--- a/LamEx.thy	Thu Dec 03 12:33:05 2009 +0100
+++ b/LamEx.thy	Thu Dec 03 13:45:52 2009 +0100
@@ -170,13 +170,11 @@
 done
 
 ML {* val qty = @{typ "lam"} *}
-ML {* val defs = @{thms Var_def App_def Lam_def perm_lam_def fv_def} *}
 ML {* val rsp_thms = @{thms perm_rsp fresh_rsp rVar_rsp rApp_rsp rLam_rsp rfv_rsp} *}
 
 ML {* val (rty, rel, rel_refl, rel_eqv) = lookup_quot_data @{context} qty *}
-ML {* val consts = lookup_quot_consts defs *}
 ML {* val (trans2, reps_same, absrep, quot) = lookup_quot_thms @{context} "lam" *}
-ML {* fun lift_tac_lam lthy t = lift_tac lthy t [rel_eqv] rty [quot] defs *}
+ML {* fun lift_tac_lam lthy t = lift_tac lthy t [rel_eqv] [quot] *}
 
 lemma pi_var: "(pi\<Colon>('x \<times> 'x) list) \<bullet> Var a = Var (pi \<bullet> a)"
 apply (tactic {* lift_tac_lam @{context} @{thm pi_var_com} 1 *})
@@ -212,6 +210,7 @@
 
 lemma a3: "\<lbrakk>(x\<Colon>lam) = [(a\<Colon>name, b\<Colon>name)] \<bullet> (xa\<Colon>lam); a \<notin> fv (Lam b x)\<rbrakk> \<Longrightarrow> Lam a x = Lam b xa"
 apply (tactic {* lift_tac_lam @{context} @{thm a3} 1 *})
+apply (simp add:perm_lam_def)
 done
 
 lemma alpha_cases: "\<lbrakk>a1 = a2; \<And>a b. \<lbrakk>a1 = Var a; a2 = Var b; a = b\<rbrakk> \<Longrightarrow> P;
@@ -219,6 +218,7 @@
      \<And>x a b xa. \<lbrakk>a1 = Lam a x; a2 = Lam b xa; x = [(a, b)] \<bullet> xa; a \<notin> fv (Lam b x)\<rbrakk> \<Longrightarrow> P\<rbrakk>
     \<Longrightarrow> P"
 apply (tactic {* lift_tac_lam @{context} @{thm alpha.cases} 1 *})
+apply (simp add:perm_lam_def)
 done
 
 lemma alpha_induct: "\<lbrakk>(qx\<Colon>lam) = (qxa\<Colon>lam); \<And>(a\<Colon>name) b\<Colon>name. a = b \<Longrightarrow> (qxb\<Colon>lam \<Rightarrow> lam \<Rightarrow> bool) (Var a) (Var b);
@@ -227,6 +227,7 @@
         \<lbrakk>x = [(a, b)] \<bullet> xa; qxb x ([(a, b)] \<bullet> xa); a \<notin> fv (Lam b x)\<rbrakk> \<Longrightarrow> qxb (Lam a x) (Lam b xa)\<rbrakk>
     \<Longrightarrow> qxb qx qxa"
 apply (tactic {* lift_tac_lam @{context} @{thm alpha.induct} 1 *})
+apply (simp add:perm_lam_def)
 done
 
 lemma var_inject: "(Var a = Var b) = (a = b)"
@@ -337,7 +338,7 @@
 prefer 2
 apply (tactic {* all_inj_repabs_tac @{context} rty [quot] [rel_refl] [trans2] 1 *})
 prefer 3
-apply (tactic {* clean_tac @{context} [quot] defs 1 *})
+apply (tactic {* clean_tac @{context} [quot] 1 *})
 
 thm all_prs
 thm REP_ABS_RSP