src/HOL/Map.thy
changeset 39379 ab1b070aa412
parent 39302 d7728f65b353
child 39992 f225a499a8e5
     1.1 --- a/src/HOL/Map.thy	Mon Sep 13 16:15:12 2010 +0200
     1.2 +++ b/src/HOL/Map.thy	Mon Sep 13 16:43:23 2010 +0200
     1.3 @@ -568,6 +568,31 @@
     1.4    "set xs = dom m \<Longrightarrow> map_of (map (\<lambda>k. (k, the (m k))) xs) = m"
     1.5    by (rule ext) (auto simp add: map_of_map_restrict restrict_map_def)
     1.6  
     1.7 +lemma map_of_eqI:
     1.8 +  assumes set_eq: "set (map fst xs) = set (map fst ys)"
     1.9 +  assumes map_eq: "\<forall>k\<in>set (map fst xs). map_of xs k = map_of ys k"
    1.10 +  shows "map_of xs = map_of ys"
    1.11 +proof (rule ext)
    1.12 +  fix k show "map_of xs k = map_of ys k"
    1.13 +  proof (cases "map_of xs k")
    1.14 +    case None then have "k \<notin> set (map fst xs)" by (simp add: map_of_eq_None_iff)
    1.15 +    with set_eq have "k \<notin> set (map fst ys)" by simp
    1.16 +    then have "map_of ys k = None" by (simp add: map_of_eq_None_iff)
    1.17 +    with None show ?thesis by simp
    1.18 +  next
    1.19 +    case (Some v) then have "k \<in> set (map fst xs)" by (auto simp add: dom_map_of_conv_image_fst [symmetric])
    1.20 +    with map_eq show ?thesis by auto
    1.21 +  qed
    1.22 +qed
    1.23 +
    1.24 +lemma map_of_eq_dom:
    1.25 +  assumes "map_of xs = map_of ys"
    1.26 +  shows "fst ` set xs = fst ` set ys"
    1.27 +proof -
    1.28 +  from assms have "dom (map_of xs) = dom (map_of ys)" by simp
    1.29 +  then show ?thesis by (simp add: dom_map_of_conv_image_fst)
    1.30 +qed
    1.31 +
    1.32  
    1.33  subsection {* @{term [source] ran} *}
    1.34