From 9ec365a182eee1d4d54d3029388ff976e0b2fe8a Mon Sep 17 00:00:00 2001 From: Kimaya Bedarkar <kbedarka@mpi-sws.org> Date: Tue, 14 Jan 2025 14:14:18 +0100 Subject: [PATCH] add some zip lemmas Co-authored-by: Robbert Krebbers <gitlab-sws@robbertkrebbers.nl> add new line back --- stdpp/list.v | 17 ++++++++++++++++- 1 file changed, 16 insertions(+), 1 deletion(-) diff --git a/stdpp/list.v b/stdpp/list.v index 64096df6..4a96bd88 100644 --- a/stdpp/list.v +++ b/stdpp/list.v @@ -4915,6 +4915,10 @@ Section zip_with. zip_with f l k !! i = Some z ↔ ∃ x y, z = f x y ∧ l !! i = Some x ∧ k !! i = Some y. Proof. rewrite lookup_zip_with. destruct (l !! i), (k !! i); naive_solver. Qed. + Lemma lookup_zip_with_None l k i : + zip_with f l k !! i = None + ↔ l !! i = None ∨ k !! i = None. + Proof. rewrite lookup_zip_with. destruct (l !! i), (k !! i); naive_solver. Qed. Lemma insert_zip_with l k i x y : <[i:=f x y]>(zip_with f l k) = zip_with f (<[i:=x]>l) (<[i:=y]>k). Proof. revert i k. induction l; intros [|?] [|??]; f_equal/=; auto. Qed. @@ -5054,10 +5058,21 @@ Section zip. Lemma elem_of_zip_l x1 x2 l k : (x1, x2) ∈ zip l k → x1 ∈ l. Proof. intros ?%elem_of_zip_with. naive_solver. Qed. - Lemma elem_of_zip_r x1 x2 l k : (x1, x2) ∈ zip l k → x2 ∈ k. Proof. intros ?%elem_of_zip_with. naive_solver. Qed. + Lemma length_zip l k : + length (zip l k) = min (length l) (length k). + Proof. by rewrite length_zip_with. Qed. + Lemma zip_nil_inv l k : + zip l k = [] → l = [] ∨ k = []. + Proof. intros. by eapply zip_with_nil_inv. Qed. + Lemma lookup_zip_Some l k i x y : + zip l k !! i = Some (x, y) ↔ l !! i = Some x ∧ k !! i = Some y. + Proof. rewrite lookup_zip_with_Some. naive_solver. Qed. + Lemma lookup_zip_None l k i : + zip l k !! i = None ↔ l !! i = None ∨ k !! i = None. + Proof. by rewrite lookup_zip_with_None. Qed. End zip. Lemma zip_diag {A} (l : list A) : -- GitLab