Use generic big op lemmas instead of uPred specific ones when possible.

theories/base_logic/lib/boxes.v

@@ -97,9 +97,8 @@ Qed.
 
 Lemma box_alloc : box N ∅ True%I.
 Proof.
-  iIntros; iExists (λ _, True)%I; iSplit.
-  - iNext. by rewrite big_sepM_empty.
-  - by rewrite big_sepM_empty.
+  iIntros; iExists (λ _, True)%I; iSplit; last done.
+  iNext. by rewrite big_opM_empty.
 Qed.
 
 Lemma slice_insert_empty E q f Q P :
@@ -116,8 +115,8 @@ Proof.
   { iNext. iExists false; eauto. }
   iModIntro; iExists γ; repeat iSplit; auto.
   iNext. iExists (<[γ:=Q]> Φ); iSplit.
-  - iNext. iRewrite "HeqP". by rewrite big_sepM_fn_insert'.
-  - rewrite (big_sepM_fn_insert (λ _ _ P',  _ ∗ _ _ P' ∗ _ _ (_ _ P')))%I //.
+  - iNext. iRewrite "HeqP". by rewrite big_opM_fn_insert'.
+  - rewrite (big_opM_fn_insert (λ _ _ P',  _ ∗ _ _ P' ∗ _ _ (_ _ P')))%I //.
     iFrame; eauto.
 Qed.
 
@@ -130,13 +129,13 @@ Proof.
   iIntros (??) "[#HγQ Hinv] H". iDestruct "H" as (Φ) "[#HeqP Hf]".
   iExists ([∗ map] γ'↦_ ∈ delete γ f, Φ γ')%I.
   iInv N as (b) "[>Hγ _]" "Hclose".
-  iDestruct (big_sepM_delete _ f _ false with "Hf")
+  iDestruct (big_opM_delete _ f _ false with "Hf")
     as "[[>Hγ' #[HγΦ ?]] ?]"; first done.
   iDestruct (box_own_auth_agree γ b false with "[-]") as %->; first by iFrame.
   iMod ("Hclose" with "[Hγ]"); first iExists false; eauto.
   iModIntro. iNext. iSplit.
   - iDestruct (box_own_agree γ Q (Φ γ) with "[#]") as "HeqQ"; first by eauto.
-    iNext. iRewrite "HeqP". iRewrite "HeqQ". by rewrite -big_sepM_delete.
+    iNext. iRewrite "HeqP". iRewrite "HeqQ". by rewrite -big_opM_delete.
   - iExists Φ; eauto.
 Qed.
 
@@ -147,13 +146,13 @@ Lemma slice_fill E q f γ P Q :
 Proof.
   iIntros (??) "#[HγQ Hinv] HQ H"; iDestruct "H" as (Φ) "[#HeqP Hf]".
   iInv N as (b') "[>Hγ _]" "Hclose".
-  iDestruct (big_sepM_delete _ f _ false with "Hf")
+  iDestruct (big_opM_delete _ f _ false with "Hf")
     as "[[>Hγ' #[HγΦ Hinv']] ?]"; first done.
   iMod (box_own_auth_update γ b' false true with "[$Hγ $Hγ']") as "[Hγ Hγ']".
   iMod ("Hclose" with "[Hγ HQ]"); first (iNext; iExists true; by iFrame).
   iModIntro; iNext; iExists Φ; iSplit.
-  - by rewrite big_sepM_insert_override.
-  - rewrite -insert_delete big_sepM_insert ?lookup_delete //.
+  - by rewrite big_opM_insert_override.
+  - rewrite -insert_delete big_opM_insert ?lookup_delete //.
     iFrame; eauto.
 Qed.
 
@@ -164,15 +163,15 @@ Lemma slice_empty E q f P Q γ :
 Proof.
   iIntros (??) "#[HγQ Hinv] H"; iDestruct "H" as (Φ) "[#HeqP Hf]".
   iInv N as (b) "[>Hγ HQ]" "Hclose".
-  iDestruct (big_sepM_delete _ f with "Hf")
+  iDestruct (big_opM_delete _ f with "Hf")
     as "[[>Hγ' #[HγΦ Hinv']] ?]"; first done.
   iDestruct (box_own_auth_agree γ b true with "[-]") as %->; first by iFrame.
   iFrame "HQ".
   iMod (box_own_auth_update γ with "[$Hγ $Hγ']") as "[Hγ Hγ']".
   iMod ("Hclose" with "[Hγ]"); first (iNext; iExists false; by repeat iSplit).
   iModIntro; iNext; iExists Φ; iSplit.
-  - by rewrite big_sepM_insert_override.
-  - rewrite -insert_delete big_sepM_insert ?lookup_delete //.
+  - by rewrite big_opM_insert_override.
+  - rewrite -insert_delete big_opM_insert ?lookup_delete //.
     iFrame; eauto.
 Qed.
 
@@ -205,11 +204,11 @@ Lemma box_fill E f P :
   box N f P -∗ ▷ P ={E}=∗ box N (const true <$> f) P.
 Proof.
   iIntros (?) "H HP"; iDestruct "H" as (Φ) "[#HeqP Hf]".
-  iExists Φ; iSplitR; first by rewrite big_sepM_fmap.
-  rewrite internal_eq_iff later_iff big_sepM_later.
+  iExists Φ; iSplitR; first by rewrite big_opM_fmap.
+  rewrite internal_eq_iff later_iff big_opM_commute.
   iDestruct ("HeqP" with "HP") as "HP".
   iCombine "Hf" "HP" as "Hf".
-  rewrite -big_sepM_sepM big_sepM_fmap; iApply (fupd_big_sepM _ _ f).
+  rewrite -big_opM_opM big_opM_fmap; iApply (fupd_big_sepM _ _ f).
   iApply (@big_sepM_impl with "[$Hf]").
   iAlways; iIntros (γ b' ?) "[(Hγ' & #$ & #$) HΦ]".
   iInv N as (b) "[>Hγ _]" "Hclose".
@@ -226,7 +225,7 @@ Proof.
   iAssert (([∗ map] γ↦b ∈ f, ▷ Φ γ) ∗
     [∗ map] γ↦b ∈ f, box_own_auth γ (◯ Excl' false) ∗  box_own_prop γ (Φ γ) ∗
       inv N (slice_inv γ (Φ γ)))%I with "[> Hf]" as "[HΦ ?]".
-  { rewrite -big_sepM_sepM -fupd_big_sepM. iApply (@big_sepM_impl with "[$Hf]").
+  { rewrite -big_opM_opM -fupd_big_sepM. iApply (@big_sepM_impl with "[$Hf]").
     iAlways; iIntros (γ b ?) "(Hγ' & #HγΦ & #Hinv)".
     assert (true = b) as <- by eauto.
     iInv N as (b) "[>Hγ HΦ]" "Hclose".
@@ -235,8 +234,8 @@ Proof.
     iMod ("Hclose" with "[Hγ]"); first (iNext; iExists false; iFrame; eauto).
     iFrame "HγΦ Hinv". by iApply "HΦ". }
   iModIntro; iSplitL "HΦ".
-  - rewrite internal_eq_iff later_iff big_sepM_later. by iApply "HeqP".
-  - iExists Φ; iSplit; by rewrite big_sepM_fmap.
+  - rewrite internal_eq_iff later_iff big_opM_commute. by iApply "HeqP".
+  - iExists Φ; iSplit; by rewrite big_opM_fmap.
 Qed.
 
 Lemma slice_iff E q f P Q Q' γ b :

theories/base_logic/lib/fractional.v

@@ -63,30 +63,22 @@ Section fractional.
   Global Instance fractional_big_sepL {A} l Ψ :
     (∀ k (x : A), Fractional (Ψ k x)) →
     Fractional (M:=M) (λ q, [∗ list] k↦x ∈ l, Ψ k x q)%I.
-  Proof.
-    intros ? q q'. rewrite -big_sepL_sepL. by setoid_rewrite fractional.
-  Qed.
+  Proof. intros ? q q'. rewrite -big_opL_opL. by setoid_rewrite fractional. Qed.
 
   Global Instance fractional_big_sepM `{Countable K} {A} (m : gmap K A) Ψ :
     (∀ k (x : A), Fractional (Ψ k x)) →
     Fractional (M:=M) (λ q, [∗ map] k↦x ∈ m, Ψ k x q)%I.
-  Proof.
-    intros ? q q'. rewrite -big_sepM_sepM. by setoid_rewrite fractional.
-  Qed.
+  Proof. intros ? q q'. rewrite -big_opM_opM. by setoid_rewrite fractional. Qed.
 
   Global Instance fractional_big_sepS `{Countable A} (X : gset A) Ψ :
     (∀ x, Fractional (Ψ x)) →
     Fractional (M:=M) (λ q, [∗ set] x ∈ X, Ψ x q)%I.
-  Proof.
-    intros ? q q'. rewrite -big_sepS_sepS. by setoid_rewrite fractional.
-  Qed.
+  Proof. intros ? q q'. rewrite -big_opS_opS. by setoid_rewrite fractional. Qed.
 
   Global Instance fractional_big_sepMS `{Countable A} (X : gmultiset A) Ψ :
     (∀ x, Fractional (Ψ x)) →
     Fractional (M:=M) (λ q, [∗ mset] x ∈ X, Ψ x q)%I.
-  Proof.
-    intros ? q q'. rewrite -big_sepMS_sepMS. by setoid_rewrite fractional.
-  Qed.
+  Proof. intros ? q q'. rewrite -big_opMS_opMS. by setoid_rewrite fractional. Qed.
 
   (** Mult instances *)
 

theories/base_logic/lib/wsat.v

@@ -105,9 +105,9 @@ Lemma ownI_open i P : wsat ∗ ownI i P ∗ ownE {[i]} ⊢ wsat ∗ ▷ P ∗ ow
 Proof.
   rewrite /ownI. iIntros "(Hw & Hi & HiE)". iDestruct "Hw" as (I) "[? HI]".
   iDestruct (invariant_lookup I i P with "[$]") as (Q) "[% #HPQ]".
-  iDestruct (big_sepM_delete _ _ i with "HI") as "[[[HQ $]|HiE'] HI]"; eauto.
+  iDestruct (big_opM_delete _ _ i with "HI") as "[[[HQ $]|HiE'] HI]"; eauto.
   - iSplitR "HQ"; last by iNext; iRewrite -"HPQ".
-    iExists I. iFrame "Hw". iApply (big_sepM_delete _ _ i); eauto.
+    iExists I. iFrame "Hw". iApply (big_opM_delete _ _ i); eauto.
     iFrame "HI"; eauto.
   - iDestruct (ownE_singleton_twice with "[$HiE $HiE']") as %[].
 Qed.
@@ -115,9 +115,9 @@ Lemma ownI_close i P : wsat ∗ ownI i P ∗ ▷ P ∗ ownD {[i]} ⊢ wsat ∗ o
 Proof.
   rewrite /ownI. iIntros "(Hw & Hi & HP & HiD)". iDestruct "Hw" as (I) "[? HI]".
   iDestruct (invariant_lookup with "[$]") as (Q) "[% #HPQ]".
-  iDestruct (big_sepM_delete _ _ i with "HI") as "[[[HQ ?]|$] HI]"; eauto.
+  iDestruct (big_opM_delete _ _ i with "HI") as "[[[HQ ?]|$] HI]"; eauto.
   - iDestruct (ownD_singleton_twice with "[$]") as %[].
-  - iExists I. iFrame "Hw". iApply (big_sepM_delete _ _ i); eauto.
+  - iExists I. iFrame "Hw". iApply (big_opM_delete _ _ i); eauto.
     iFrame "HI". iLeft. iFrame "HiD". by iNext; iRewrite "HPQ".
 Qed.
 
@@ -139,7 +139,7 @@ Proof.
   iModIntro; iExists i;  iSplit; [done|]. rewrite /ownI; iFrame "HiP".
   iExists (<[i:=P]>I); iSplitL "Hw".
   { by rewrite fmap_insert insert_singleton_op ?lookup_fmap ?HIi. }
-  iApply (big_sepM_insert _ I); first done.
+  iApply (big_opM_insert _ I); first done.
   iFrame "HI". iLeft. by rewrite /ownD; iFrame.
 Qed.
 
@@ -162,7 +162,7 @@ Proof.
   rewrite -/(ownD _). iFrame "HD".
   iIntros "HE". iExists (<[i:=P]>I); iSplitL "Hw".
   { by rewrite fmap_insert insert_singleton_op ?lookup_fmap ?HIi. }
-  iApply (big_sepM_insert _ I); first done.
+  iApply (big_opM_insert _ I); first done.
   iFrame "HI". by iRight.
 Qed.
 End wsat.

theories/base_logic/tactics.v

@@ -28,7 +28,7 @@ Module uPred_reflection. Section uPred_reflection.
   Lemma eval_flatten Σ e : eval Σ e ⊣⊢ eval_list Σ (flatten e).
   Proof.
     induction e as [| |e1 IH1 e2 IH2];
-      rewrite /= ?right_id ?big_sepL_app ?IH1 ?IH2 //.
+      rewrite /= ?right_id ?big_opL_app ?IH1 ?IH2 //.
   Qed.
   Lemma flatten_entails Σ e1 e2 :
     flatten e2 ⊆+ flatten e1 → eval Σ e1 ⊢ eval Σ e2.
@@ -89,7 +89,7 @@ Module uPred_reflection. Section uPred_reflection.
   Proof.
     intros ??. rewrite !eval_flatten.
     rewrite (flatten_cancel e1 e1' ns) // (flatten_cancel e2 e2' ns) //; csimpl.
-    rewrite !big_sepL_app. apply sep_mono_r.
+    rewrite !big_opL_app. apply sep_mono_r.
   Qed.
 
   Fixpoint to_expr (l : list nat) : expr :=
@@ -109,7 +109,7 @@ Module uPred_reflection. Section uPred_reflection.
     cancel ns e = Some e' → eval Σ e ⊣⊢ (eval Σ (to_expr ns) ∗ eval Σ e').
   Proof.
     intros He%flatten_cancel.
-    by rewrite eval_flatten He big_sepL_app eval_to_expr eval_flatten.
+    by rewrite eval_flatten He big_opL_app eval_to_expr eval_flatten.
   Qed.
   Lemma split_r Σ e ns e' :
     cancel ns e = Some e' → eval Σ e ⊣⊢ (eval Σ e' ∗ eval Σ (to_expr ns)).

theories/heap_lang/lib/barrier/proof.v

@@ -76,15 +76,15 @@ Lemma ress_split i i1 i2 Q R1 R2 P I :
   ress P ({[i1;i2]} ∪ I ∖ {[i]}).
 Proof.
   iIntros (????) "#HQ #H1 #H2 HQR"; iDestruct 1 as (Ψ) "[HPΨ HΨ]".
-  iDestruct (big_sepS_delete _ _ i with "HΨ") as "[#HΨi HΨ]"; first done.
+  iDestruct (big_opS_delete _ _ i with "HΨ") as "[#HΨi HΨ]"; first done.
   iExists (<[i1:=R1]> (<[i2:=R2]> Ψ)). iSplitL "HQR HPΨ".
   - iPoseProof (saved_prop_agree i Q (Ψ i) with "[#]") as "Heq"; first by iSplit.
     iNext. iRewrite "Heq" in "HQR". iIntros "HP". iSpecialize ("HPΨ" with "HP").
-    iDestruct (big_sepS_delete _ _ i with "HPΨ") as "[HΨ HPΨ]"; first done.
+    iDestruct (big_opS_delete _ _ i with "HPΨ") as "[HΨ HPΨ]"; first done.
     iDestruct ("HQR" with "HΨ") as "[HR1 HR2]".
-    rewrite -assoc_L !big_sepS_fn_insert'; [|abstract set_solver ..].
+    rewrite -assoc_L !big_opS_fn_insert'; [|abstract set_solver ..].
     by iFrame.
-  - rewrite -assoc_L !big_sepS_fn_insert; [|abstract set_solver ..]. eauto.
+  - rewrite -assoc_L !big_opS_fn_insert; [|abstract set_solver ..]. eauto.
 Qed.
 
 (** Actual proofs *)
@@ -98,7 +98,7 @@ Proof.
   iMod (sts_alloc (barrier_inv l P) _ N (State Low {[ γ ]}) with "[-]")
     as (γ') "[#? Hγ']"; eauto.
   { iNext. rewrite /barrier_inv /=. iFrame.
-    iExists (const P). rewrite !big_sepS_singleton /=. eauto. }
+    iExists (const P). rewrite !big_opS_singleton /=. eauto. }
   iAssert (barrier_ctx γ' l P)%I as "#?".
   { done. }
   iAssert (sts_ownS γ' (i_states γ) {[Change γ]}
@@ -147,9 +147,9 @@ Proof.
   - (* a High state: the comparison succeeds, and we perform a transition and
     return to the client *)
     iDestruct "Hr" as (Ψ) "[HΨ Hsp]".
-    iDestruct (big_sepS_delete _ _ i with "Hsp") as "[#HΨi Hsp]"; first done.
+    iDestruct (big_opS_delete _ _ i with "Hsp") as "[#HΨi Hsp]"; first done.
     iAssert (▷ Ψ i ∗ ▷ [∗ set] j ∈ I ∖ {[i]}, Ψ j)%I with "[HΨ]" as "[HΨ HΨ']".
-    { iNext. iApply (big_sepS_delete _ _ i); first done. by iApply "HΨ". }
+    { iNext. iApply (big_opS_delete _ _ i); first done. by iApply "HΨ". }
     iMod ("Hclose" $! (State High (I ∖ {[ i ]})) (∅ : set token) with "[HΨ' Hl Hsp]").
     { iSplit; [iPureIntro; by eauto using wait_step|].
       rewrite /barrier_inv /=. iNext. iFrame "Hl". iExists Ψ; iFrame. auto. }

theories/program_logic/adequacy.v

@@ -30,7 +30,7 @@ Proof.
   iMod (own_alloc (GSet ∅)) as (γD) "HD"; first done.
   iModIntro; iExists (WsatG _ _ _ _ γI γE γD).
   rewrite /wsat /ownE; iFrame.
-  iExists ∅. rewrite fmap_empty big_sepM_empty. by iFrame.
+  iExists ∅. rewrite fmap_empty big_opM_empty. by iFrame.
 Qed.
 
 (* Program logic adequacy *)

theories/proofmode/class_instances.v

@@ -181,7 +181,7 @@ Global Instance into_laterN_big_sepL n {A} (Φ Ψ : nat → A → uPred M) (l: l
   IntoLaterN' n ([∗ list] k ↦ x ∈ l, Φ k x) ([∗ list] k ↦ x ∈ l, Ψ k x).
 Proof.
   rewrite /IntoLaterN' /IntoLaterN=> ?.
-  rewrite big_sepL_laterN. by apply big_sepL_mono.
+  rewrite big_opL_commute. by apply big_sepL_mono.
 Qed.
 Global Instance into_laterN_big_sepM n `{Countable K} {A}
     (Φ Ψ : K → A → uPred M) (m : gmap K A) :
@@ -189,7 +189,7 @@ Global Instance into_laterN_big_sepM n `{Countable K} {A}
   IntoLaterN' n ([∗ map] k ↦ x ∈ m, Φ k x) ([∗ map] k ↦ x ∈ m, Ψ k x).
 Proof.
   rewrite /IntoLaterN' /IntoLaterN=> ?.
-  rewrite big_sepM_laterN; by apply big_sepM_mono.
+  rewrite big_opM_commute; by apply big_sepM_mono.
 Qed.
 Global Instance into_laterN_big_sepS n `{Countable A}
     (Φ Ψ : A → uPred M) (X : gset A) :
@@ -197,7 +197,7 @@ Global Instance into_laterN_big_sepS n `{Countable A}
   IntoLaterN' n ([∗ set] x ∈ X, Φ x) ([∗ set] x ∈ X, Ψ x).
 Proof.
   rewrite /IntoLaterN' /IntoLaterN=> ?.
-  rewrite big_sepS_laterN; by apply big_sepS_mono.
+  rewrite big_opS_commute; by apply big_sepS_mono.
 Qed.
 Global Instance into_laterN_big_sepMS n `{Countable A}
     (Φ Ψ : A → uPred M) (X : gmultiset A) :
@@ -205,7 +205,7 @@ Global Instance into_laterN_big_sepMS n `{Countable A}
   IntoLaterN' n ([∗ mset] x ∈ X, Φ x) ([∗ mset] x ∈ X, Ψ x).
 Proof.
   rewrite /IntoLaterN' /IntoLaterN=> ?.
-  rewrite big_sepMS_laterN; by apply big_sepMS_mono.
+  rewrite big_opMS_commute; by apply big_sepMS_mono.
 Qed.
 
 (* FromLater *)
@@ -464,7 +464,7 @@ Global Instance frame_big_sepL_app {A} p (Φ : nat → A → uPred M) R Q l l1 l
   Frame p R (([∗ list] k ↦ y ∈ l1, Φ k y) ∗
            [∗ list] k ↦ y ∈ l2, Φ (length l1 + k) y) Q →
   Frame p R ([∗ list] k ↦ y ∈ l, Φ k y) Q.
-Proof. rewrite /IsApp=>->. by rewrite /Frame big_sepL_app. Qed.
+Proof. rewrite /IsApp=>->. by rewrite /Frame big_opL_app. Qed.
 
 Class MakeAnd (P Q PQ : uPred M) := make_and : P ∧ Q ⊣⊢ PQ.
 Global Instance make_and_true_l P : MakeAnd True P P.

theories/proofmode/coq_tactics.v

@@ -234,14 +234,14 @@ Proof.
       intros j. apply (env_app_disjoint _ _ _ j) in Happ.
       naive_solver eauto using env_app_fresh.
     + rewrite (env_app_perm _ _ Γp') //.
-      rewrite big_sepL_app always_sep. solve_sep_entails.
+      rewrite big_opL_app always_sep. solve_sep_entails.
   - destruct (env_app Γ Γp) eqn:Happ,
       (env_app Γ Γs) as [Γs'|] eqn:?; simplify_eq/=.
     apply wand_intro_l, sep_intro_True_l; [apply pure_intro|].
     + destruct Hwf; constructor; simpl; eauto using env_app_wf.
       intros j. apply (env_app_disjoint _ _ _ j) in Happ.
       naive_solver eauto using env_app_fresh.
-    + rewrite (env_app_perm _ _ Γs') // big_sepL_app. solve_sep_entails.
+    + rewrite (env_app_perm _ _ Γs') // big_opL_app. solve_sep_entails.
 Qed.
 
 Lemma envs_simple_replace_sound' Δ Δ' i p Γ :
@@ -257,14 +257,14 @@ Proof.
       intros j. apply (env_app_disjoint _ _ _ j) in Happ.
       destruct (decide (i = j)); try naive_solver eauto using env_replace_fresh.
     + rewrite (env_replace_perm _ _ Γp') //.
-      rewrite big_sepL_app always_sep. solve_sep_entails.
+      rewrite big_opL_app always_sep. solve_sep_entails.
   - destruct (env_app Γ Γp) eqn:Happ,
       (env_replace i Γ Γs) as [Γs'|] eqn:?; simplify_eq/=.
     apply wand_intro_l, sep_intro_True_l; [apply pure_intro|].
     + destruct Hwf; constructor; simpl; eauto using env_replace_wf.
       intros j. apply (env_app_disjoint _ _ _ j) in Happ.
       destruct (decide (i = j)); try naive_solver eauto using env_replace_fresh.
-    + rewrite (env_replace_perm _ _ Γs') // big_sepL_app. solve_sep_entails.
+    + rewrite (env_replace_perm _ _ Γs') // big_opL_app. solve_sep_entails.
 Qed.
 
 Lemma envs_simple_replace_sound Δ Δ' i p P Γ :