--- a/Quot/QuotMain.thy	Tue Jan 26 08:55:55 2010 +0100
+++ b/Quot/QuotMain.thy	Tue Jan 26 09:28:32 2010 +0100
@@ -47,8 +47,7 @@
 qed
 
 theorem thm10:
-  shows "abs (rep a) \<equiv> a"
-  apply  (rule eq_reflection)
+  shows "abs (rep a) = a"
   unfolding abs_def rep_def
 proof -
   from rep_prop
@@ -112,10 +111,10 @@
 text {* Lemmas about simplifying id's. *}
 lemmas [id_simps] =
   id_def[symmetric]
-  fun_map_id[THEN eq_reflection]
+  fun_map_id
   id_apply[THEN eq_reflection]
-  id_o[THEN eq_reflection]
-  o_id[THEN eq_reflection]
+  id_o
+  o_id
   eq_comp_r
 
 text {* Translation functions for the lifting process. *}