diff -r 5d5be87330b5 -r 7ae4dcf332ae src/HOL/List.thy
--- a/src/HOL/List.thy	Sat Feb 08 15:18:58 2020 +0100
+++ b/src/HOL/List.thy	Sun Feb 09 10:21:01 2020 +0000
@@ -2791,6 +2791,15 @@
     by (induct xs ys rule: list_induct2) (simp_all add: prod_eqI)
 qed
 
+lemma hd_zip:
+  \<open>hd (zip xs ys) = (hd xs, hd ys)\<close> if \<open>xs \<noteq> []\<close> and \<open>ys \<noteq> []\<close>
+  using that by (cases xs; cases ys) simp_all
+
+lemma last_zip:
+  \<open>last (zip xs ys) = (last xs, last ys)\<close> if \<open>xs \<noteq> []\<close> and \<open>ys \<noteq> []\<close>
+    and \<open>length xs = length ys\<close>
+  using that by (cases xs rule: rev_cases; cases ys rule: rev_cases) simp_all
+
 
 subsubsection \<open>\<^const>\<open>list_all2\<close>\<close>