--- a/src/HOL/MicroJava/BV/Kildall_Lift.thy Wed Jun 19 11:48:01 2002 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,105 +0,0 @@
-(* Title: HOL/MicroJava/BV/Kildall_Lift.thy
- ID: $Id$
- Author: Gerwin Klein
- Copyright 2001 TUM
-*)
-
-theory Kildall_Lift = Kildall + Typing_Framework_err:
-
-constdefs
- app_mono :: "'s ord \<Rightarrow> (nat \<Rightarrow> 's \<Rightarrow> bool) \<Rightarrow> nat \<Rightarrow> 's set \<Rightarrow> bool"
-"app_mono r app n A ==
- \<forall>s p t. s \<in> A \<and> p < n \<and> s <=_r t \<longrightarrow> app p t \<longrightarrow> app p s"
-
-lemma bounded_lift:
- "bounded step n \<Longrightarrow> bounded (err_step n app step) n"
- apply (unfold bounded_def err_step_def error_def)
- apply clarify
- apply (erule allE, erule impE, assumption)
- apply (case_tac s)
- apply (auto simp add: map_snd_def split: split_if_asm)
- done
-
-lemma le_list_map_OK [simp]:
- "\<And>b. map OK a <=[Err.le r] map OK b = (a <=[r] b)"
- apply (induct a)
- apply simp
- apply simp
- apply (case_tac b)
- apply simp
- apply simp
- done
-
-
-lemma map_snd_lessI:
- "x <=|r| y \<Longrightarrow> map_snd OK x <=|Err.le r| map_snd OK y"
- apply (induct x)
- apply (unfold lesubstep_type_def map_snd_def)
- apply auto
- done
-
-
-lemma mono_lift:
- "order r \<Longrightarrow> app_mono r app n A \<Longrightarrow> bounded (err_step n app step) n \<Longrightarrow>
- \<forall>s p t. s \<in> A \<and> p < n \<and> s <=_r t \<longrightarrow> app p t \<longrightarrow> step p s <=|r| step p t \<Longrightarrow>
- mono (Err.le r) (err_step n app step) n (err A)"
-apply (unfold app_mono_def mono_def err_step_def)
-apply clarify
-apply (case_tac s)
- apply simp
-apply simp
-apply (case_tac t)
- apply simp
- apply clarify
- apply (simp add: lesubstep_type_def error_def)
- apply clarify
- apply (drule in_map_sndD)
- apply clarify
- apply (drule bounded_err_stepD, assumption+)
- apply (rule exI [of _ Err])
- apply simp
-apply simp
-apply (erule allE, erule allE, erule allE, erule impE)
- apply (rule conjI, assumption)
- apply (rule conjI, assumption)
- apply assumption
-apply (rule conjI)
-apply clarify
-apply (erule allE, erule allE, erule allE, erule impE)
- apply (rule conjI, assumption)
- apply (rule conjI, assumption)
- apply assumption
-apply (erule impE, assumption)
-apply (rule map_snd_lessI, assumption)
-apply clarify
-apply (simp add: lesubstep_type_def error_def)
-apply clarify
-apply (drule in_map_sndD)
-apply clarify
-apply (drule bounded_err_stepD, assumption+)
-apply (rule exI [of _ Err])
-apply simp
-done
-
-lemma in_errorD:
- "(x,y) \<in> set (error n) \<Longrightarrow> y = Err"
- by (auto simp add: error_def)
-
-lemma pres_type_lift:
- "\<forall>s\<in>A. \<forall>p. p < n \<longrightarrow> app p s \<longrightarrow> (\<forall>(q, s')\<in>set (step p s). s' \<in> A)
- \<Longrightarrow> pres_type (err_step n app step) n (err A)"
-apply (unfold pres_type_def err_step_def)
-apply clarify
-apply (case_tac b)
- apply simp
-apply (case_tac s)
- apply simp
- apply (drule in_errorD)
- apply simp
-apply (simp add: map_snd_def split: split_if_asm)
- apply fast
-apply (drule in_errorD)
-apply simp
-done
-
-end