--- 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)