--- a/Nominal/Test.thy	Wed Mar 03 10:39:43 2010 +0100
+++ b/Nominal/Test.thy	Wed Mar 03 11:42:15 2010 +0100
@@ -17,6 +17,41 @@
 the first two terms are created? Should be ommitted. Also
 something wrong with the permutations. *)
 
+lemma "alpha_weird_raw a b \<Longrightarrow> alpha_weird_raw (p \<bullet> a) (p \<bullet> b)"
+apply (erule alpha_weird_raw.induct)
+defer
+apply (simp add: alpha_weird_raw.intros)
+apply (simp add: alpha_weird_raw.intros)
+apply (simp only: permute_weird_raw.simps)
+apply (rule alpha_weird_raw.intros)
+apply (erule exi[of _ _ "p"])
+apply (erule exi[of _ _ "p"])
+apply (erule exi[of _ _ "p"])
+apply (erule exi[of _ _ "p"])
+apply (erule conjE)+
+apply (rule conjI)
+apply (erule alpha_gen_compose_eqvt[of _ _ _ _ "p"])
+apply (simp add: eqvts)
+apply (simp add: eqvts)
+apply (rule conjI)
+defer
+apply (erule alpha_gen_compose_eqvt[of _ _ _ _ "p"])
+apply (simp add: eqvts)
+apply (simp add: eqvts)
+apply (rule conjI)
+defer
+apply (simp add: supp_eqvt[symmetric] inter_eqvt[symmetric] empty_eqvt)
+apply(simp add: alpha_gen.simps)
+apply(erule conjE)+
+  apply(rule conjI)
+  apply(rule_tac ?p1="- p" in permute_eq_iff[THEN iffD1])
+apply (simp add: eqvts)
+  apply(rule conjI)
+  apply(rule_tac ?p1="- p" in fresh_star_permute_iff[THEN iffD1])
+apply (simp add: eqvts add_perm_eqvt)
+apply (simp add: permute_eqvt[symmetric])
+done
+
 primrec 
   fv_weird
 where
@@ -209,14 +244,15 @@
 
 (* example 4 from Terms.thy *)
 
-(* fv_eqvt does not work, we need to repaire defined permute functions...
-nominal_datatype trm4 =
+(* fv_eqvt does not work, we need to repaire defined permute functions
+   defined fv and defined alpha... *)
+(*nominal_datatype trm4 =
   Vr4 "name"
 | Ap4 "trm4" "trm4 list"
 | Lm4 x::"name" t::"trm4"  bind x in t
 
 thm alpha_trm4_raw_alpha_trm4_raw_list.intros[no_vars]
-thm fv_trm4_raw_fv_trm4_raw_list.simps[no_vars]
+thm fv_trm4_raw_fv_trm4_raw_list.simps[no_vars]*)
 
 (* example 5 from Terms.thy *)