIntros (Φ) "(#(%&?&?) & Hγf) HΦ".
     rewrite /read /=. wp_let. iInv N as (c) ">[Hγ Hl]" "Hclose". wp_load.
-    iDestruct (own_valid_2 with "[$Hγ $Hγf]")
+    iDestruct (own_valid_2 with "Hγ Hγf")
       as %[[? ?%nat_included]%Some_pair_included_total_2 _]%auth_valid_discrete_2.
     iMod ("Hclose" with "[Hl Hγ]") as "_"; [iNext; iExists c; by iFrame|].
     iApply ("HΦ" with "[-]"); rewrite /ccounter; eauto 10.
@@ -161,7 +161,7 @@ Section contrib_spec.
   Proof.
     iIntros (Φ) "(#(%&?&?) & Hγf) HΦ".
     rewrite /read /=. wp_let. iInv N as (c) ">[Hγ Hl]" "Hclose". wp_load.
-    iDestruct (own_valid_2 with "[$Hγ $Hγf]") as %[Hn _]%auth_valid_discrete_2.
+    iDestruct (own_valid_2 with "Hγ Hγf") as %[Hn _]%auth_valid_discrete_2.
     apply (Some_included_exclusive _) in Hn as [= ->]%leibniz_equiv; last done.
     iMod ("Hclose" with "[Hl Hγ]") as "_"; [iNext; iExists c; by iFrame|].
     by iApply "HΦ".

heap_lang/lib/spin_lock.v

@@ -32,7 +32,7 @@ Section proof.
   Definition locked (γ : gname): iProp Σ := own γ (Excl ()).
 
   Lemma locked_exclusive (γ : gname) : locked γ ∗ locked γ ⊢ False.
-  Proof. rewrite /locked own_valid_2. by iIntros (?). Qed.
+  Proof. rewrite /locked -own_op own_valid. by iIntros (?). Qed.
 
   Global Instance lock_inv_ne n γ l : Proper (dist n ==> dist n) (lock_inv γ l).
   Proof. solve_proper. Qed.

heap_lang/lib/ticket_lock.v

@@ -101,7 +101,7 @@ Section proof.
         iModIntro. wp_let. wp_op=>[_|[]] //.
         wp_if. 
         iApply ("HΦ" with "[-]"). rewrite /locked. iFrame. eauto.
-      + iDestruct (own_valid_2 with "[$Ht $Haown]") as % [_ ?%gset_disj_valid_op].
+      + iDestruct (own_valid_2 with "Ht Haown") as % [_ ?%gset_disj_valid_op].
         set_solver.
     - iMod ("Hclose" with "[Hlo Hln Ha]").
       { iNext. iExists o, n. by iFrame. }
@@ -149,18 +149,18 @@ Section proof.
     rewrite /release. wp_let. wp_proj. wp_proj. wp_bind (! _)%E.
     iInv N as (o' n) "(>Hlo & >Hln & >Hauth & Haown)" "Hclose".
     wp_load.
-    iDestruct (own_valid_2 with "[$Hauth $Hγo]") as
+    iDestruct (own_valid_2 with "Hauth Hγo") as
       %[[<-%Excl_included%leibniz_equiv _]%prod_included _]%auth_valid_discrete_2.
     iMod ("Hclose" with "[Hlo Hln Hauth Haown]") as "_".
     { iNext. iExists o, n. by iFrame. }
     iModIntro. wp_op.
     iInv N as (o' n') "(>Hlo & >Hln & >Hauth & Haown)" "Hclose".
     wp_store.
-    iDestruct (own_valid_2 with "[$Hauth $Hγo]") as
+    iDestruct (own_valid_2 with "Hauth Hγo") as
       %[[<-%Excl_included%leibniz_equiv _]%prod_included _]%auth_valid_discrete_2.
     iDestruct "Haown" as "[[Hγo' _]|?]".
-    { iDestruct (own_valid_2 with "[$Hγo $Hγo']") as %[[] ?]. }
-    iMod (own_update_2 with "[$Hauth $Hγo]") as "[Hauth Hγo]".
+    { iDestruct (own_valid_2 with "Hγo Hγo'") as %[[] ?]. }
+    iMod (own_update_2 with "Hauth Hγo") as "[Hauth Hγo]".
     { apply auth_update, prod_local_update_1.
       by apply option_local_update, (exclusive_local_update _ (Excl (S o))). }
     iMod ("Hclose" with "[Hlo Hln Hauth Haown Hγo HR]") as "_"; last by iApply "HΦ".

program_logic/weakestpre.v

@@ -115,13 +115,13 @@ Implicit Types e : expr Λ.
 
 (* Physical state *)
 Lemma ownP_twice σ1 σ2 : ownP σ1 ∗ ownP σ2 ⊢ False.
-Proof. rewrite /ownP own_valid_2. by iIntros (?). Qed.
+Proof. rewrite /ownP -own_op own_valid. by iIntros (?). Qed.
 Global Instance ownP_timeless σ : TimelessP (@ownP (state Λ) Σ _ σ).
 Proof. rewrite /ownP; apply _. Qed.
 
 Lemma ownP_agree σ1 σ2 : ownP_auth σ1 ∗ ownP σ2 ⊢ σ1 = σ2.
 Proof.
-  rewrite /ownP /ownP_auth own_valid_2 -auth_both_op.
+  rewrite /ownP /ownP_auth -own_op own_valid -auth_both_op.
   by iIntros ([[[] [=]%leibniz_equiv] _]%auth_valid_discrete).
 Qed.
 Lemma ownP_update σ1 σ2 : ownP_auth σ1 ∗ ownP σ1 ==∗ ownP_auth σ2 ∗ ownP σ2.