From edfdba1518abb44fabe93e1b267e4608a74eae30 Mon Sep 17 00:00:00 2001 From: Dan Frumin Date: Mon, 26 Aug 2019 12:43:28 +0200 Subject: [PATCH] Add `big_sepL2_swap` --- theories/bi/big_op.v | 15 +++++++++++++++ 1 file changed, 15 insertions(+) diff --git a/theories/bi/big_op.v b/theories/bi/big_op.v index c7dda09a6..6120bf009 100644 --- a/theories/bi/big_op.v +++ b/theories/bi/big_op.v @@ -1475,6 +1475,13 @@ Section list2. auto using and_mono, laterN_intro. Qed. + Lemma big_sepL2_flip Φ l1 l2 : + ([∗ list] k↦y1;y2 ∈ l2; l1, Φ k y2 y1) ⊣⊢ ([∗ list] k↦y1;y2 ∈ l1; l2, Φ k y1 y2). + Proof. + revert Φ l2. induction l1 as [|x1 l1 IH]=> Φ -[|x2 l2]//=; simplify_eq. + by rewrite IH. + Qed. + Global Instance big_sepL2_nil_timeless `{!Timeless (emp%I : PROP)} Φ : Timeless ([∗ list] k↦y1;y2 ∈ []; [], Φ k y1 y2). Proof. simpl; apply _. Qed. @@ -1541,6 +1548,14 @@ Section gmap2. apply big_sepM2_mono. eauto. Qed. + Lemma big_sepM2_flip Φ m1 m2 : + ([∗ map] k↦y1;y2 ∈ m2; m1, Φ k y2 y1) ⊣⊢ ([∗ map] k↦y1;y2 ∈ m1; m2, Φ k y1 y2). + Proof. + rewrite /big_sepM2. apply and_proper; [apply pure_proper; naive_solver |]. + rewrite -map_zip_with_flip map_zip_with_map_zip big_sepM_fmap. + apply big_sepM_proper. by intros k [b a]. + Qed. + Global Instance big_sepM2_empty_timeless `{!Timeless (emp%I : PROP)} Φ : Timeless ([∗ map] k↦x1;x2 ∈ ∅;∅, Φ k x1 x2). Proof. rewrite /big_sepM2 map_zip_with_empty. apply _. Qed. -- GitLab