Notations `⊆@{A}` and `⊂@{A}`.

theories/base.v

@@ -812,6 +812,10 @@ Notation "X ⊈ Y" := (¬X ⊆ Y) (at level 70) : stdpp_scope.
 Notation "(⊈)" := (λ X Y, X ⊈ Y) (only parsing) : stdpp_scope.
 Notation "( X ⊈)" := (λ Y, X ⊈ Y) (only parsing) : stdpp_scope.
 Notation "(⊈ X )" := (λ Y, Y ⊈ X) (only parsing) : stdpp_scope.
+
+Infix "⊆@{ A }" := (@subseteq A _) (at level 70, only parsing) : stdpp_scope.
+Notation "(⊆@{ A } )" := (@subseteq A _) (only parsing) : stdpp_scope.
+
 Infix "⊆*" := (Forall2 (⊆)) (at level 70) : stdpp_scope.
 Notation "(⊆*)" := (Forall2 (⊆)) (only parsing) : stdpp_scope.
 Infix "⊆**" := (Forall2 (⊆*)) (at level 70) : stdpp_scope.
@@ -833,6 +837,9 @@ Notation "(⊄)" := (λ X Y, X ⊄ Y) (only parsing) : stdpp_scope.
 Notation "( X ⊄)" := (λ Y, X ⊄ Y) (only parsing) : stdpp_scope.
 Notation "(⊄ X )" := (λ Y, Y ⊄ X) (only parsing) : stdpp_scope.
 
+Infix "⊂@{ A }" := (strict (⊆@{A})) (at level 70, only parsing) : stdpp_scope.
+Notation "(⊂@{ A } )" := (strict (⊆@{A})) (only parsing) : stdpp_scope.
+
 Notation "X ⊆ Y ⊆ Z" := (X ⊆ Y ∧ Y ⊆ Z) (at level 70, Y at next level) : stdpp_scope.
 Notation "X ⊆ Y ⊂ Z" := (X ⊆ Y ∧ Y ⊂ Z) (at level 70, Y at next level) : stdpp_scope.
 Notation "X ⊂ Y ⊆ Z" := (X ⊂ Y ∧ Y ⊆ Z) (at level 70, Y at next level) : stdpp_scope.

theories/coPset.v

@@ -199,7 +199,7 @@ Proof.
  refine (λ X Y, cast_if (decide (X ∩ Y = ∅)));
   abstract (by rewrite disjoint_intersection_L).
 Defined.
-Instance mapset_subseteq_dec : RelDecision (@subseteq coPset _).
+Instance mapset_subseteq_dec : RelDecision (⊆@{coPset}).
 Proof.
  refine (λ X Y, cast_if (decide (X ∪ Y = Y))); abstract (by rewrite subseteq_union_L).
 Defined.

theories/collections.v

@@ -315,10 +315,10 @@ Section simple_collection.
   Proof. set_solver. Qed.
 
   (** Subset relation *)
-  Global Instance collection_subseteq_antisymm: AntiSymm (≡) ((⊆) : relation C).
+  Global Instance collection_subseteq_antisymm: AntiSymm (≡) (⊆@{C}).
   Proof. intros ??. set_solver. Qed.
 
-  Global Instance collection_subseteq_preorder: PreOrder ((⊆) : relation C).
+  Global Instance collection_subseteq_preorder: PreOrder (⊆@{C}).
   Proof. split. by intros ??. intros ???; set_solver. Qed.
 
   Lemma subseteq_union X Y : X ⊆ Y ↔ X ∪ Y ≡ Y.
@@ -467,8 +467,7 @@ Section simple_collection.
     Proof. unfold_leibniz. apply collection_equiv_spec. Qed.
 
     (** Subset relation *)
-    Global Instance collection_subseteq_partialorder :
-      PartialOrder ((⊆) : relation C).
+    Global Instance collection_subseteq_partialorder : PartialOrder (⊆@{C}).
     Proof. split. apply _. intros ??. unfold_leibniz. apply (anti_symm _). Qed.
 
     Lemma subseteq_union_L X Y : X ⊆ Y ↔ X ∪ Y = Y.

theories/fin_collections.v

@@ -149,7 +149,7 @@ Proof.
 Qed.
 
 (** * Induction principles *)
-Lemma collection_wf : wf (strict (@subseteq C _)).
+Lemma collection_wf : wf (⊂@{C}).
 Proof. apply (wf_projected (<) size); auto using subset_size, lt_wf. Qed.
 Lemma collection_ind (P : C → Prop) :
   Proper ((≡) ==> iff) P →

theories/fin_maps.v

@@ -224,7 +224,7 @@ Proof.
   destruct (m1 !! i), (m2 !! i), (m3 !! i); simplify_eq/=;
     done || etrans; eauto.
 Qed.
-Global Instance map_subseteq_po : PartialOrder ((⊆) : relation (M A)).
+Global Instance map_subseteq_po : PartialOrder (⊆@{M A}).
 Proof.
   split; [apply _|].
   intros m1 m2; rewrite !map_subseteq_spec.
@@ -965,7 +965,7 @@ Proof.
   destruct (insert_subset_inv m m2 i x) as (m2'&?&?&?); auto; subst.
   rewrite !map_to_list_insert; simpl; auto with arith.
 Qed.
-Lemma map_wf {A} : wf (strict (@subseteq (M A) _)).
+Lemma map_wf {A} : wf (⊂@{M A}).
 Proof.
   apply (wf_projected (<) (length ∘ map_to_list)).
   - by apply map_to_list_length.
@@ -1596,13 +1596,13 @@ Lemma map_union_cancel_l {A} (m1 m2 m3 : M A) :
   m1 ##ₘ m3 → m2 ##ₘ m3 → m3 ∪ m1 = m3 ∪ m2 → m1 = m2.
 Proof.
   intros. apply (anti_symm (⊆)); apply map_union_reflecting_l with m3;
-    auto using (reflexive_eq (R:=@subseteq (M A) _)).
+    auto using (reflexive_eq (R:=(⊆@{M A}))).
 Qed.
 Lemma map_union_cancel_r {A} (m1 m2 m3 : M A) :
   m1 ##ₘ m3 → m2 ##ₘ m3 → m1 ∪ m3 = m2 ∪ m3 → m1 = m2.
 Proof.
   intros. apply (anti_symm (⊆)); apply map_union_reflecting_r with m3;
-    auto using (reflexive_eq (R:=@subseteq (M A) _)).
+    auto using (reflexive_eq (R:=(⊆@{M A}))).
 Qed.
 Lemma map_disjoint_union_l {A} (m1 m2 m3 : M A) :
   m1 ∪ m2 ##ₘ m3 ↔ m1 ##ₘ m3 ∧ m2 ##ₘ m3.

theories/gmultiset.v

@@ -231,7 +231,7 @@ Proof.
 Qed.
 
 (* Order stuff *)
-Global Instance gmultiset_po : PartialOrder (@subseteq (gmultiset A) _).
+Global Instance gmultiset_po : PartialOrder (⊆@{gmultiset A}).
 Proof.
   split; [split|].
   - by intros X x.
@@ -246,7 +246,7 @@ Proof.
   apply forall_proper; intros x. unfold multiplicity.
   destruct (gmultiset_car X !! x), (gmultiset_car Y !! x); naive_solver omega.
 Qed.
-Global Instance gmultiset_subseteq_dec : RelDecision (@subseteq (gmultiset A) _).
+Global Instance gmultiset_subseteq_dec : RelDecision (⊆@{gmultiset A}).
 Proof.
  refine (λ X Y, cast_if (decide (map_relation (≤)
    (λ _, False) (λ _, True) (gmultiset_car X) (gmultiset_car Y))));
@@ -342,7 +342,7 @@ Proof.
 Qed.
 
 (* Well-foundedness *)
-Lemma gmultiset_wf : wf (strict (@subseteq (gmultiset A) _)).
+Lemma gmultiset_wf : wf (⊂@{gmultiset A}).
 Proof.
   apply (wf_projected (<) size); auto using gmultiset_subset_size, lt_wf.
 Qed.

theories/list.v

@@ -2124,7 +2124,7 @@ Section submseteq_dec.
 End submseteq_dec.
 
 (** ** Properties of [included] *)
-Global Instance list_subseteq_po : PreOrder (@subseteq (list A) _).
+Global Instance list_subseteq_po : PreOrder (⊆@{list A}).
 Proof. split; firstorder. Qed.
 Lemma list_subseteq_nil l : [] ⊆ l.
 Proof. intros x. by rewrite elem_of_nil. Qed.

theories/mapset.v

@@ -85,7 +85,7 @@ Section deciders.
    refine (λ X1 X2, cast_if (decide (X1 ∩ X2 = ∅)));
     abstract (by rewrite disjoint_intersection_L).
   Defined.
-  Global Instance mapset_subseteq_dec : RelDecision (@subseteq (mapset M) _).
+  Global Instance mapset_subseteq_dec : RelDecision (⊆@{mapset M}).
   Proof.
    refine (λ X1 X2, cast_if (decide (X1 ∪ X2 = X2)));
     abstract (by rewrite subseteq_union_L).