Merge branch 'list_renaming_stuff'

theories/algebra/cmra_big_op.v

@@ -101,9 +101,9 @@ Proof.
   - by trans (big_op xs2).
 Qed.
 
-Lemma big_op_contains xs ys : xs `contains` ys → [⋅] xs ≼ [⋅] ys.
+Lemma big_op_submseteq xs ys : xs ⊆+ ys → [⋅] xs ≼ [⋅] ys.
 Proof.
-  intros [xs' ->]%contains_Permutation.
+  intros [xs' ->]%submseteq_Permutation.
   rewrite big_op_app; apply cmra_included_l.
 Qed.
 
@@ -158,9 +158,9 @@ Section list.
   Lemma big_opL_permutation (f : A → M) l1 l2 :
     l1 ≡ₚ l2 → ([⋅ list] x ∈ l1, f x) ≡ ([⋅ list] x ∈ l2, f x).
   Proof. intros Hl. by rewrite /big_opL !imap_const Hl. Qed.
-  Lemma big_opL_contains (f : A → M) l1 l2 :
-    l1 `contains` l2 → ([⋅ list] x ∈ l1, f x) ≼ ([⋅ list] x ∈ l2, f x).
-  Proof. intros Hl. apply big_op_contains. rewrite !imap_const. by rewrite ->Hl. Qed.
+  Lemma big_opL_submseteq (f : A → M) l1 l2 :
+    l1 ⊆+ l2 → ([⋅ list] x ∈ l1, f x) ≼ ([⋅ list] x ∈ l2, f x).
+  Proof. intros Hl. apply big_op_submseteq. rewrite !imap_const. by rewrite ->Hl. Qed.
 
   Global Instance big_opL_ne l n :
     Proper (pointwise_relation _ (pointwise_relation _ (dist n)) ==> (dist n))
@@ -230,7 +230,7 @@ Section gmap.
     ([⋅ map] k ↦ x ∈ m1, f k x) ≼ [⋅ map] k ↦ x ∈ m2, g k x.
   Proof.
     intros Hm Hf. trans ([⋅ map] k↦x ∈ m2, f k x).
-    - by apply big_op_contains, fmap_contains, map_to_list_contains.
+    - by apply big_op_submseteq, fmap_submseteq, map_to_list_submseteq.
     - apply big_opM_forall; apply _ || auto.
   Qed.
   Lemma big_opM_ext f g m :
@@ -345,7 +345,7 @@ Section gset.
     ([⋅ set] x ∈ X, f x) ≼ [⋅ set] x ∈ Y, g x.
   Proof.
     intros HX Hf. trans ([⋅ set] x ∈ Y, f x).
-    - by apply big_op_contains, fmap_contains, elements_contains.
+    - by apply big_op_submseteq, fmap_submseteq, elements_submseteq.
     - apply big_opS_forall; apply _ || auto.
   Qed.
   Lemma big_opS_ext f g X :
@@ -446,7 +446,7 @@ Section gmultiset.
     ([⋅ mset] x ∈ X, f x) ≼ [⋅ mset] x ∈ Y, g x.
   Proof.
     intros HX Hf. trans ([⋅ mset] x ∈ Y, f x).
-    - by apply big_op_contains, fmap_contains, gmultiset_elements_contains.
+    - by apply big_op_submseteq, fmap_submseteq, gmultiset_elements_submseteq.
     - apply big_opMS_forall; apply _ || auto.
   Qed.
   Lemma big_opMS_ext f g X :

theories/algebra/cmra_tactics.v

@@ -29,9 +29,9 @@ Module ra_reflection. Section ra_reflection.
     by rewrite fmap_app IH1 IH2 big_op_app.
   Qed.
   Lemma flatten_correct Σ e1 e2 :
-    flatten e1 `contains` flatten e2 → eval Σ e1 ≼ eval Σ e2.
+    flatten e1 ⊆+ flatten e2 → eval Σ e1 ≼ eval Σ e2.
   Proof.
-    by intros He; rewrite !eval_flatten; apply big_op_contains; rewrite ->He.
+    by intros He; rewrite !eval_flatten; apply big_op_submseteq; rewrite ->He.
   Qed.
 
   Class Quote (Σ1 Σ2 : list A) (l : A) (e : expr) := {}.

theories/base_logic/big_op.v

@@ -133,8 +133,8 @@ Proof. by induction 1 as [|P Q Ps Qs HPQ ? IH]; rewrite /= ?HPQ ?IH. Qed.
 Lemma big_sep_app Ps Qs : [∗] (Ps ++ Qs) ⊣⊢ [∗] Ps ∗ [∗] Qs.
 Proof. by rewrite big_op_app. Qed.
 
-Lemma big_sep_contains Ps Qs : Qs `contains` Ps → [∗] Ps ⊢ [∗] Qs.
-Proof. intros. apply uPred_included. by apply: big_op_contains. Qed.
+Lemma big_sep_submseteq Ps Qs : Qs ⊆+ Ps → [∗] Ps ⊢ [∗] Qs.
+Proof. intros. apply uPred_included. by apply: big_op_submseteq. Qed.
 Lemma big_sep_elem_of Ps P : P ∈ Ps → [∗] Ps ⊢ P.
 Proof. intros. apply uPred_included. by apply: big_sep_elem_of. Qed.
 Lemma big_sep_elem_of_acc Ps P : P ∈ Ps → [∗] Ps ⊢ P ∗ (P -∗ [∗] Ps).
@@ -220,9 +220,9 @@ Section list.
     (∀ k y, l !! k = Some y → Φ k y ⊣⊢ Ψ k y) →
     ([∗ list] k ↦ y ∈ l, Φ k y) ⊣⊢ ([∗ list] k ↦ y ∈ l, Ψ k y).
   Proof. apply big_opL_proper. Qed.
-  Lemma big_sepL_contains (Φ : A → uPred M) l1 l2 :
-    l1 `contains` l2 → ([∗ list] y ∈ l2, Φ y) ⊢ [∗ list] y ∈ l1, Φ y.
-  Proof. intros ?. apply uPred_included. by apply: big_opL_contains. Qed.
+  Lemma big_sepL_submseteq (Φ : A → uPred M) l1 l2 :
+    l1 ⊆+ l2 → ([∗ list] y ∈ l2, Φ y) ⊢ [∗ list] y ∈ l1, Φ y.
+  Proof. intros ?. apply uPred_included. by apply: big_opL_submseteq. Qed.
 
   Global Instance big_sepL_mono' l :
     Proper (pointwise_relation _ (pointwise_relation _ (⊢)) ==> (⊢))
@@ -353,8 +353,8 @@ Section gmap.
     ([∗ map] k ↦ x ∈ m1, Φ k x) ⊢ [∗ map] k ↦ x ∈ m2, Ψ k x.
   Proof.
     intros Hm HΦ. trans ([∗ map] k↦x ∈ m2, Φ k x)%I.
-    - apply uPred_included. apply: big_op_contains.
-      by apply fmap_contains, map_to_list_contains.
+    - apply uPred_included. apply: big_op_submseteq.
+      by apply fmap_submseteq, map_to_list_submseteq.
     - apply big_opM_forall; apply _ || auto.
   Qed.
   Lemma big_sepM_proper Φ Ψ m :
@@ -517,8 +517,8 @@ Section gset.
     ([∗ set] x ∈ X, Φ x) ⊢ [∗ set] x ∈ Y, Ψ x.
   Proof.
     intros HX HΦ. trans ([∗ set] x ∈ Y, Φ x)%I.
-    - apply uPred_included. apply: big_op_contains.
-      by apply fmap_contains, elements_contains.
+    - apply uPred_included. apply: big_op_submseteq.
+      by apply fmap_submseteq, elements_submseteq.
     - apply big_opS_forall; apply _ || auto.
   Qed.
   Lemma big_sepS_proper Φ Ψ X :
@@ -666,8 +666,8 @@ Section gmultiset.
     ([∗ mset] x ∈ X, Φ x) ⊢ [∗ mset] x ∈ Y, Ψ x.
   Proof.
     intros HX HΦ. trans ([∗ mset] x ∈ Y, Φ x)%I.
-    - apply uPred_included. apply: big_op_contains.
-      by apply fmap_contains, gmultiset_elements_contains.
+    - apply uPred_included. apply: big_op_submseteq.
+      by apply fmap_submseteq, gmultiset_elements_submseteq.
     - apply big_opMS_forall; apply _ || auto.
   Qed.
   Lemma big_sepMS_proper Φ Ψ X :

theories/base_logic/tactics.v

@@ -30,9 +30,9 @@ Module uPred_reflection. Section uPred_reflection.
       rewrite /= ?right_id ?fmap_app ?big_sep_app ?IH1 ?IH2 //. 
   Qed.
   Lemma flatten_entails Σ e1 e2 :
-    flatten e2 `contains` flatten e1 → eval Σ e1 ⊢ eval Σ e2.
+    flatten e2 ⊆+ flatten e1 → eval Σ e1 ⊢ eval Σ e2.
   Proof.
-    intros. rewrite !eval_flatten. by apply big_sep_contains, fmap_contains.
+    intros. rewrite !eval_flatten. by apply big_sep_submseteq, fmap_submseteq.
   Qed.
   Lemma flatten_equiv Σ e1 e2 :
     flatten e2 ≡ₚ flatten e1 → eval Σ e1 ⊣⊢ eval Σ e2.

theories/prelude/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/prelude/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/prelude/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/prelude/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.