# HG changeset patch
# User paulson
# Date 1606423780 0
# Node ID 98fe7a10ace3c9002b4f8eea7d0983e9093e18f5
# Parent  e0ceaca7344a31dce6a3bdc8590c1b37f1f6bd71# Parent  7553c18808158682ea5639b3aada19dba066d674
merged

diff -r 7553c1880815 -r 98fe7a10ace3 CONTRIBUTORS
--- a/CONTRIBUTORS	Thu Nov 26 18:09:15 2020 +0000
+++ b/CONTRIBUTORS	Thu Nov 26 20:49:40 2020 +0000
@@ -5,6 +5,8 @@
 
 Contributions to this Isabelle version
 --------------------------------------
+* November 2020: Stepan Holub
+  Removed preconditions from lemma comm_append_are_replicate
 
 * November 2020: Florian Haftmann
   Bundle mixins for locale and class expressions.
diff -r 7553c1880815 -r 98fe7a10ace3 src/HOL/Data_Structures/Interval_Tree.thy
--- a/src/HOL/Data_Structures/Interval_Tree.thy	Thu Nov 26 18:09:15 2020 +0000
+++ b/src/HOL/Data_Structures/Interval_Tree.thy	Thu Nov 26 20:49:40 2020 +0000
@@ -265,10 +265,13 @@
   fixes has_overlap :: "'t \<Rightarrow> 'a::linorder ivl \<Rightarrow> bool"
   assumes set_overlap: "invar s \<Longrightarrow> has_overlap s x = Interval_Tree.has_overlap (set s) x"
 
+fun invar :: "('a::{linorder,order_bot}) ivl_tree \<Rightarrow> bool" where
+"invar t = (inv_max_hi t \<and> sorted(inorder t))"
+
 interpretation S: Interval_Set
   where empty = Leaf and insert = insert and delete = delete
   and has_overlap = search and isin = isin and set = set_tree
-  and invar = "\<lambda>t. inv_max_hi t \<and> sorted (inorder t)"
+  and invar = invar
 proof (standard, goal_cases)
   case 1
   then show ?case by auto
diff -r 7553c1880815 -r 98fe7a10ace3 src/HOL/List.thy
--- a/src/HOL/List.thy	Thu Nov 26 18:09:15 2020 +0000
+++ b/src/HOL/List.thy	Thu Nov 26 20:49:40 2020 +0000
@@ -4542,27 +4542,25 @@
   "replicate (length (filter (\<lambda>y. x = y) xs)) x = filter (\<lambda>y. x = y) xs"
   by (induct xs) auto
 
-text \<open>This stronger version is thanks to Stepan Holub\<close>
 lemma comm_append_are_replicate:
-  "xs @ ys = ys @ xs
-  \<Longrightarrow> \<exists>m n zs. concat (replicate m zs) = xs \<and> concat (replicate n zs) = ys"
+  "xs @ ys = ys @ xs \<Longrightarrow> \<exists>m n zs. concat (replicate m zs) = xs \<and> concat (replicate n zs) = ys"
 proof (induction "length (xs @ ys) + length xs" arbitrary: xs ys rule: less_induct)
   case less
-  consider "length ys < length xs" | "xs = []" | "length xs \<le> length ys \<and> xs \<noteq> []"
+  consider (1) "length ys < length xs" | (2) "xs = []" | (3) "length xs \<le> length ys \<and> xs \<noteq> []"
     by linarith
   then show ?case
   proof (cases)
-    assume "length ys < length xs"
+    case 1
     then show ?thesis
       using less.hyps[OF _ less.prems[symmetric]] nat_add_left_cancel_less by auto
   next
-    assume "xs = []"
+    case 2
     then have "concat (replicate 0 ys) = xs \<and> concat (replicate 1 ys) = ys"
       by simp
-    then show ?case
+    then show ?thesis
       by blast
   next
-    assume "length xs \<le> length ys \<and> xs \<noteq> []"
+    case 3
     then have "length xs \<le> length ys" and "xs \<noteq> []"
       by blast+
     from \<open>length xs \<le> length ys\<close> and  \<open>xs @ ys = ys @ xs\<close>
@@ -4580,7 +4578,7 @@
     then have "concat (replicate (m+n') zs) = ys"
       using \<open>ys = xs @ ws\<close>
       by (simp add: replicate_add)
-    then show ?case
+    then show ?thesis
       using \<open>concat (replicate m zs) = xs\<close> by blast
   qed
 qed
@@ -4593,7 +4591,7 @@
 proof -
   obtain m n zs where "concat (replicate m zs) = xs"
     and "concat (replicate n zs) = ys"
-    using comm_append_are_replicate[of xs ys] assms by blast
+    using comm_append_are_replicate[OF assms(3)] by blast
   then have "m + n > 1" and "concat (replicate (m+n) zs) = xs @ ys"
     using \<open>xs \<noteq> []\<close> and \<open>ys \<noteq> []\<close>
     by (auto simp: replicate_add)