# HG changeset patch
# User wenzelm
# Date 966786320 -7200
# Node ID 4cae97480a6d89be61a2bee1ac01a1d336d02251
# Parent  e4d58f1be05b8476b63041e1f7132cb1fa66ea5e
open cases;

diff -r e4d58f1be05b -r 4cae97480a6d src/HOL/MicroJava/BV/Convert.thy
--- a/src/HOL/MicroJava/BV/Convert.thy	Sat Aug 19 12:49:19 2000 +0200
+++ b/src/HOL/MicroJava/BV/Convert.thy	Sun Aug 20 17:45:20 2000 +0200
@@ -241,7 +241,7 @@
     { 
       fix b
       have "?Q (l#ls) b"
-      proof (cases b)
+      proof (cases (open) b)
         case Nil
         thus ?thesis by (auto dest: sup_loc_length)
       next
diff -r e4d58f1be05b -r 4cae97480a6d src/HOL/MicroJava/BV/LBVComplete.thy
--- a/src/HOL/MicroJava/BV/LBVComplete.thy	Sat Aug 19 12:49:19 2000 +0200
+++ b/src/HOL/MicroJava/BV/LBVComplete.thy	Sun Aug 20 17:45:20 2000 +0200
@@ -282,7 +282,7 @@
                "G \<turnstile> s2 <=s s1" "i = ins!pc"
 
   show ?thesis
-  proof (cases "cert!pc")
+  proof (cases (open) "cert!pc")
     case None
     with wtl fits
     show ?thesis 
diff -r e4d58f1be05b -r 4cae97480a6d src/HOL/MicroJava/BV/LBVCorrect.thy
--- a/src/HOL/MicroJava/BV/LBVCorrect.thy	Sat Aug 19 12:49:19 2000 +0200
+++ b/src/HOL/MicroJava/BV/LBVCorrect.thy	Sun Aug 20 17:45:20 2000 +0200
@@ -47,7 +47,7 @@
   have "\<forall> s0 pc. wtl_inst_list is G rT s0 s2 cert (pc+length is) pc 
      \<longrightarrow> (\<exists> phi. pc + length is < length phi \<and> fits_partial phi pc is G rT s0 s2 cert)"
     (is "?P is")
-  proof (induct "?P" "is")
+  proof (induct (open) ?P "is")
     case Nil
     show "?P []" by (simp add: fits_partial_def exists_list)
     case Cons
diff -r e4d58f1be05b -r 4cae97480a6d src/HOL/MicroJava/BV/LBVSpec.thy
--- a/src/HOL/MicroJava/BV/LBVSpec.thy	Sat Aug 19 12:49:19 2000 +0200
+++ b/src/HOL/MicroJava/BV/LBVSpec.thy	Sun Aug 20 17:45:20 2000 +0200
@@ -11,82 +11,82 @@
 
 types
   certificate       = "state_type option list" 
-  class_certificate = "sig \\<Rightarrow> certificate"
-  prog_certificate  = "cname \\<Rightarrow> class_certificate"
+  class_certificate = "sig \<Rightarrow> certificate"
+  prog_certificate  = "cname \<Rightarrow> class_certificate"
 
 constdefs
-wtl_inst :: "[instr,jvm_prog,ty,state_type,state_type,certificate,p_count,p_count] \\<Rightarrow> bool"
+wtl_inst :: "[instr,jvm_prog,ty,state_type,state_type,certificate,p_count,p_count] \<Rightarrow> bool"
 
-"wtl_inst i G rT s s' cert max_pc pc \\<equiv> app (i,G,rT,s) \\<and> 
+"wtl_inst i G rT s s' cert max_pc pc \<equiv> app (i,G,rT,s) \<and> 
                                        (let s'' = the (step (i,G,s)) in
-                                          (\\<forall> pc' \\<in> (succs i pc). pc' < max_pc \\<and>  
-                                             ((pc' \\<noteq> pc+1) \\<longrightarrow> cert!pc' \\<noteq> None \\<and> G \\<turnstile> s'' <=s the (cert!pc'))) \\<and>  
-                                          (if (pc+1) \\<in> (succs i pc) then  
+                                          (\<forall> pc' \<in> (succs i pc). pc' < max_pc \<and>  
+                                             ((pc' \<noteq> pc+1) \<longrightarrow> cert!pc' \<noteq> None \<and> G \<turnstile> s'' <=s the (cert!pc'))) \<and>  
+                                          (if (pc+1) \<in> (succs i pc) then  
                                              s' = s'' 
                                            else 
                                              cert ! (pc+1) = Some s'))" 
 
 lemma [simp]: 
-"succs i pc = {pc+1} \\<Longrightarrow> 
-  wtl_inst i G rT s s' cert max_pc pc = (app (i,G,rT,s) \\<and> pc+1 < max_pc \\<and> (s' = the (step (i,G,s))))"
+"succs i pc = {pc+1} \<Longrightarrow> 
+  wtl_inst i G rT s s' cert max_pc pc = (app (i,G,rT,s) \<and> pc+1 < max_pc \<and> (s' = the (step (i,G,s))))"
 by (unfold wtl_inst_def, auto)
 
 lemma [simp]:
-"succs i pc = {} \\<Longrightarrow> wtl_inst i G rT s s' cert max_pc pc = (app (i,G,rT,s) \\<and> cert!(pc+1) = Some s')"
+"succs i pc = {} \<Longrightarrow> wtl_inst i G rT s s' cert max_pc pc = (app (i,G,rT,s) \<and> cert!(pc+1) = Some s')"
 by (unfold wtl_inst_def, auto)
 
 
 constdefs
-wtl_inst_option :: "[instr,jvm_prog,ty,state_type,state_type,certificate,p_count,p_count] \\<Rightarrow> bool"
-"wtl_inst_option i G rT s0 s1 cert max_pc pc \\<equiv>
+wtl_inst_option :: "[instr,jvm_prog,ty,state_type,state_type,certificate,p_count,p_count] \<Rightarrow> bool"
+"wtl_inst_option i G rT s0 s1 cert max_pc pc \<equiv>
      (case cert!pc of 
-          None     \\<Rightarrow> wtl_inst i G rT s0 s1 cert max_pc pc
-        | Some s0' \\<Rightarrow> (G \\<turnstile> s0 <=s s0') \\<and>
+          None     \<Rightarrow> wtl_inst i G rT s0 s1 cert max_pc pc
+        | Some s0' \<Rightarrow> (G \<turnstile> s0 <=s s0') \<and>
                       wtl_inst i G rT s0' s1 cert max_pc pc)"
   
 consts
- wtl_inst_list :: "[instr list,jvm_prog,ty,state_type,state_type,certificate,p_count,p_count] \\<Rightarrow> bool"
+ wtl_inst_list :: "[instr list,jvm_prog,ty,state_type,state_type,certificate,p_count,p_count] \<Rightarrow> bool"
 primrec
   "wtl_inst_list [] G rT s0 s2 cert max_pc pc = (s0 = s2)"
 
   "wtl_inst_list (instr#is) G rT s0 s2 cert max_pc pc =
-     (\\<exists>s1. wtl_inst_option instr G rT s0 s1 cert max_pc pc \\<and> 
+     (\<exists>s1. wtl_inst_option instr G rT s0 s1 cert max_pc pc \<and> 
            wtl_inst_list is G rT s1 s2 cert max_pc (pc+1))"
 
 constdefs
- wtl_method :: "[jvm_prog,cname,ty list,ty,nat,instr list,certificate] \\<Rightarrow> bool" 
- "wtl_method G C pTs rT mxl ins cert \\<equiv> 
+ wtl_method :: "[jvm_prog,cname,ty list,ty,nat,instr list,certificate] \<Rightarrow> bool" 
+ "wtl_method G C pTs rT mxl ins cert \<equiv> 
 	let max_pc = length ins 
         in 
-	0 < max_pc \\<and>  
-        (\\<exists>s2. wtl_inst_list ins G rT 
+	0 < max_pc \<and>  
+        (\<exists>s2. wtl_inst_list ins G rT 
                             ([],(Some(Class C))#((map Some pTs))@(replicate mxl None))
                             s2 cert max_pc 0)"
 
- wtl_jvm_prog :: "[jvm_prog,prog_certificate] \\<Rightarrow> bool"
- "wtl_jvm_prog G cert \\<equiv> 
-    wf_prog (\\<lambda>G C (sig,rT,maxl,b). 
+ wtl_jvm_prog :: "[jvm_prog,prog_certificate] \<Rightarrow> bool"
+ "wtl_jvm_prog G cert \<equiv> 
+    wf_prog (\<lambda>G C (sig,rT,maxl,b). 
                wtl_method G C (snd sig) rT maxl b (cert C sig)) G" 
 
 text {* \medskip *}
 
-lemma rev_eq: "\\<lbrakk>length a = n; length x = n; rev a @ b # c = rev x @ y # z\\<rbrakk> \\<Longrightarrow> a = x \\<and> b = y \\<and> c = z"
+lemma rev_eq: "\<lbrakk>length a = n; length x = n; rev a @ b # c = rev x @ y # z\<rbrakk> \<Longrightarrow> a = x \<and> b = y \<and> c = z"
 by auto
 
 lemma wtl_inst_unique: 
-"wtl_inst i G rT s0 s1 cert max_pc pc \\<longrightarrow>
- wtl_inst i G rT s0 s1' cert max_pc pc \\<longrightarrow> s1 = s1'" (is "?P i")
+"wtl_inst i G rT s0 s1 cert max_pc pc \<longrightarrow>
+ wtl_inst i G rT s0 s1' cert max_pc pc \<longrightarrow> s1 = s1'" (is "?P i")
 by (unfold wtl_inst_def, auto)
 
 lemma wtl_inst_option_unique:
-"\\<lbrakk>wtl_inst_option i G rT s0 s1 cert max_pc pc; 
-  wtl_inst_option i G rT s0 s1' cert max_pc pc\\<rbrakk> \\<Longrightarrow> s1 = s1'"
+"\<lbrakk>wtl_inst_option i G rT s0 s1 cert max_pc pc; 
+  wtl_inst_option i G rT s0 s1' cert max_pc pc\<rbrakk> \<Longrightarrow> s1 = s1'"
 by (cases "cert!pc") (auto simp add: wtl_inst_unique wtl_inst_option_def)
 
 lemma wtl_inst_list_unique: 
-"\\<forall> s0 pc. wtl_inst_list is G rT s0 s1 cert max_pc pc \\<longrightarrow> 
- wtl_inst_list is G rT s0 s1' cert max_pc pc \\<longrightarrow> s1=s1'" (is "?P is")
-proof (induct "?P" "is") 
+"\<forall> s0 pc. wtl_inst_list is G rT s0 s1 cert max_pc pc \<longrightarrow> 
+ wtl_inst_list is G rT s0 s1' cert max_pc pc \<longrightarrow> s1=s1'" (is "?P is")
+proof (induct (open) ?P "is")
   case Nil
   show "?P []" by simp
 
@@ -110,13 +110,13 @@
 qed
         
 lemma wtl_partial:
-"\\<forall> pc' pc s. 
-   wtl_inst_list is G rT s s' cert mpc pc \\<longrightarrow> \
-   pc' < length is \\<longrightarrow> \
-   (\\<exists> a b s1. a @ b = is \\<and> length a = pc' \\<and> \
-              wtl_inst_list a G rT s  s1 cert mpc pc \\<and> \
+"\<forall> pc' pc s. 
+   wtl_inst_list is G rT s s' cert mpc pc \<longrightarrow> \
+   pc' < length is \<longrightarrow> \
+   (\<exists> a b s1. a @ b = is \<and> length a = pc' \<and> \
+              wtl_inst_list a G rT s  s1 cert mpc pc \<and> \
               wtl_inst_list b G rT s1 s' cert mpc (pc+length a))" (is "?P is")
-proof (induct "?P" "is")
+proof (induct (open) ?P "is")
   case Nil
   show "?P []" by auto
   
@@ -126,12 +126,12 @@
     fix pc' pc s
     assume length: "pc' < length (a # list)"
     assume wtl:    "wtl_inst_list (a # list) G rT s s' cert mpc pc"
-    show "\\<exists> a' b s1. 
-            a' @ b = a#list \\<and> length a' = pc' \\<and> \
-            wtl_inst_list a' G rT s  s1 cert mpc pc \\<and> \
+    show "\<exists> a' b s1. 
+            a' @ b = a#list \<and> length a' = pc' \<and> \
+            wtl_inst_list a' G rT s  s1 cert mpc pc \<and> \
             wtl_inst_list b G rT s1 s' cert mpc (pc+length a')"
-        (is "\\<exists> a b s1. ?E a b s1")
-    proof (cases "pc'")
+        (is "\<exists> a b s1. ?E a b s1")
+    proof (cases (open) pc')
       case 0
       with wtl
       have "?E [] (a#list) s" by simp
@@ -158,8 +158,8 @@
 qed
 
 lemma "wtl_append1":
-"\\<lbrakk>wtl_inst_list x G rT s0 s1 cert (length (x@y)) 0; 
-  wtl_inst_list y G rT s1 s2 cert (length (x@y)) (length x)\\<rbrakk> \\<Longrightarrow>
+"\<lbrakk>wtl_inst_list x G rT s0 s1 cert (length (x@y)) 0; 
+  wtl_inst_list y G rT s1 s2 cert (length (x@y)) (length x)\<rbrakk> \<Longrightarrow>
   wtl_inst_list (x@y) G rT s0 s2 cert (length (x@y)) 0"
 proof -
   assume w:
@@ -167,11 +167,11 @@
     "wtl_inst_list y G rT s1 s2 cert (length (x@y)) (length x)"
 
   have
-    "\\<forall> pc s0. 
-    wtl_inst_list x G rT s0 s1 cert (pc+length (x@y)) pc \\<longrightarrow> 
-    wtl_inst_list y G rT s1 s2 cert (pc+length (x@y)) (pc+length x) \\<longrightarrow>
+    "\<forall> pc s0. 
+    wtl_inst_list x G rT s0 s1 cert (pc+length (x@y)) pc \<longrightarrow> 
+    wtl_inst_list y G rT s1 s2 cert (pc+length (x@y)) (pc+length x) \<longrightarrow>
     wtl_inst_list (x@y) G rT s0 s2 cert (pc+length (x@y)) pc" (is "?P x")
-  proof (induct "?P" "x")
+  proof (induct (open) ?P x)
     case Nil
     show "?P []" by simp
   next
@@ -204,9 +204,9 @@
 qed
 
 lemma wtl_cons_appendl:
-"\\<lbrakk>wtl_inst_list a G rT s0 s1 cert (length (a@i#b)) 0; 
+"\<lbrakk>wtl_inst_list a G rT s0 s1 cert (length (a@i#b)) 0; 
   wtl_inst_option i G rT s1 s2 cert (length (a@i#b)) (length a); 
-  wtl_inst_list b G rT s2 s3 cert (length (a@i#b)) (Suc (length a))\\<rbrakk> \\<Longrightarrow> 
+  wtl_inst_list b G rT s2 s3 cert (length (a@i#b)) (Suc (length a))\<rbrakk> \<Longrightarrow> 
   wtl_inst_list (a@i#b) G rT s0 s3 cert (length (a@i#b)) 0"
 proof -
   assume a: "wtl_inst_list a G rT s0 s1 cert (length (a@i#b)) 0"
@@ -222,24 +222,24 @@
 qed
 
 lemma "wtl_append":
-"\\<lbrakk>wtl_inst_list a G rT s0 s1 cert (length (a@i#b)) 0; 
+"\<lbrakk>wtl_inst_list a G rT s0 s1 cert (length (a@i#b)) 0; 
   wtl_inst_option i G rT s1 s2 cert (length (a@i#b)) (length a); 
-  wtl_inst_list b G rT s2 s3 cert (length (a@i#b)) (Suc (length a))\\<rbrakk> \\<Longrightarrow> 
+  wtl_inst_list b G rT s2 s3 cert (length (a@i#b)) (Suc (length a))\<rbrakk> \<Longrightarrow> 
   wtl_inst_list (a@[i]) G rT s0 s2 cert (length (a@i#b)) 0"
 proof -
   assume a: "wtl_inst_list a G rT s0 s1 cert (length (a@i#b)) 0"
   assume i: "wtl_inst_option i G rT s1 s2 cert (length (a@i#b)) (length a)"
   assume b: "wtl_inst_list b G rT s2 s3 cert (length (a@i#b)) (Suc (length a))"
 
-  have "\\<forall> s0 pc. wtl_inst_list a G rT s0 s1 cert (pc+length (a@i#b)) pc \\<longrightarrow> 
-        wtl_inst_option i G rT s1 s2 cert (pc+length (a@i#b)) (pc + length a) \\<longrightarrow> 
-        wtl_inst_list b G rT s2 s3 cert (pc+length (a@i#b)) (Suc pc + length a) \\<longrightarrow> 
+  have "\<forall> s0 pc. wtl_inst_list a G rT s0 s1 cert (pc+length (a@i#b)) pc \<longrightarrow> 
+        wtl_inst_option i G rT s1 s2 cert (pc+length (a@i#b)) (pc + length a) \<longrightarrow> 
+        wtl_inst_list b G rT s2 s3 cert (pc+length (a@i#b)) (Suc pc + length a) \<longrightarrow> 
           wtl_inst_list (a@[i]) G rT s0 s2 cert (pc+length (a@i#b)) pc" (is "?P a")
-  proof (induct "?P" "a")
+  proof (induct (open) ?P a)
     case Nil
     show "?P []" by (simp del: split_paired_Ex)
     case Cons
-    show "?P (a#list)" (is "\\<forall>s0 pc. ?x s0 pc \\<longrightarrow> ?y s0 pc \\<longrightarrow> ?z s0 pc \\<longrightarrow> ?p s0 pc") 
+    show "?P (a#list)" (is "\<forall>s0 pc. ?x s0 pc \<longrightarrow> ?y s0 pc \<longrightarrow> ?z s0 pc \<longrightarrow> ?p s0 pc") 
     proof intro
       fix s0 pc
       assume y: "?y s0 pc"
diff -r e4d58f1be05b -r 4cae97480a6d src/HOL/MicroJava/BV/Step.thy
--- a/src/HOL/MicroJava/BV/Step.thy	Sat Aug 19 12:49:19 2000 +0200
+++ b/src/HOL/MicroJava/BV/Step.thy	Sun Aug 20 17:45:20 2000 +0200
@@ -187,7 +187,7 @@
 
 lemma appIAdd[simp]:
 "app (IAdd, G, rT, s) = (\<exists> ST LT. s = (PrimT Integer#PrimT Integer#ST,LT))"  (is "?app s = ?P s")
-proof (cases s)
+proof (cases (open) s)
   case Pair
   have "?app (a,b) = ?P (a,b)"
   proof (cases "a")
@@ -234,7 +234,7 @@
                                        G \<turnstile> X \<preceq> Class C \<and>  
                                        (\<forall>(aT,fT)\<in>set(zip apTs fpTs). G \<turnstile> aT \<preceq> fT) \<and> 
                                        method (G,C) (mn,fpTs) \<noteq> None)" (is "?app s = ?P s")
-proof (cases s)
+proof (cases (open) s)
   case Pair
   have "?app (a,b) \<Longrightarrow> ?P (a,b)"
   proof -
diff -r e4d58f1be05b -r 4cae97480a6d src/HOL/MicroJava/BV/StepMono.thy
--- a/src/HOL/MicroJava/BV/StepMono.thy	Sat Aug 19 12:49:19 2000 +0200
+++ b/src/HOL/MicroJava/BV/StepMono.thy	Sun Aug 20 17:45:20 2000 +0200
@@ -15,7 +15,7 @@
 
 lemma sup_loc_some [rulify]:
 "\<forall> y n. (G \<turnstile> b <=l y) \<longrightarrow> n < length y \<longrightarrow> y!n = Some t \<longrightarrow> (\<exists>t. b!n = Some t \<and> (G \<turnstile> (b!n) <=o (y!n)))" (is "?P b")
-proof (induct "?P" b)
+proof (induct (open) ?P b)
   show "?P []" by simp
 
   case Cons
@@ -59,7 +59,7 @@
 
 lemma append_length_n [rulify]: 
 "\<forall>n. n \<le> length x \<longrightarrow> (\<exists>a b. x = a@b \<and> length a = n)" (is "?P x")
-proof (induct "?P" "x")
+proof (induct (open) ?P x)
   show "?P []" by simp
 
   fix l ls assume Cons: "?P ls"
@@ -122,7 +122,7 @@
   assume app: "app (i, G, rT, s1)"
   
   show ?thesis
-  proof (cases i)
+  proof (cases (open) i)
     case Load
     
     from G
@@ -308,7 +308,7 @@
     by (auto dest!: app_step_some);
 
   have "G \<turnstile> (a1',b1') <=s (a2',b2')"
-  proof (cases i)
+  proof (cases (open) i)
     case Load
 
     with s app1