--- a/Nominal/Nominal2_Abs.thy	Mon Jun 20 10:16:12 2011 +0900
+++ b/Nominal/Nominal2_Abs.thy	Mon Jun 20 20:08:16 2011 +0900
@@ -1063,6 +1063,33 @@
   apply(simp add: eqv)
   done
 
+lemma Abs_set_fcb:
+  fixes xs ys :: "'a :: fs"
+    and S T :: "'b :: fs"
+  assumes e: "(Abs_set (ba xs) T) = (Abs_set (ba ys) S)"
+    and f1: "\<And>x. x \<in> ba xs \<Longrightarrow> x \<sharp> f xs T"
+    and f2: "\<And>x. supp T - ba xs = supp S - ba ys \<Longrightarrow> x \<in> ba ys \<Longrightarrow> x \<sharp> f xs T"
+    and eqv: "\<And>p. p \<bullet> T = S \<Longrightarrow> p \<bullet> ba xs = ba ys \<Longrightarrow> supp p \<subseteq> ba xs \<union> ba ys \<Longrightarrow> p \<bullet> (f xs T) = f ys S"
+  shows "f xs T = f ys S"
+  using e apply -
+  apply(subst (asm) Abs_eq_iff2)
+  apply(simp add: alphas)
+  apply(elim exE conjE)
+  apply(rule trans)
+  apply(rule_tac p="p" in supp_perm_eq[symmetric])
+  apply(rule fresh_star_supp_conv)
+  apply(drule fresh_star_perm_set_conv)
+  apply(rule finite_Diff)
+  apply(rule finite_supp)
+  apply(subgoal_tac "(ba xs \<union> ba ys) \<sharp>* f xs T")
+  apply(metis Un_absorb2 fresh_star_Un)
+  apply(subst fresh_star_Un)
+  apply(rule conjI)
+  apply(simp add: fresh_star_def f1)
+  apply(simp add: fresh_star_def f2)
+  apply(simp add: eqv)
+  done
+
 lemma Abs_res_fcb:
   fixes xs ys :: "('a :: at_base) set"
     and S T :: "'b :: fs"