--- a/src/HOL/Data_Structures/Tree_Map.thy Fri Nov 13 12:43:54 2015 +0000
+++ b/src/HOL/Data_Structures/Tree_Map.thy Fri Nov 13 16:17:30 2015 +0100
@@ -34,18 +34,10 @@
"sorted1(inorder t) \<Longrightarrow> lookup t x = map_of (inorder t) x"
by (induction t) (auto simp: map_of_simps split: option.split)
-
lemma inorder_update:
"sorted1(inorder t) \<Longrightarrow> inorder(update a b t) = upd_list a b (inorder t)"
by(induction t) (auto simp: upd_list_simps)
-
-lemma del_minD:
- "del_min t = (x,t') \<Longrightarrow> t \<noteq> Leaf \<Longrightarrow> sorted1(inorder t) \<Longrightarrow>
- x # inorder t' = inorder t"
-by(induction t arbitrary: t' rule: del_min.induct)
- (auto simp: del_list_simps split: prod.splits if_splits)
-
lemma inorder_delete:
"sorted1(inorder t) \<Longrightarrow> inorder(delete x t) = del_list x (inorder t)"
by(induction t) (auto simp: del_list_simps del_minD split: prod.splits)