Put `LeibnizEquiv` lemmas for `dom` in section.

theories/fin_map_dom.v

@@ -142,32 +142,34 @@ Global Instance dom_proper_L `{!Equiv A, !LeibnizEquiv D} :
   Proper ((≡@{M A}) ==> (=)) (dom D) | 0.
 Proof. intros ???. unfold_leibniz. by apply dom_proper. Qed.
 
-Context `{!LeibnizEquiv D}.
-Lemma dom_map_filter_L {A} (P : K * A → Prop) `{!∀ x, Decision (P x)} (m : M A) X :
-  (∀ i, i ∈ X ↔ ∃ x, m !! i = Some x ∧ P (i, x)) →
-  dom D (filter P m) = X.
-Proof. unfold_leibniz. apply dom_map_filter. Qed.
-Lemma dom_empty_L {A} : dom D (@empty (M A) _) = ∅.
-Proof. unfold_leibniz; apply dom_empty. Qed.
-Lemma dom_empty_inv_L {A} (m : M A) : dom D m = ∅ → m = ∅.
-Proof. by intros; apply dom_empty_inv; unfold_leibniz. Qed.
-Lemma dom_alter_L {A} f (m : M A) i : dom D (alter f i m) = dom D m.
-Proof. unfold_leibniz; apply dom_alter. Qed.
-Lemma dom_insert_L {A} (m : M A) i x : dom D (<[i:=x]>m) = {[ i ]} ∪ dom D m.
-Proof. unfold_leibniz; apply dom_insert. Qed.
-Lemma dom_singleton_L {A} (i : K) (x : A) : dom D ({[i := x]} : M A) = {[ i ]}.
-Proof. unfold_leibniz; apply dom_singleton. Qed.
-Lemma dom_delete_L {A} (m : M A) i : dom D (delete i m) = dom D m ∖ {[ i ]}.
-Proof. unfold_leibniz; apply dom_delete. Qed.
-Lemma dom_union_L {A} (m1 m2 : M A) : dom D (m1 ∪ m2) = dom D m1 ∪ dom D m2.
-Proof. unfold_leibniz; apply dom_union. Qed.
-Lemma dom_intersection_L {A} (m1 m2 : M A) :
-  dom D (m1 ∩ m2) = dom D m1 ∩ dom D m2.
-Proof. unfold_leibniz; apply dom_intersection. Qed.
-Lemma dom_difference_L {A} (m1 m2 : M A) : dom D (m1 ∖ m2) = dom D m1 ∖ dom D m2.
-Proof. unfold_leibniz; apply dom_difference. Qed.
-Lemma dom_fmap_L {A B} (f : A → B) (m : M A) : dom D (f <$> m) = dom D m.
-Proof. unfold_leibniz; apply dom_fmap. Qed.
+Section leibniz.
+  Context `{!LeibnizEquiv D}.
+  Lemma dom_map_filter_L {A} (P : K * A → Prop) `{!∀ x, Decision (P x)} (m : M A) X :
+    (∀ i, i ∈ X ↔ ∃ x, m !! i = Some x ∧ P (i, x)) →
+    dom D (filter P m) = X.
+  Proof. unfold_leibniz. apply dom_map_filter. Qed.
+  Lemma dom_empty_L {A} : dom D (@empty (M A) _) = ∅.
+  Proof. unfold_leibniz; apply dom_empty. Qed.
+  Lemma dom_empty_inv_L {A} (m : M A) : dom D m = ∅ → m = ∅.
+  Proof. by intros; apply dom_empty_inv; unfold_leibniz. Qed.
+  Lemma dom_alter_L {A} f (m : M A) i : dom D (alter f i m) = dom D m.
+  Proof. unfold_leibniz; apply dom_alter. Qed.
+  Lemma dom_insert_L {A} (m : M A) i x : dom D (<[i:=x]>m) = {[ i ]} ∪ dom D m.
+  Proof. unfold_leibniz; apply dom_insert. Qed.
+  Lemma dom_singleton_L {A} (i : K) (x : A) : dom D ({[i := x]} : M A) = {[ i ]}.
+  Proof. unfold_leibniz; apply dom_singleton. Qed.
+  Lemma dom_delete_L {A} (m : M A) i : dom D (delete i m) = dom D m ∖ {[ i ]}.
+  Proof. unfold_leibniz; apply dom_delete. Qed.
+  Lemma dom_union_L {A} (m1 m2 : M A) : dom D (m1 ∪ m2) = dom D m1 ∪ dom D m2.
+  Proof. unfold_leibniz; apply dom_union. Qed.
+  Lemma dom_intersection_L {A} (m1 m2 : M A) :
+    dom D (m1 ∩ m2) = dom D m1 ∩ dom D m2.
+  Proof. unfold_leibniz; apply dom_intersection. Qed.
+  Lemma dom_difference_L {A} (m1 m2 : M A) : dom D (m1 ∖ m2) = dom D m1 ∖ dom D m2.
+  Proof. unfold_leibniz; apply dom_difference. Qed.
+  Lemma dom_fmap_L {A B} (f : A → B) (m : M A) : dom D (f <$> m) = dom D m.
+  Proof. unfold_leibniz; apply dom_fmap. Qed.
+End leibniz.
 End fin_map_dom.
 
 Lemma dom_seq `{FinMapDom nat M D} {A} start (xs : list A) :