--- a/FSet.thy	Mon Nov 30 12:14:20 2009 +0100
+++ b/FSet.thy	Mon Nov 30 15:32:14 2009 +0100
@@ -313,7 +313,6 @@
   val qtrm = @{term "\<forall>x. x memb [] = False"}
   val aps = find_aps rtrm qtrm 
 *}
-unfolding IN_def EMPTY_def
 apply(tactic {* clean_tac @{context} [quot] defs aps 1*})
 done
 
@@ -354,10 +353,12 @@
 lemma cheat: "P" sorry
 
 lemma "\<lbrakk>P EMPTY; \<And>a x. P x \<Longrightarrow> P (INSERT a x)\<rbrakk> \<Longrightarrow> P l"
+apply (tactic {* (ObjectLogic.full_atomize_tac THEN' gen_frees_tac @{context}) 1 *})
+ML_prf {* val qtm = #concl (fst (Subgoal.focus @{context} 1 (#goal (Isar.goal ())))) *}
 apply(tactic {* procedure_tac @{context} @{thm list.induct} 1 *})
 apply(tactic {* regularize_tac @{context} [rel_eqv] 1 *})
 prefer 2
-apply(rule cheat)
+apply(tactic {* clean_tac @{context} [quot] defs [] 1 *})
 apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 3 *) (* Ball-Ball *)
 apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *)
 apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 2 *) (* lam-lam-elim for R = (===>) *) 
@@ -454,6 +455,8 @@
 lemma "P (x :: 'a list) (EMPTY :: 'c fset) \<Longrightarrow> (\<And>e t. P x t \<Longrightarrow> P x (INSERT e t)) \<Longrightarrow> P x l"
 apply (tactic {* procedure_tac @{context} @{thm list_induct_part} 1 *})
 apply (tactic {* regularize_tac @{context} [rel_eqv] 1 *})
+prefer 2
+apply (tactic {* clean_tac @{context} [quot] defs [(@{typ "('a list \<Rightarrow> 'c list \<Rightarrow> bool)"},@{typ "('a list \<Rightarrow> 'c fset \<Rightarrow> bool)"})] 1 *})
 apply (tactic {* (APPLY_RSP_TAC rty @{context}) 1 *})
 apply (rule FUN_QUOTIENT)
 apply (rule FUN_QUOTIENT)
@@ -523,7 +526,6 @@
 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
 apply (tactic {* (inj_repabs_tac_fset @{context}) 1 *})
-apply (tactic {* clean_tac @{context} [quot] defs [(@{typ "('a list \<Rightarrow> 'c list \<Rightarrow> bool)"},@{typ "('a list \<Rightarrow> 'c fset \<Rightarrow> bool)"})] 1 *})
 done
 
 end