# HG changeset patch
# User bulwahn
# Date 1504251956 -7200
# Node ID acb02fa48ef3f2c1b9652a531207a78b9ae3c70d
# Parent  ac183ddc9fefec52b801e125d6a2ebbe5a2e96a7
more facts on Map.map_of and List.zip

diff -r ac183ddc9fef -r acb02fa48ef3 src/HOL/List.thy
--- a/src/HOL/List.thy	Sun Aug 27 06:56:29 2017 +0200
+++ b/src/HOL/List.thy	Fri Sep 01 09:45:56 2017 +0200
@@ -2607,6 +2607,24 @@
   \<and> n < length xs \<and> n < length ys)"
 by (cases p) (auto simp add: set_zip)
 
+lemma in_set_impl_in_set_zip1:
+  assumes "length xs = length ys"
+  assumes "x \<in> set xs"
+  obtains y where "(x, y) \<in> set (zip xs ys)"
+proof -
+  from assms have "x \<in> set (map fst (zip xs ys))" by simp
+  from this that show ?thesis by fastforce
+qed
+
+lemma in_set_impl_in_set_zip2:
+  assumes "length xs = length ys"
+  assumes "y \<in> set ys"
+  obtains x where "(x, y) \<in> set (zip xs ys)"
+proof -
+  from assms have "y \<in> set (map snd (zip xs ys))" by simp
+  from this that show ?thesis by fastforce
+qed
+
 lemma pair_list_eqI:
   assumes "map fst xs = map fst ys" and "map snd xs = map snd ys"
   shows "xs = ys"
diff -r ac183ddc9fef -r acb02fa48ef3 src/HOL/Map.thy
--- a/src/HOL/Map.thy	Sun Aug 27 06:56:29 2017 +0200
+++ b/src/HOL/Map.thy	Fri Sep 01 09:45:56 2017 +0200
@@ -202,6 +202,20 @@
   ultimately show ?case by simp
 qed
 
+lemma map_of_zip_nth:
+  assumes "length xs = length ys"
+  assumes "distinct xs"
+  assumes "i < length ys"
+  shows "map_of (zip xs ys) (xs ! i) = Some (ys ! i)"
+using assms proof (induct arbitrary: i rule: list_induct2)
+  case Nil
+  then show ?case by simp
+next
+  case (Cons x xs y ys)
+  then show ?case
+    using less_Suc_eq_0_disj by auto
+qed
+
 lemma map_of_zip_map:
   "map_of (zip xs (map f xs)) = (\<lambda>x. if x \<in> set xs then Some (f x) else None)"
   by (induct xs) (simp_all add: fun_eq_iff)
@@ -661,6 +675,11 @@
   ultimately show ?case by (simp only: map_of.simps ran_map_upd) simp
 qed
 
+lemma ran_map_of_zip:
+  assumes "length xs = length ys" "distinct xs"
+  shows "ran (map_of (zip xs ys)) = set ys"
+using assms by (simp add: ran_distinct set_map[symmetric])
+
 lemma ran_map_option: "ran (\<lambda>x. map_option f (m x)) = f ` ran m"
   by (auto simp add: ran_def)