Renaming in prelude/list.

Rename:

- prefix_of -> prefix and suffix_of -> suffix because that saves keystrokes
  in lemma names. However, keep the infix notations with l1 `prefix_of` l2 and
  l1 `suffix_of` l2 because those are easier to read.
- change the notation l1 `sublist` l2 into l1 `sublist_of` l2 to be consistent.
- rename contains -> submseteq and use the notation ⊆+

theories/fin_collections.v

@@ -69,9 +69,9 @@ Proof.
   apply Permutation_singleton. by rewrite <-(right_id ∅ (∪) {[x]}),
     elements_union_singleton, elements_empty by set_solver.
 Qed.
-Lemma elements_contains X Y : X ⊆ Y → elements X `contains` elements Y.
+Lemma elements_submseteq X Y : X ⊆ Y → elements X ⊆+ elements Y.
 Proof.
-  intros; apply NoDup_contains; auto using NoDup_elements.
+  intros; apply NoDup_submseteq; auto using NoDup_elements.
   intros x. rewrite !elem_of_elements; auto.
 Qed.
 

theories/fin_maps.v

@@ -699,10 +699,10 @@ Proof.
   by rewrite map_to_list_insert, map_to_list_empty by auto using lookup_empty.
 Qed.
 
-Lemma map_to_list_contains {A} (m1 m2 : M A) :
-  m1 ⊆ m2 → map_to_list m1 `contains` map_to_list m2.
+Lemma map_to_list_submseteq {A} (m1 m2 : M A) :
+  m1 ⊆ m2 → map_to_list m1 ⊆+ map_to_list m2.
 Proof.
-  intros; apply NoDup_contains; auto using NoDup_map_to_list.
+  intros; apply NoDup_submseteq; auto using NoDup_map_to_list.
   intros [i x]. rewrite !elem_of_map_to_list; eauto using lookup_weaken.
 Qed.
 Lemma map_to_list_fmap {A B} (f : A → B) m :

theories/finite.v

@@ -107,17 +107,17 @@ Proof.
   unfold card; intros. destruct finA as [[|x ?] ??]; simpl in *; [exfalso;lia|].
   constructor; exact x.
 Qed.
-Lemma finite_inj_contains `{finA: Finite A} `{finB: Finite B} (f: A → B)
-  `{!Inj (=) (=) f} : f <$> enum A `contains` enum B.
+Lemma finite_inj_submseteq `{finA: Finite A} `{finB: Finite B} (f: A → B)
+  `{!Inj (=) (=) f} : f <$> enum A ⊆+ enum B.
 Proof.
-  intros. destruct finA, finB. apply NoDup_contains; auto using NoDup_fmap_2.
+  intros. destruct finA, finB. apply NoDup_submseteq; auto using NoDup_fmap_2.
 Qed.
 Lemma finite_inj_Permutation `{Finite A} `{Finite B} (f : A → B)
   `{!Inj (=) (=) f} : card A = card B → f <$> enum A ≡ₚ enum B.
 Proof.
-  intros. apply contains_Permutation_length_eq.
+  intros. apply submseteq_Permutation_length_eq.
   - by rewrite fmap_length.
-  - by apply finite_inj_contains.
+  - by apply finite_inj_submseteq.
 Qed.
 Lemma finite_inj_surj `{Finite A} `{Finite B} (f : A → B)
   `{!Inj (=) (=) f} : card A = card B → Surj (=) f.
@@ -144,7 +144,7 @@ Proof.
     destruct (finite_surj A B) as (g&?); auto with lia.
     destruct (surj_cancel g) as (f&?). exists f. apply cancel_inj.
   - intros [f ?]. unfold card. rewrite <-(fmap_length f).
-    by apply contains_length, (finite_inj_contains f).
+    by apply submseteq_length, (finite_inj_submseteq f).
 Qed.
 Lemma finite_bijective A `{Finite A} B `{Finite B} :
   card A = card B ↔ ∃ f : A → B, Inj (=) (=) f ∧ Surj (=) f.

theories/gmultiset.v

@@ -345,14 +345,14 @@ Proof.
 Qed.
 
 (* Mononicity *)
-Lemma gmultiset_elements_contains X Y : X ⊆ Y → elements X `contains` elements Y.
+Lemma gmultiset_elements_submseteq X Y : X ⊆ Y → elements X ⊆+ elements Y.
 Proof.
   intros ->%gmultiset_union_difference. rewrite gmultiset_elements_union.
-  by apply contains_inserts_r.
+  by apply submseteq_inserts_r.
 Qed.
 
 Lemma gmultiset_subseteq_size X Y : X ⊆ Y → size X ≤ size Y.
-Proof. intros. by apply contains_length, gmultiset_elements_contains. Qed.
+Proof. intros. by apply submseteq_length, gmultiset_elements_submseteq. Qed.
 
 Lemma gmultiset_subset_size X Y : X ⊂ Y → size X < size Y.
 Proof.