--- a/Quot/Nominal/Abs.thy	Wed Feb 03 12:13:22 2010 +0100
+++ b/Quot/Nominal/Abs.thy	Wed Feb 03 12:31:58 2010 +0100
@@ -133,17 +133,18 @@
   assumes a: "\<And>x. pi \<bullet> (f x) = f (pi \<bullet> x)"
   and     b: "\<exists>pia. ({atom a}, t) \<approx>gen (\<lambda>x1 x2. R x1 x2 \<and> R (pi \<bullet> x1) (pi \<bullet> x2)) f pia ({atom b}, s)"
   shows  "\<exists>pia. ({atom (pi \<bullet> a)}, pi \<bullet> t) \<approx>gen R f pia ({atom (pi \<bullet> b)}, pi \<bullet> s)"
-  using b apply -
+  using b 
+  apply -
   apply(erule exE)
   apply(rule_tac x="pi \<bullet> pia" in exI)
   apply(simp add: alpha_gen.simps)
   apply(erule conjE)+
   apply(rule conjI)
   apply(rule_tac ?p1="- pi" in permute_eq_iff[THEN iffD1])
-  apply(simp add: a[symmetric] atom_eqvt eqvts)
+  apply(simp add: a[symmetric] atom_eqvt Diff_eqvt insert_eqvt set_eqvt empty_eqvt)
   apply(rule conjI)
   apply(rule_tac ?p1="- pi" in fresh_star_permute_iff[THEN iffD1])
-  apply(simp add: a[symmetric] eqvts atom_eqvt)
+  apply(simp add: a[symmetric] atom_eqvt Diff_eqvt insert_eqvt set_eqvt empty_eqvt)
   apply(subst permute_eqvt[symmetric])
   apply(simp)
   done