Test changes

theories/algebra/big_op.v

@@ -28,42 +28,42 @@ Fixpoint big_opL `{Monoid M o} {A} (f : nat → A → M) (xs : list A) : M :=
 Instance: Params (@big_opL) 4 := {}.
 Arguments big_opL {M} o {_ A} _ !_ /.
 Typeclasses Opaque big_opL.
-Notation "'[^' o 'list]' k ↦ x ∈ l , P" := (big_opL o (λ k x, P) l)
+Notation "'[' '^' o 'list]' k ↦ x ∈ l , P" := (big_opL o (λ k x, P) l)
   (at level 200, o at level 1, l at level 10, k, x at level 1, right associativity,
-   format "[^ o  list]  k ↦ x  ∈  l ,  P") : stdpp_scope.
-Notation "'[^' o 'list]' x ∈ l , P" := (big_opL o (λ _ x, P) l)
+   format "[ ^ o  list]  k ↦ x  ∈  l ,  P") : stdpp_scope.
+Notation "'[' '^' o 'list]' x ∈ l , P" := (big_opL o (λ _ x, P) l)
   (at level 200, o at level 1, l at level 10, x at level 1, right associativity,
-   format "[^ o  list]  x  ∈  l ,  P") : stdpp_scope.
+   format "[ ^ o  list]  x  ∈  l ,  P") : stdpp_scope.
 
 Definition big_opM `{Monoid M o} `{Countable K} {A} (f : K → A → M)
     (m : gmap K A) : M := big_opL o (λ _, curry f) (map_to_list m).
 Instance: Params (@big_opM) 7 := {}.
 Arguments big_opM {M} o {_ K _ _ A} _ _ : simpl never.
 Typeclasses Opaque big_opM.
-Notation "'[^' o 'map]' k ↦ x ∈ m , P" := (big_opM o (λ k x, P) m)
+Notation "'[' '^' o 'map]' k ↦ x ∈ m , P" := (big_opM o (λ k x, P) m)
   (at level 200, o at level 1, m at level 10, k, x at level 1, right associativity,
-   format "[^  o  map]  k ↦ x  ∈  m ,  P") : stdpp_scope.
-Notation "'[^' o 'map]' x ∈ m , P" := (big_opM o (λ _ x, P) m)
+   format "[ ^  o  map]  k ↦ x  ∈  m ,  P") : stdpp_scope.
+Notation "'[' '^' o 'map]' x ∈ m , P" := (big_opM o (λ _ x, P) m)
   (at level 200, o at level 1, m at level 10, x at level 1, right associativity,
-   format "[^ o  map]  x  ∈  m ,  P") : stdpp_scope.
+   format "[ ^ o  map]  x  ∈  m ,  P") : stdpp_scope.
 
 Definition big_opS `{Monoid M o} `{Countable A} (f : A → M)
   (X : gset A) : M := big_opL o (λ _, f) (elements X).
 Instance: Params (@big_opS) 6 := {}.
 Arguments big_opS {M} o {_ A _ _} _ _ : simpl never.
 Typeclasses Opaque big_opS.
-Notation "'[^' o 'set]' x ∈ X , P" := (big_opS o (λ x, P) X)
+Notation "'[' '^' o 'set]' x ∈ X , P" := (big_opS o (λ x, P) X)
   (at level 200, o at level 1, X at level 10, x at level 1, right associativity,
-   format "[^ o  set]  x  ∈  X ,  P") : stdpp_scope.
+   format "[ ^ o  set]  x  ∈  X ,  P") : stdpp_scope.
 
 Definition big_opMS `{Monoid M o} `{Countable A} (f : A → M)
   (X : gmultiset A) : M := big_opL o (λ _, f) (elements X).
 Instance: Params (@big_opMS) 7 := {}.
 Arguments big_opMS {M} o {_ A _ _} _ _ : simpl never.
 Typeclasses Opaque big_opMS.
-Notation "'[^' o 'mset]' x ∈ X , P" := (big_opMS o (λ x, P) X)
+Notation "'[' '^' o 'mset]' x ∈ X , P" := (big_opMS o (λ x, P) X)
   (at level 200, o at level 1, X at level 10, x at level 1, right associativity,
-   format "[^ o  mset]  x  ∈  X ,  P") : stdpp_scope.
+   format "[ ^ o  mset]  x  ∈  X ,  P") : stdpp_scope.
 
 (** * Properties about big ops *)
 Section big_op.
@@ -80,7 +80,7 @@ Section list.
   Lemma big_opL_nil f : ([^o list] k↦y ∈ [], f k y) = monoid_unit.
   Proof. done. Qed.
   Lemma big_opL_cons f x l :
-    ([^o list] k↦y ∈ x :: l, f k y) = f 0 x `o` [^o list] k↦y ∈ l, f (S k) y.
+    ([^o list] k↦y ∈ x :: l, f k y) = f 0 x `o` ([^o list] k↦y ∈ l, f (S k) y).
   Proof. done. Qed.
   Lemma big_opL_singleton f x : ([^o list] k↦y ∈ [x], f k y) ≡ f 0 x.
   Proof. by rewrite /= right_id. Qed.
@@ -106,7 +106,7 @@ Section list.
 
   Lemma big_opL_ext f g l :
     (∀ k y, l !! k = Some y → f k y = g k y) →
-    ([^o list] k ↦ y ∈ l, f k y) = [^o list] k ↦ y ∈ l, g k y.
+    ([^o list] k ↦ y ∈ l, f k y) = ([^o list] k ↦ y ∈ l, g k y).
   Proof. apply big_opL_forall; apply _. Qed.
   Lemma big_opL_proper f g l :
     (∀ k y, l !! k = Some y → f k y ≡ g k y) →
@@ -135,10 +135,10 @@ Section list.
   Proof. intros f f' Hf l ? <-. apply big_opL_forall; apply _ || intros; apply Hf. Qed.
 
   Lemma big_opL_consZ_l (f : Z → A → M) x l :
-    ([^o list] k↦y ∈ x :: l, f k y) = f 0 x `o` [^o list] k↦y ∈ l, f (1 + k)%Z y.
+    ([^o list] k↦y ∈ x :: l, f k y) = f 0 x `o` ([^o list] k↦y ∈ l, f (1 + k)%Z y).
   Proof. rewrite big_opL_cons. auto using big_opL_ext with f_equal lia. Qed.
   Lemma big_opL_consZ_r (f : Z → A → M) x l :
-    ([^o list] k↦y ∈ x :: l, f k y) = f 0 x `o` [^o list] k↦y ∈ l, f (k + 1)%Z y.
+    ([^o list] k↦y ∈ x :: l, f k y) = f 0 x `o` ([^o list] k↦y ∈ l, f (k + 1)%Z y).
   Proof. rewrite big_opL_cons. auto using big_opL_ext with f_equal lia. Qed.
 
   Lemma big_opL_fmap {B} (h : A → B) (f : nat → B → M) l :
@@ -198,12 +198,12 @@ Section gmap.
 
   Lemma big_opM_insert f m i x :
     m !! i = None →
-    ([^o map] k↦y ∈ <[i:=x]> m, f k y) ≡ f i x `o` [^o map] k↦y ∈ m, f k y.
+    ([^o map] k↦y ∈ <[i:=x]> m, f k y) ≡ f i x `o` ([^o map] k↦y ∈ m, f k y).
   Proof. intros ?. by rewrite /big_opM map_to_list_insert. Qed.
 
   Lemma big_opM_delete f m i x :
     m !! i = Some x →
-    ([^o map] k↦y ∈ m, f k y) ≡ f i x `o` [^o map] k↦y ∈ delete i m, f k y.
+    ([^o map] k↦y ∈ m, f k y) ≡ f i x `o` ([^o map] k↦y ∈ delete i m, f k y).
   Proof.
     intros. rewrite -big_opM_insert ?lookup_delete //.
     by rewrite insert_delete insert_id.
@@ -236,7 +236,7 @@ Section gmap.
   Lemma big_opM_fn_insert {B} (g : K → A → B → M) (f : K → B) m i (x : A) b :
     m !! i = None →
     ([^o map] k↦y ∈ <[i:=x]> m, g k y (<[i:=b]> f k))
-    ≡ g i x b `o` [^o map] k↦y ∈ m, g k y (f k).
+    ≡ g i x b `o` ([^o map] k↦y ∈ m, g k y (f k)).
   Proof.
     intros. rewrite big_opM_insert // fn_lookup_insert.
     f_equiv; apply big_opM_proper; auto=> k y ?.
@@ -244,7 +244,7 @@ Section gmap.
   Qed.
   Lemma big_opM_fn_insert' (f : K → M) m i x P :
     m !! i = None →
-    ([^o map] k↦y ∈ <[i:=x]> m, <[i:=P]> f k) ≡ (P `o` [^o map] k↦y ∈ m, f k).
+    ([^o map] k↦y ∈ <[i:=x]> m, <[i:=P]> f k) ≡ (P `o` ([^o map] k↦y ∈ m, f k)).
   Proof. apply (big_opM_fn_insert (λ _ _, id)). Qed.
 
   Lemma big_opM_union f m1 m2 :
@@ -301,19 +301,19 @@ Section gset.
   Proof. by rewrite /big_opS elements_empty. Qed.
 
   Lemma big_opS_insert f X x :
-    x ∉ X → ([^o set] y ∈ {[ x ]} ∪ X, f y) ≡ (f x `o` [^o set] y ∈ X, f y).
+    x ∉ X → ([^o set] y ∈ {[ x ]} ∪ X, f y) ≡ (f x `o` ([^o set] y ∈ X, f y)).
   Proof. intros. by rewrite /big_opS elements_union_singleton. Qed.
   Lemma big_opS_fn_insert {B} (f : A → B → M) h X x b :
     x ∉ X →
     ([^o set] y ∈ {[ x ]} ∪ X, f y (<[x:=b]> h y))
-    ≡ f x b `o` [^o set] y ∈ X, f y (h y).
+    ≡ f x b `o` ([^o set] y ∈ X, f y (h y)).
   Proof.
     intros. rewrite big_opS_insert // fn_lookup_insert.
     f_equiv; apply big_opS_proper; auto=> y ?.
     by rewrite fn_lookup_insert_ne; last set_solver.
   Qed.
   Lemma big_opS_fn_insert' f X x P :
-    x ∉ X → ([^o set] y ∈ {[ x ]} ∪ X, <[x:=P]> f y) ≡ (P `o` [^o set] y ∈ X, f y).
+    x ∉ X → ([^o set] y ∈ {[ x ]} ∪ X, <[x:=P]> f y) ≡ (P `o` ([^o set] y ∈ X, f y)).
   Proof. apply (big_opS_fn_insert (λ y, id)). Qed.
 
   Lemma big_opS_union f X Y :
@@ -327,7 +327,7 @@ Section gset.
   Qed.
 
   Lemma big_opS_delete f X x :
-    x ∈ X → ([^o set] y ∈ X, f y) ≡ f x `o` [^o set] y ∈ X ∖ {[ x ]}, f y.
+    x ∈ X → ([^o set] y ∈ X, f y) ≡ f x `o` ([^o set] y ∈ X ∖ {[ x ]}, f y).
   Proof.
     intros. rewrite -big_opS_insert; last set_solver.
     by rewrite -union_difference_L; last set_solver.
@@ -388,7 +388,7 @@ Section gmultiset.
   Proof. by rewrite /big_opMS gmultiset_elements_empty. Qed.
 
   Lemma big_opMS_disj_union f X Y :
-    ([^o mset] y ∈ X ⊎ Y, f y) ≡ ([^o mset] y ∈ X, f y) `o` [^o mset] y ∈ Y, f y.
+    ([^o mset] y ∈ X ⊎ Y, f y) ≡ ([^o mset] y ∈ X, f y) `o` ([^o mset] y ∈ Y, f y).
   Proof. by rewrite /big_opMS gmultiset_elements_disj_union big_opL_app. Qed.
 
   Lemma big_opMS_singleton f x : ([^o mset] y ∈ {[ x ]}, f y) ≡ f x.
@@ -397,7 +397,7 @@ Section gmultiset.
   Qed.
 
   Lemma big_opMS_delete f X x :
-    x ∈ X → ([^o mset] y ∈ X, f y) ≡ f x `o` [^o mset] y ∈ X ∖ {[ x ]}, f y.
+    x ∈ X → ([^o mset] y ∈ X, f y) ≡ f x `o` ([^o mset] y ∈ X ∖ {[ x ]}, f y).
   Proof.
     intros. rewrite -big_opMS_singleton -big_opMS_disj_union.
     by rewrite -gmultiset_disj_union_difference'.