Rename preserving -> mono.

To be consistent with Iris, see Iris commit 9ee62b3a.

theories/collections.v

@@ -346,11 +346,11 @@ Section simple_collection.
   Proof. set_solver. Qed.
   Lemma elem_of_union_r x X Y : x ∈ Y → x ∈ X ∪ Y.
   Proof. set_solver. Qed.
-  Lemma union_preserving_l X Y1 Y2 : Y1 ⊆ Y2 → X ∪ Y1 ⊆ X ∪ Y2.
+  Lemma union_mono_l X Y1 Y2 : Y1 ⊆ Y2 → X ∪ Y1 ⊆ X ∪ Y2.
   Proof. set_solver. Qed.
-  Lemma union_preserving_r X1 X2 Y : X1 ⊆ X2 → X1 ∪ Y ⊆ X2 ∪ Y.
+  Lemma union_mono_r X1 X2 Y : X1 ⊆ X2 → X1 ∪ Y ⊆ X2 ∪ Y.
   Proof. set_solver. Qed.
-  Lemma union_preserving X1 X2 Y1 Y2 : X1 ⊆ X2 → Y1 ⊆ Y2 → X1 ∪ Y1 ⊆ X2 ∪ Y2.
+  Lemma union_mono X1 X2 Y1 Y2 : X1 ⊆ X2 → Y1 ⊆ Y2 → X1 ∪ Y1 ⊆ X2 ∪ Y2.
   Proof. set_solver. Qed.
 
   Global Instance union_idemp : IdemP ((≡) : relation C) (∪).
@@ -444,8 +444,8 @@ Section simple_collection.
     by rewrite reverse_cons, union_list_app,
       union_list_singleton, (comm _), IH.
   Qed.
-  Lemma union_list_preserving Xs Ys : Xs ⊆* Ys → ⋃ Xs ⊆ ⋃ Ys.
-  Proof. induction 1; simpl; auto using union_preserving. Qed.
+  Lemma union_list_mono Xs Ys : Xs ⊆* Ys → ⋃ Xs ⊆ ⋃ Ys.
+  Proof. induction 1; simpl; auto using union_mono. Qed.
   Lemma empty_union_list Xs : ⋃ Xs ≡ ∅ ↔ Forall (≡ ∅) Xs.
   Proof.
     split.
@@ -565,11 +565,11 @@ Section collection.
   Lemma intersection_greatest X Y Z : Z ⊆ X → Z ⊆ Y → Z ⊆ X ∩ Y.
   Proof. set_solver. Qed.
 
-  Lemma intersection_preserving_l X Y1 Y2 : Y1 ⊆ Y2 → X ∩ Y1 ⊆ X ∩ Y2.
+  Lemma intersection_mono_l X Y1 Y2 : Y1 ⊆ Y2 → X ∩ Y1 ⊆ X ∩ Y2.
   Proof. set_solver. Qed.
-  Lemma intersection_preserving_r X1 X2 Y : X1 ⊆ X2 → X1 ∩ Y ⊆ X2 ∩ Y.
+  Lemma intersection_mono_r X1 X2 Y : X1 ⊆ X2 → X1 ∩ Y ⊆ X2 ∩ Y.
   Proof. set_solver. Qed.
-  Lemma intersection_preserving X1 X2 Y1 Y2 :
+  Lemma intersection_mono X1 X2 Y1 Y2 :
     X1 ⊆ X2 → Y1 ⊆ Y2 → X1 ∩ Y1 ⊆ X2 ∩ Y2.
   Proof. set_solver. Qed.
 
@@ -612,12 +612,12 @@ Section collection.
   Lemma difference_disjoint X Y : X ⊥ Y → X ∖ Y ≡ X.
   Proof. set_solver. Qed.
 
-  Lemma difference_preserving X1 X2 Y1 Y2 :
+  Lemma difference_mono X1 X2 Y1 Y2 :
     X1 ⊆ X2 → Y2 ⊆ Y1 → X1 ∖ Y1 ⊆ X2 ∖ Y2.
   Proof. set_solver. Qed.
-  Lemma difference_preserving_l X Y1 Y2 : Y2 ⊆ Y1 → X ∖ Y1 ⊆ X ∖ Y2.
+  Lemma difference_mono_l X Y1 Y2 : Y2 ⊆ Y1 → X ∖ Y1 ⊆ X ∖ Y2.
   Proof. set_solver. Qed.
-  Lemma difference_preserving_r X1 X2 Y : X1 ⊆ X2 → X1 ∖ Y ⊆ X2 ∖ Y.
+  Lemma difference_mono_r X1 X2 Y : X1 ⊆ X2 → X1 ∖ Y ⊆ X2 ∖ Y.
   Proof. set_solver. Qed.
 
   (** Disjointness *)

theories/fin_maps.v

@@ -1322,17 +1322,17 @@ Proof. intros. trans m2; auto using map_union_subseteq_l. Qed.
 Lemma map_union_subseteq_r_alt {A} (m1 m2 m3 : M A) :
   m2 ⊥ₘ m3 → m1 ⊆ m3 → m1 ⊆ m2 ∪ m3.
 Proof. intros. trans m3; auto using map_union_subseteq_r. Qed.
-Lemma map_union_preserving_l {A} (m1 m2 m3 : M A) : m1 ⊆ m2 → m3 ∪ m1 ⊆ m3 ∪ m2.
+Lemma map_union_mono_l {A} (m1 m2 m3 : M A) : m1 ⊆ m2 → m3 ∪ m1 ⊆ m3 ∪ m2.
 Proof.
   rewrite !map_subseteq_spec. intros ???.
   rewrite !lookup_union_Some_raw. naive_solver.
 Qed.
-Lemma map_union_preserving_r {A} (m1 m2 m3 : M A) :
+Lemma map_union_mono_r {A} (m1 m2 m3 : M A) :
   m2 ⊥ₘ m3 → m1 ⊆ m2 → m1 ∪ m3 ⊆ m2 ∪ m3.
 Proof.
   intros. rewrite !(map_union_comm _ m3)
     by eauto using map_disjoint_weaken_l.
-  by apply map_union_preserving_l.
+  by apply map_union_mono_l.
 Qed.
 Lemma map_union_reflecting_l {A} (m1 m2 m3 : M A) :
   m3 ⊥ₘ m1 → m3 ⊥ₘ m2 → m3 ∪ m1 ⊆ m3 ∪ m2 → m1 ⊆ m2.

theories/gmultiset.v

@@ -288,12 +288,12 @@ Lemma gmultiset_union_subseteq_l X Y : X ⊆ X ∪ Y.
 Proof. intros x. rewrite multiplicity_union. omega. Qed.
 Lemma gmultiset_union_subseteq_r X Y : Y ⊆ X ∪ Y.
 Proof. intros x. rewrite multiplicity_union. omega. Qed.
-Lemma gmultiset_union_preserving X1 X2 Y1 Y2 : X1 ⊆ X2 → Y1 ⊆ Y2 → X1 ∪ Y1 ⊆ X2 ∪ Y2.
+Lemma gmultiset_union_mono X1 X2 Y1 Y2 : X1 ⊆ X2 → Y1 ⊆ Y2 → X1 ∪ Y1 ⊆ X2 ∪ Y2.
 Proof. intros ?? x. rewrite !multiplicity_union. by apply Nat.add_le_mono. Qed.
-Lemma gmultiset_union_preserving_l X Y1 Y2 : Y1 ⊆ Y2 → X ∪ Y1 ⊆ X ∪ Y2.
-Proof. intros. by apply gmultiset_union_preserving. Qed.
-Lemma gmultiset_union_preserving_r X1 X2 Y : X1 ⊆ X2 → X1 ∪ Y ⊆ X2 ∪ Y.
-Proof. intros. by apply gmultiset_union_preserving. Qed.
+Lemma gmultiset_union_mono_l X Y1 Y2 : Y1 ⊆ Y2 → X ∪ Y1 ⊆ X ∪ Y2.
+Proof. intros. by apply gmultiset_union_mono. Qed.
+Lemma gmultiset_union_mono_r X1 X2 Y : X1 ⊆ X2 → X1 ∪ Y ⊆ X2 ∪ Y.
+Proof. intros. by apply gmultiset_union_mono. Qed.
 
 Lemma gmultiset_subset X Y : X ⊆ Y → size X < size Y → X ⊂ Y.
 Proof. intros. apply strict_spec_alt; split; naive_solver auto with omega. Qed.