# HG changeset patch # User haftmann # Date 1746441760 -7200 # Node ID 700f9b01c9d9996fb0434fae6ed689f135d095ca # Parent 43f4f9c5c6bdd2fcd6a3335ffebf77a87062d1e3 more theorems diff -r 43f4f9c5c6bd -r 700f9b01c9d9 src/HOL/Map.thy --- a/src/HOL/Map.thy Sun May 04 21:03:04 2025 +0100 +++ b/src/HOL/Map.thy Mon May 05 12:42:40 2025 +0200 @@ -297,6 +297,10 @@ "map_of (map (\(k, v). (k, f v)) xs) = map_option f \ map_of xs" by (induct xs) (auto simp: fun_eq_iff) +lemma map_of_filter: + "map_of (filter (\x. P (fst x)) xs) = map_of xs |` Collect P" + by (induct xs) (simp_all add: fun_eq_iff restrict_map_def) + lemma dom_map_option: "dom (\k. map_option (f k) (m k)) = dom m" by (simp add: dom_def)