--- a/LFex.thy	Sat Dec 05 23:35:09 2009 +0100
+++ b/LFex.thy	Sun Dec 06 00:00:47 2009 +0100
@@ -220,6 +220,7 @@
   val quot = @{thms Quotient_KIND Quotient_TY Quotient_TRM}
   val rel_refl = map (fn x => @{thm equivp_reflp} OF [x]) @{thms alpha_equivps}
   val reps_same = map (fn x => @{thm Quotient_rel_rep} OF [x]) quot
+  val trans2 = map (fn x => @{thm equals_rsp} OF [x]) quot
 *}
 
 lemma 
@@ -256,12 +257,11 @@
          ((x5 :: TRM) = x6 \<longrightarrow> P3 x5 x6)"
 using a0 a1 a2 a3 a4 a5 a6 a7 a8 a9 a10 a11
 apply - 
-apply(tactic {* lift_tac @{context} @{thm akind_aty_atrm.induct} @{thms alpha_equivps} 1 *})
-(*apply(tactic {* regularize_tac @{context} @{thms alpha_equivps} 1 *})
+apply(tactic {* procedure_tac @{context} @{thm akind_aty_atrm.induct} 1 *})
+apply(tactic {* regularize_tac @{context} @{thms alpha_equivps} 1 *})
 apply(tactic {* all_inj_repabs_tac @{context} rel_refl trans2 1 *})
+apply(fold perm_kind_def perm_ty_def perm_trm_def FV_ty_def[simplified id_simps] FV_kind_def[simplified id_simps] FV_trm_def[simplified id_simps])
 apply(tactic {* clean_tac @{context} 1 *})
-*)
-(*apply(tactic {* all_inj_repabs_tac @{context} rel_refl trans2 1 *})*)
 (*
 Profiling:
 ML_prf {* fun ith i =  (#concl (fst (Subgoal.focus @{context} i (#goal (Isar.goal ()))))) *}
@@ -270,8 +270,6 @@
 ML_prf {* PolyML.profiling 1 *}
 ML_prf {* profile 2 Seq.list_of ((all_inj_repabs_tac @{context} quot rel_refl trans2 1) (#goal (Isar.goal ()))) *}
 *)
-apply(unfold perm_kind_def perm_ty_def perm_trm_def)
-apply(tactic {* clean_tac @{context} 1 *})
 done
 
 (* Does not work: