src/HOL/MicroJava/BV/BVSpec.thy

 theory BVSpec = Step:
 
 constdefs
 wt_instr :: "[instr,jvm_prog,ty,method_type,nat,p_count,p_count] => bool"
 "wt_instr i G rT phi mxs max_pc pc == 
-    app i G mxs rT (phi!pc) \\<and>
-   (\\<forall> pc' \\<in> set (succs i pc). pc' < max_pc \\<and> (G \\<turnstile> step i G (phi!pc) <=' phi!pc'))"
+    app i G mxs rT (phi!pc) \<and>
+   (\<forall> pc' \<in> set (succs i pc). pc' < max_pc \<and> (G \<turnstile> step i G (phi!pc) <=' phi!pc'))"
 
 wt_start :: "[jvm_prog,cname,ty list,nat,method_type] => bool"
 "wt_start G C pTs mxl phi == 
-    G \\<turnstile> Some ([],(OK (Class C))#((map OK pTs))@(replicate mxl Err)) <=' phi!0"
+    G \<turnstile> Some ([],(OK (Class C))#((map OK pTs))@(replicate mxl Err)) <=' phi!0"
 
 
 wt_method :: "[jvm_prog,cname,ty list,ty,nat,nat,instr list,method_type] => bool"
 "wt_method G C pTs rT mxs mxl ins phi ==
 	let max_pc = length ins
         in
-	0 < max_pc \\<and> wt_start G C pTs mxl phi \\<and> 
-	(\\<forall>pc. pc<max_pc --> wt_instr (ins ! pc) G rT phi mxs max_pc pc)"
+	0 < max_pc \<and> wt_start G C pTs mxl phi \<and> 
+	(\<forall>pc. pc<max_pc --> wt_instr (ins ! pc) G rT phi mxs max_pc pc)"
 
 wt_jvm_prog :: "[jvm_prog,prog_type] => bool"
 "wt_jvm_prog G phi ==
-   wf_prog (\\<lambda>G C (sig,rT,(maxs,maxl,b)).
+   wf_prog (\<lambda>G C (sig,rT,(maxs,maxl,b)).
               wt_method G C (snd sig) rT maxs maxl b (phi C sig)) G"
 
 
 
 lemma wt_jvm_progD:
-"wt_jvm_prog G phi ==> (\\<exists>wt. wf_prog wt G)"
+"wt_jvm_prog G phi ==> (\<exists>wt. wf_prog wt G)"
 by (unfold wt_jvm_prog_def, blast)
 
 lemma wt_jvm_prog_impl_wt_instr:
 "[| wt_jvm_prog G phi; is_class G C;
     method (G,C) sig = Some (C,rT,maxs,maxl,ins); pc < length ins |] 

     simp, simp, simp add: wf_mdecl_def wt_method_def)
 
 lemma wt_jvm_prog_impl_wt_start:
 "[| wt_jvm_prog G phi; is_class G C;
     method (G,C) sig = Some (C,rT,maxs,maxl,ins) |] ==> 
- 0 < (length ins) \\<and> wt_start G C (snd sig) maxl (phi C sig)"
+ 0 < (length ins) \<and> wt_start G C (snd sig) maxl (phi C sig)"
 by (unfold wt_jvm_prog_def, drule method_wf_mdecl, 
     simp, simp, simp add: wf_mdecl_def wt_method_def)
 
 text {* for most instructions wt\_instr collapses: *}
 lemma  
 "succs i pc = [pc+1] ==> wt_instr i G rT phi mxs max_pc pc = 
- (app i G mxs rT (phi!pc) \\<and> pc+1 < max_pc \\<and> (G \\<turnstile> step i G (phi!pc) <=' phi!(pc+1)))"
+ (app i G mxs rT (phi!pc) \<and> pc+1 < max_pc \<and> (G \<turnstile> step i G (phi!pc) <=' phi!(pc+1)))"
 by (simp add: wt_instr_def) 
 
 
-(* ### move to WellForm *)
-
-lemma methd:
-  "[| wf_prog wf_mb G; (C,S,fs,mdecls) \\<in> set G; (sig,rT,code) \\<in> set mdecls |]
-  ==> method (G,C) sig = Some(C,rT,code) \\<and> is_class G C"
-proof -
-  assume wf: "wf_prog wf_mb G" 
-  assume C:  "(C,S,fs,mdecls) \\<in> set G"
-
-  assume m: "(sig,rT,code) \\<in> set mdecls"
-  moreover
-  from wf
-  have "class G Object = Some (arbitrary, [], [])"
-    by simp 
-  moreover
-  from wf C
-  have c: "class G C = Some (S,fs,mdecls)"
-    by (auto simp add: wf_prog_def class_def is_class_def intro: map_of_SomeI)
-  ultimately
-  have O: "C \\<noteq> Object"
-    by auto
-      
-  from wf C
-  have "unique mdecls"
-    by (unfold wf_prog_def wf_cdecl_def) auto
-
-  hence "unique (map (\\<lambda>(s,m). (s,C,m)) mdecls)"
-    by - (induct mdecls, auto)
-
-  with m
-  have "map_of (map (\\<lambda>(s,m). (s,C,m)) mdecls) sig = Some (C,rT,code)"
-    by (force intro: map_of_SomeI)
-
-  with wf C m c O
-  show ?thesis
-    by (auto simp add: is_class_def dest: method_rec [of _ _ C])
-qed
 
 
 end