diff -r 1e7c5bbea36d -r 6f38b7abb648 src/HOL/Data_Structures/Tree23_Set.thy --- a/src/HOL/Data_Structures/Tree23_Set.thy Sun Aug 07 12:10:49 2016 +0200 +++ b/src/HOL/Data_Structures/Tree23_Set.thy Tue Aug 09 17:00:36 2016 +0200 @@ -191,7 +191,7 @@ lemma inorder_del: "\ bal t ; sorted(inorder t) \ \ inorder(tree\<^sub>d (del x t)) = del_list x (inorder t)" by(induction t rule: del.induct) - (auto simp: del_list_simps inorder_nodes del_minD split: prod.splits) + (auto simp: del_list_simps inorder_nodes del_minD split!: if_split prod.splits) lemma inorder_delete: "\ bal t ; sorted(inorder t) \ \ inorder(delete x t) = del_list x (inorder t)" @@ -217,7 +217,7 @@ end lemma bal_ins: "bal t \ bal (tree\<^sub>i(ins a t)) \ height(ins a t) = height t" -by (induct t) (auto split: up\<^sub>i.split) (* 15 secs in 2015 *) +by (induct t) (auto split!: if_split up\<^sub>i.split) (* 15 secs in 2015 *) text{* Now an alternative proof (by Brian Huffman) that runs faster because two properties (balance and height) are combined in one predicate. *}