--- a/Nominal/Term5n.thy	Mon Mar 22 14:07:35 2010 +0100
+++ b/Nominal/Term5n.thy	Mon Mar 22 15:27:01 2010 +0100
@@ -123,31 +123,9 @@
 local_setup {* snd o Local_Theory.note ((@{binding alpha_dis}, []), (flat (map (distinct_rel @{context} @{thms alpha_rtrm5.cases alpha_rlts.cases alpha_rbv5.cases}) [(@{thms rtrm5.distinct}, @{term alpha_rtrm5}), (@{thms rlts.distinct}, @{term alpha_rlts}), (@{thms rlts.distinct}, @{term alpha_rbv5})]))) *}
 print_theorems
 
-lemma alpha_rbv_rsp_pre:
-  "x \<approx>l y \<Longrightarrow> \<forall>z. alpha_rbv5 x z = alpha_rbv5 y z"
-  apply (erule alpha_rtrm5_alpha_rlts_alpha_rbv5.inducts(2))
-  apply (simp_all add: alpha_dis alpha5_inj)
-  apply clarify
-  apply (case_tac [!] z)
-  apply (simp_all add: alpha_dis alpha5_inj)
-  apply clarify
-  apply auto
-  apply (meson alpha5_symp alpha5_transp)
-  apply (meson alpha5_symp alpha5_transp)
-  done
+local_setup {* snd o Local_Theory.note ((@{binding alpha_bn_rsp}, []), prove_alpha_bn_rsp [@{term alpha_rtrm5}, @{term alpha_rlts}] @{thms alpha_rtrm5_alpha_rlts_alpha_rbv5.inducts} @{thms alpha5_inj alpha_dis} @{thms alpha5_equivp} @{context} (@{term alpha_rbv5}, 1)) *}
+thm alpha_bn_rsp
 
-lemma alpha_rbv_rsp_pre2:
-  "x \<approx>l y \<Longrightarrow> \<forall>z. alpha_rbv5 z x = alpha_rbv5 z y"
-  apply (erule alpha_rtrm5_alpha_rlts_alpha_rbv5.inducts(2))
-  apply (simp_all add: alpha_dis alpha5_inj)
-  apply clarify
-  apply (case_tac [!] z)
-  apply (simp_all add: alpha_dis alpha5_inj)
-  apply clarify
-  apply auto
-  apply (meson alpha5_symp alpha5_transp)
-  apply (meson alpha5_symp alpha5_transp)
-  done
 
 lemma [quot_respect]:
   "(alpha_rlts ===> op =) fv_rlts fv_rlts"
@@ -161,7 +139,7 @@
   "(op = ===> alpha_rtrm5 ===> alpha_rtrm5) permute permute"
   "(op = ===> alpha_rlts ===> alpha_rlts) permute permute"
   "(alpha_rlts ===> alpha_rlts ===> op =) alpha_rbv5 alpha_rbv5"
-  apply (simp_all add: alpha5_inj alpha5_rfv alpha5_eqvt bv_list_rsp alpha_rbv_rsp_pre alpha_rbv_rsp_pre2 alpha5_reflp)
+  apply (simp_all add: alpha5_inj alpha5_rfv alpha5_eqvt bv_list_rsp alpha5_reflp alpha_bn_rsp)
   apply (clarify)
   apply (rule_tac x="0" in exI) apply (simp add: fresh_star_def fresh_zero_perm alpha_gen alpha5_rfv)
 done