--- a/Quot/Nominal/Terms.thy	Mon Feb 22 16:16:04 2010 +0100
+++ b/Quot/Nominal/Terms.thy	Mon Feb 22 16:44:58 2010 +0100
@@ -116,33 +116,37 @@
   apply(simp add: permute_eqvt[symmetric])
   done
 
-
+ML {*
+build_equivps [@{term alpha_rtrm1}, @{term alpha_bp}] @{thm rtrm1_bp.induct} @{thm alpha_rtrm1_alpha_bp.induct} @{thms rtrm1.inject bp.inject} @{thms alpha1_inj} @{thms rtrm1.distinct bp.distinct} @{thms alpha_rtrm1.cases alpha_bp.cases} @{thms alpha1_eqvt} @{context}
+*}
+ML Variable.export
 
-prove alpha1_reflp_aux: {* fst (build_alpha_refl_gl [@{term alpha_rtrm1}, @{term alpha_bp}]) *}
+prove alpha1_reflp_aux: {* fst (build_alpha_refl_gl [@{term alpha_rtrm1}, @{term alpha_bp}] ("x","y","z")) *}
 by (tactic {* reflp_tac @{thm rtrm1_bp.induct} @{thms alpha1_inj} 1 *})
 
-prove alpha1_symp_aux: {* (fst o snd) (build_alpha_refl_gl [@{term alpha_rtrm1}, @{term alpha_bp}]) *}
+prove alpha1_symp_aux: {* (fst o snd) (build_alpha_refl_gl [@{term alpha_rtrm1}, @{term alpha_bp}] ("x","y","z")) *}
 by (tactic {* symp_tac @{thm alpha_rtrm1_alpha_bp.induct} @{thms alpha1_inj} @{thms alpha1_eqvt} 1 *})
 
-prove alpha1_transp_aux: {* (snd o snd) (build_alpha_refl_gl [@{term alpha_rtrm1}, @{term alpha_bp}]) *}
+prove alpha1_transp_aux: {* (snd o snd) (build_alpha_refl_gl [@{term alpha_rtrm1}, @{term alpha_bp}] ("x","y","z")) *}
 by (tactic {* transp_tac @{thm alpha_rtrm1_alpha_bp.induct} @{thms alpha1_inj} @{thms rtrm1.inject bp.inject} @{thms rtrm1.distinct bp.distinct} @{thms alpha_rtrm1.cases alpha_bp.cases} @{thms alpha1_eqvt} 1 *})
 
-lemma helper: "(\<forall>x y z. R x y \<and> R y z \<longrightarrow> R x z) = (\<forall>xa ya. R xa ya \<longrightarrow> (\<forall>z. R ya z \<longrightarrow> R xa z))"
-by meson
+lemma transp_aux:
+  "(\<And>xa ya. R xa ya \<longrightarrow> (\<forall>z. R ya z \<longrightarrow> R xa z)) \<Longrightarrow> transp R"
+  unfolding transp_def
+  by blast
 
 lemma alpha1_equivp:
   "equivp alpha_rtrm1"
   "equivp alpha_bp"
-unfolding equivp_reflp_symp_transp reflp_def
-apply (simp_all add: alpha1_reflp_aux)
-unfolding symp_def
-apply (simp_all add: alpha1_symp_aux)
-unfolding transp_def
-apply (simp_all only: helper)
-apply (rule allI)+
-apply (rule conjunct1[OF alpha1_transp_aux])
-apply (rule allI)+
-apply (rule conjunct2[OF alpha1_transp_aux])
+apply (tactic {*
+  (simp_tac (HOL_ss addsimps @{thms equivp_reflp_symp_transp reflp_def symp_def})
+  THEN' rtac @{thm conjI} THEN' rtac @{thm allI} THEN'
+  resolve_tac (HOLogic.conj_elims @{thm alpha1_reflp_aux})
+  THEN' rtac @{thm conjI} THEN' rtac @{thm allI} THEN' rtac @{thm allI} THEN'
+  resolve_tac (HOLogic.conj_elims @{thm alpha1_symp_aux}) THEN' rtac @{thm transp_aux}
+  THEN' resolve_tac (HOLogic.conj_elims @{thm alpha1_transp_aux})
+)
+1 *})
 done
 
 quotient_type trm1 = rtrm1 / alpha_rtrm1
@@ -526,13 +530,13 @@
   apply (simp)
   done
 
-prove alpha5_reflp_aux: {* fst (build_alpha_refl_gl [@{term alpha_rtrm5}, @{term alpha_rlts}]) *}
+prove alpha5_reflp_aux: {* fst (build_alpha_refl_gl [@{term alpha_rtrm5}, @{term alpha_rlts}] ("x","y","z")) *}
 by (tactic {* reflp_tac @{thm rtrm5_rlts.induct} @{thms alpha5_inj} 1 *})
 
-prove alpha5_symp_aux: {* (fst o snd) (build_alpha_refl_gl [@{term alpha_rtrm5}, @{term alpha_rlts}]) *}
+prove alpha5_symp_aux: {* (fst o snd) (build_alpha_refl_gl [@{term alpha_rtrm5}, @{term alpha_rlts}] ("x","y","z")) *}
 by (tactic {* symp_tac @{thm alpha_rtrm5_alpha_rlts.induct} @{thms alpha5_inj} @{thms alpha5_eqvt} 1 *})
 
-prove alpha5_transp_aux: {* (snd o snd) (build_alpha_refl_gl [@{term alpha_rtrm5}, @{term alpha_rlts}]) *}
+prove alpha5_transp_aux: {* (snd o snd) (build_alpha_refl_gl [@{term alpha_rtrm5}, @{term alpha_rlts}] ("x","y","z")) *}
 by (tactic {* transp_tac @{thm alpha_rtrm5_alpha_rlts.induct} @{thms alpha5_inj} @{thms rtrm5.inject rlts.inject} @{thms rtrm5.distinct rlts.distinct} @{thms alpha_rtrm5.cases alpha_rlts.cases} @{thms alpha5_eqvt} 1 *})
 
 lemma alpha5_equivps: