author nipkow Tue May 14 20:35:09 2019 +0200 (5 days ago ago) changeset 70453 40b6bc5a4721 parent 70452 81403d7b9038 child 70454 4065e3b0e5bf
tuned
```     1.1 --- a/src/HOL/Data_Structures/Tries_Binary.thy	Tue May 14 17:21:13 2019 +0200
1.2 +++ b/src/HOL/Data_Structures/Tries_Binary.thy	Tue May 14 20:35:09 2019 +0200
1.3 @@ -184,7 +184,7 @@
1.4  apply(auto split: list.split)
1.5  done
1.6
1.7 -lemma isinP:
1.8 +lemma abs_trieP_isinP:
1.9    "isinP t ks = isin (abs_trieP t) ks"
1.10  apply(induction t arbitrary: ks rule: abs_trieP.induct)
1.11   apply(auto simp: isin_prefix_trie split: list.split)
1.12 @@ -260,21 +260,26 @@
1.13  definition set_trieP :: "trieP \<Rightarrow> bool list set" where
1.14  "set_trieP = set_trie o abs_trieP"
1.15
1.16 +lemma isinP_set_trieP: "isinP t xs = (xs \<in> set_trieP t)"
1.17 +by(simp add: abs_trieP_isinP set_trie_isin set_trieP_def)
1.18 +
1.19  lemma set_trieP_insertP: "set_trieP (insertP xs t) = set_trieP t \<union> {xs}"
1.20  by(simp add: abs_trieP_insertP set_trie_insert set_trieP_def)
1.21
1.22 +lemma set_trieP_deleteP: "set_trieP (deleteP xs t) = set_trieP t - {xs}"
1.23 +by(auto simp: set_trie_delete set_trieP_def simp flip: delete_abs_trieP)
1.24 +
1.25  interpretation SP: Set
1.26  where empty = emptyP and isin = isinP and insert = insertP and delete = deleteP
1.27  and set = set_trieP and invar = "\<lambda>t. True"
1.28  proof (standard, goal_cases)
1.29    case 1 show ?case by (simp add: set_trieP_def set_trie_def)
1.30  next
1.31 -  case 2 thus ?case by(simp add: isinP set_trieP_def set_trie_def)
1.32 +  case 2 show ?case by(rule isinP_set_trieP)
1.33  next
1.34    case 3 thus ?case by (auto simp: set_trieP_insertP)
1.35  next
1.36 -  case 4 thus ?case
1.37 -    by(auto simp: isin_delete set_trieP_def set_trie_def simp flip: delete_abs_trieP)
1.38 +  case 4 thus ?case by(auto simp: set_trieP_deleteP)
1.39  qed (rule TrueI)+
1.40
1.41  end
```