Fix inconsistent names for bigop lemmas.

Notably, `big_andL_andL` and `big_andL_and` where a ⊣⊢ and ⊢ version
of the same lemma. I favored the `big_opL_op` naming scheme.

theories/algebra/big_op.v

@@ -145,7 +145,7 @@ Section list.
     ([^o list] k↦y ∈ h <$> l, f k y) ≡ ([^o list] k↦y ∈ l, f k (h y)).
   Proof. revert f. induction l as [|x l IH]=> f; csimpl=> //. by rewrite IH. Qed.
 
-  Lemma big_opL_opL f g l :
+  Lemma big_opL_op f g l :
     ([^o list] k↦x ∈ l, f k x `o` g k x)
     ≡ ([^o list] k↦x ∈ l, f k x) `o` ([^o list] k↦x ∈ l, g k x).
   Proof.
@@ -253,10 +253,10 @@ Section gmap.
     rewrite -assoc IH //.
   Qed.
 
-  Lemma big_opM_opM f g m :
+  Lemma big_opM_op f g m :
     ([^o map] k↦x ∈ m, f k x `o` g k x)
     ≡ ([^o map] k↦x ∈ m, f k x) `o` ([^o map] k↦x ∈ m, g k x).
-  Proof. rewrite /big_opM -big_opL_opL. by apply big_opL_proper=> ? [??]. Qed.
+  Proof. rewrite /big_opM -big_opL_op. by apply big_opL_proper=> ? [??]. Qed.
 End gmap.
 
 
@@ -335,9 +335,9 @@ Section gset.
     induction X using set_ind_L; rewrite /= ?big_opS_insert ?left_id //.
   Qed.
 
-  Lemma big_opS_opS f g X :
+  Lemma big_opS_op f g X :
     ([^o set] y ∈ X, f y `o` g y) ≡ ([^o set] y ∈ X, f y) `o` ([^o set] y ∈ X, g y).
-  Proof. by rewrite /big_opS -big_opL_opL. Qed.
+  Proof. by rewrite /big_opS -big_opL_op. Qed.
 End gset.
 
 Lemma big_opM_dom `{Countable K} {A} (f : K → M) (m : gmap K A) :
@@ -403,9 +403,9 @@ Section gmultiset.
       rewrite /= ?big_opMS_disj_union ?big_opMS_singleton ?left_id //.
   Qed.
 
-  Lemma big_opMS_opMS f g X :
+  Lemma big_opMS_op f g X :
     ([^o mset] y ∈ X, f y `o` g y) ≡ ([^o mset] y ∈ X, f y) `o` ([^o mset] y ∈ X, g y).
-  Proof. by rewrite /big_opMS -big_opL_opL. Qed.
+  Proof. by rewrite /big_opMS -big_opL_op. Qed.
 End gmultiset.
 End big_op.
 

theories/base_logic/lib/boxes.v

@@ -210,7 +210,7 @@ Proof.
   iEval (rewrite internal_eq_iff later_iff big_sepM_later) in "HeqP".
   iDestruct ("HeqP" with "HP") as "HP".
   iCombine "Hf" "HP" as "Hf".
-  rewrite -big_opM_opM big_opM_fmap; iApply (fupd_big_sepM _ _ f).
+  rewrite -big_sepM_sep big_opM_fmap; iApply (fupd_big_sepM _ _ f).
   iApply (@big_sepM_impl with "Hf").
   iIntros "!#" (γ b' ?) "[(Hγ' & #$ & #$) HΦ]".
   iInv N as (b) "[>Hγ _]".
@@ -227,7 +227,7 @@ Proof.
   iAssert (([∗ map] γ↦b ∈ f, ▷ Φ γ) ∗
     [∗ map] γ↦b ∈ f, box_own_auth γ (◯ Excl' false) ∗  box_own_prop γ (Φ γ) ∗
       inv N (slice_inv γ (Φ γ)))%I with "[> Hf]" as "[HΦ ?]".
-  { rewrite -big_opM_opM -fupd_big_sepM. iApply (@big_sepM_impl with "[$Hf]").
+  { rewrite -big_sepM_sep -fupd_big_sepM. iApply (@big_sepM_impl with "[$Hf]").
     iIntros "!#" (γ b ?) "(Hγ' & #HγΦ & #Hinv)".
     assert (true = b) as <- by eauto.
     iInv N as (b) "[>Hγ HΦ]".

theories/bi/big_op.v

@@ -132,10 +132,10 @@ Section sep_list.
     ([∗ list] k↦y ∈ f <$> l, Φ k y) ⊣⊢ ([∗ list] k↦y ∈ l, Φ k (f y)).
   Proof. by rewrite big_opL_fmap. Qed.
 
-  Lemma big_sepL_sepL Φ Ψ l :
+  Lemma big_sepL_sep Φ Ψ l :
     ([∗ list] k↦x ∈ l, Φ k x ∗ Ψ k x)
     ⊣⊢ ([∗ list] k↦x ∈ l, Φ k x) ∗ ([∗ list] k↦x ∈ l, Ψ k x).
-  Proof. by rewrite big_opL_opL. Qed.
+  Proof. by rewrite big_opL_op. Qed.
 
   Lemma big_sepL_and Φ Ψ l :
     ([∗ list] k↦x ∈ l, Φ k x ∧ Ψ k x)
@@ -392,11 +392,11 @@ Section sep_list2.
     by f_equiv; f_equiv=> k [??].
   Qed.
 
-  Lemma big_sepL2_sepL2 Φ Ψ l1 l2 :
+  Lemma big_sepL2_sep Φ Ψ l1 l2 :
     ([∗ list] k↦y1;y2 ∈ l1;l2, Φ k y1 y2 ∗ Ψ k y1 y2)
     ⊣⊢ ([∗ list] k↦y1;y2 ∈ l1;l2, Φ k y1 y2) ∗ ([∗ list] k↦y1;y2 ∈ l1;l2, Ψ k y1 y2).
   Proof.
-    rewrite !big_sepL2_alt big_sepL_sepL !persistent_and_affinely_sep_l.
+    rewrite !big_sepL2_alt big_sepL_sep !persistent_and_affinely_sep_l.
     rewrite -assoc (assoc _ _ (<affine> _)%I). rewrite -(comm bi_sep (<affine> _)%I).
     rewrite -assoc (assoc _ _ (<affine> _)%I) -!persistent_and_affinely_sep_l.
     by rewrite affinely_and_r persistent_and_affinely_sep_l idemp.
@@ -507,15 +507,10 @@ Section and_list.
     ([∧ list] k↦y ∈ f <$> l, Φ k y) ⊣⊢ ([∧ list] k↦y ∈ l, Φ k (f y)).
   Proof. by rewrite big_opL_fmap. Qed.
 
-  Lemma big_andL_andL Φ Ψ l :
-    ([∧ list] k↦x ∈ l, Φ k x ∧ Ψ k x)
-    ⊣⊢ ([∧ list] k↦x ∈ l, Φ k x) ∧ ([∧ list] k↦x ∈ l, Ψ k x).
-  Proof. by rewrite big_opL_opL. Qed.
-
   Lemma big_andL_and Φ Ψ l :
     ([∧ list] k↦x ∈ l, Φ k x ∧ Ψ k x)
-    ⊢ ([∧ list] k↦x ∈ l, Φ k x) ∧ ([∧ list] k↦x ∈ l, Ψ k x).
-  Proof. auto using and_intro, big_andL_mono, and_elim_l, and_elim_r. Qed.
+    ⊣⊢ ([∧ list] k↦x ∈ l, Φ k x) ∧ ([∧ list] k↦x ∈ l, Ψ k x).
+  Proof. by rewrite big_opL_op. Qed.
 
   Lemma big_andL_persistently Φ l :
     <pers> ([∧ list] k↦x ∈ l, Φ k x) ⊣⊢ [∧ list] k↦x ∈ l, <pers> (Φ k x).
@@ -667,10 +662,10 @@ Section map.
     ⊣⊢ ([∗ map] k↦y ∈ m1, Φ k y) ∗ ([∗ map] k↦y ∈ m2, Φ k y).
   Proof. apply big_opM_union. Qed.
 
-  Lemma big_sepM_sepM Φ Ψ m :
+  Lemma big_sepM_sep Φ Ψ m :
     ([∗ map] k↦x ∈ m, Φ k x ∗ Ψ k x)
     ⊣⊢ ([∗ map] k↦x ∈ m, Φ k x) ∗ ([∗ map] k↦x ∈ m, Ψ k x).
-  Proof. apply big_opM_opM. Qed.
+  Proof. apply big_opM_op. Qed.
 
   Lemma big_sepM_and Φ Ψ m :
     ([∗ map] k↦x ∈ m, Φ k x ∧ Ψ k x)
@@ -962,7 +957,7 @@ Section map2.
     ⊣⊢ ([∗ map] k↦y1;y2 ∈ m1;m2, Φ k y1 (g y2)).
   Proof. rewrite -{1}(map_fmap_id m1). apply big_sepM2_fmap. Qed.
 
-  Lemma big_sepM2_sepM2 Φ Ψ m1 m2 :
+  Lemma big_sepM2_sep Φ Ψ m1 m2 :
     ([∗ map] k↦y1;y2 ∈ m1;m2, Φ k y1 y2 ∗ Ψ k y1 y2)
     ⊣⊢ ([∗ map] k↦y1;y2 ∈ m1;m2, Φ k y1 y2) ∗ ([∗ map] k↦y1;y2 ∈ m1;m2, Ψ k y1 y2).
   Proof.
@@ -972,7 +967,7 @@ Section map2.
     rewrite !persistent_and_affinely_sep_l /=.
     rewrite -sep_assoc. apply sep_proper=>//.
     rewrite sep_assoc (sep_comm _ (<affine> _)%I) -sep_assoc.
-    apply sep_proper=>//. apply big_sepM_sepM.
+    apply sep_proper=>//. apply big_sepM_sep.
   Qed.
 
   Lemma big_sepM2_and Φ Ψ m1 m2 :
@@ -1148,9 +1143,9 @@ Section gset.
       (([∗ set] y ∈ Y, ⌜P y⌝ → Φ y) -∗ [∗ set] y ∈ X, Φ y).
   Proof. intros. setoid_rewrite <-decide_emp. by apply big_sepS_filter_acc'. Qed.
 
-  Lemma big_sepS_sepS Φ Ψ X :
+  Lemma big_sepS_sep Φ Ψ X :
     ([∗ set] y ∈ X, Φ y ∗ Ψ y) ⊣⊢ ([∗ set] y ∈ X, Φ y) ∗ ([∗ set] y ∈ X, Ψ y).
-  Proof. apply big_opS_opS. Qed.
+  Proof. apply big_opS_op. Qed.
 
   Lemma big_sepS_and Φ Ψ X :
     ([∗ set] y ∈ X, Φ y ∧ Ψ y) ⊢ ([∗ set] y ∈ X, Φ y) ∧ ([∗ set] y ∈ X, Ψ y).
@@ -1256,9 +1251,9 @@ Section gmultiset.
   Lemma big_sepMS_singleton Φ x : ([∗ mset] y ∈ {[ x ]}, Φ y) ⊣⊢ Φ x.
   Proof. apply big_opMS_singleton. Qed.
 
-  Lemma big_sepMS_sepMS Φ Ψ X :
+  Lemma big_sepMS_sep Φ Ψ X :
     ([∗ mset] y ∈ X, Φ y ∗ Ψ y) ⊣⊢ ([∗ mset] y ∈ X, Φ y) ∗ ([∗ mset] y ∈ X, Ψ y).
-  Proof. apply big_opMS_opMS. Qed.
+  Proof. apply big_opMS_op. Qed.
 
   Lemma big_sepMS_and Φ Ψ X :
     ([∗ mset] y ∈ X, Φ y ∧ Ψ y) ⊢ ([∗ mset] y ∈ X, Φ y) ∧ ([∗ mset] y ∈ X, Ψ y).

theories/bi/lib/fractional.v

@@ -64,22 +64,22 @@ Section fractional.
   Global Instance fractional_big_sepL {A} l Ψ :
     (∀ k (x : A), Fractional (Ψ k x)) →
     Fractional (PROP:=PROP) (λ q, [∗ list] k↦x ∈ l, Ψ k x q)%I.
-  Proof. intros ? q q'. rewrite -big_opL_opL. by setoid_rewrite fractional. Qed.
+  Proof. intros ? q q'. rewrite -big_sepL_sep. 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 (PROP:=PROP) (λ q, [∗ map] k↦x ∈ m, Ψ k x q)%I.
-  Proof. intros ? q q'. rewrite -big_opM_opM. by setoid_rewrite fractional. Qed.
+  Proof. intros ? q q'. rewrite -big_sepM_sep. by setoid_rewrite fractional. Qed.
 
   Global Instance fractional_big_sepS `{Countable A} (X : gset A) Ψ :
     (∀ x, Fractional (Ψ x)) →
     Fractional (PROP:=PROP) (λ q, [∗ set] x ∈ X, Ψ x q)%I.
-  Proof. intros ? q q'. rewrite -big_opS_opS. by setoid_rewrite fractional. Qed.
+  Proof. intros ? q q'. rewrite -big_sepS_sep. by setoid_rewrite fractional. Qed.
 
   Global Instance fractional_big_sepMS `{Countable A} (X : gmultiset A) Ψ :
     (∀ x, Fractional (Ψ x)) →
     Fractional (PROP:=PROP) (λ q, [∗ mset] x ∈ X, Ψ x q)%I.
-  Proof. intros ? q q'. rewrite -big_opMS_opMS. by setoid_rewrite fractional. Qed.
+  Proof. intros ? q q'. rewrite -big_sepMS_sep. by setoid_rewrite fractional. Qed.
 
   (** Mult instances *)