From 596e8767fbf61533b09c93b870519cb0fa3399b7 Mon Sep 17 00:00:00 2001
From: Ralf Jung <jung@mpi-sws.org>
Date: Tue, 12 Jan 2021 19:32:30 +0100
Subject: [PATCH] some big_sepL lemmas

---
 iris/bi/big_op.v | 45 ++++++++++++++++++++++++++++++++-------------
 1 file changed, 32 insertions(+), 13 deletions(-)

diff --git a/iris/bi/big_op.v b/iris/bi/big_op.v
index 6edadcd30..70f425334 100644
--- a/iris/bi/big_op.v
+++ b/iris/bi/big_op.v
@@ -291,21 +291,30 @@ Section sep_list.
   Proof. induction 1; simpl; apply _. Qed.
 End sep_list.
 
-Section sep_list_more.
-  Context {A : Type}.
-  Implicit Types l : list A.
-  Implicit Types Φ Ψ : nat → A → PROP.
-  (* Some lemmas depend on the generalized versions of the above ones. *)
+(* Some lemmas depend on the generalized versions of the above ones. *)
 
-  Lemma big_sepL_zip_with {B C} Φ f (l1 : list B) (l2 : list C) :
-    ([∗ list] k↦x ∈ zip_with f l1 l2, Φ k x)
+Lemma big_sepL_sep_zip {A B} (Φ : nat → A → PROP) (Ψ : nat → B → PROP) l1 l2 :
+  length l1 = length l2 →
+  ([∗ list] k↦x ∈ l1, Φ k x) ∗ ([∗ list] k↦x ∈ l2, Ψ k x) ⊣⊢
+  ([∗ list] k↦xy ∈ zip l1 l2, Φ k xy.1 ∗ Ψ k xy.2).
+Proof.
+  intros Hlen. rewrite big_sepL_sep. f_equiv.
+  - trans ([∗ list] k↦x ∈ fst <$> zip l1 l2, Φ k x)%I.
+    + rewrite fst_zip; auto with lia.
+    + rewrite big_sepL_fmap //.
+  - trans ([∗ list] k↦x ∈ snd <$> zip l1 l2, Ψ k x)%I.
+    + rewrite snd_zip; auto with lia.
+    + rewrite big_sepL_fmap //.
+Qed.
+
+Lemma big_sepL_zip_with {A B C} (Φ : nat → A → PROP) f (l1 : list B) (l2 : list C) :
+  ([∗ list] k↦x ∈ zip_with f l1 l2, Φ k x)
     ⊣⊢ ([∗ list] k↦x ∈ l1, if l2 !! k is Some y then Φ k (f x y) else emp).
-  Proof.
-    revert Φ l2; induction l1 as [|x l1 IH]=> Φ [|y l2] //=.
-    - by rewrite big_sepL_emp left_id.
-    - by rewrite IH.
-  Qed.
-End sep_list_more.
+Proof.
+  revert Φ l2; induction l1 as [|x l1 IH]=> Φ [|y l2] //=.
+  - by rewrite big_sepL_emp left_id.
+  - by rewrite IH.
+Qed.
 
 Lemma big_sepL2_alt {A B} (Φ : nat → A → B → PROP) l1 l2 :
   ([∗ list] k↦y1;y2 ∈ l1; l2, Φ k y1 y2)
@@ -619,6 +628,16 @@ Section sep_list2.
     by rewrite IH.
   Qed.
 
+  Lemma big_sepL2_merge (Φ : nat → A → PROP) (Ψ : nat → B → PROP) (l1 : list A) (l2 : list B):
+    length l1 = length l2 →
+    ([∗ list] k↦y1 ∈ l1, Φ k y1) -∗
+    ([∗ list] k↦y2 ∈ l2, Ψ k y2) -∗
+    ([∗ list] k↦y1;y2 ∈ l1;l2, Φ k y1 ∗ Ψ k y2).
+  Proof.
+    intros Hlen. apply wand_intro_r.
+    rewrite big_sepL_sep_zip // big_sepL2_alt pure_True // left_id //.
+  Qed.
+
   Global Instance big_sepL2_nil_persistent Φ :
     Persistent ([∗ list] k↦y1;y2 ∈ []; [], Φ k y1 y2).
   Proof. simpl; apply _. Qed.
-- 
GitLab