--- a/FSet.thy	Fri Dec 04 18:32:19 2009 +0100
+++ b/FSet.thy	Fri Dec 04 21:42:55 2009 +0100
@@ -286,6 +286,10 @@
   apply (auto simp add: memb_rsp rsp_fold_def)
 done
 
+lemma list_equiv_rsp[quotient_rsp]:
+  shows "(op \<approx> ===> op \<approx> ===> op =) op \<approx> op \<approx>"
+by (auto intro: list_eq.intros)
+
 print_quotients
 
 ML {* val qty = @{typ "'a fset"} *}
@@ -342,54 +346,9 @@
 apply (tactic {* (ObjectLogic.full_atomize_tac THEN' gen_frees_tac @{context}) 1 *})
 apply(tactic {* procedure_tac @{context} @{thm list.induct} 1 *})
 apply(tactic {* regularize_tac @{context} [rel_eqv] 1 *})
-prefer 2
+defer
 apply(tactic {* clean_tac @{context} 1 *})
-apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 3 *) (* Ball-Ball *)
-apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *)
-apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 2 *) (* lam-lam-elim for R = (===>) *)
-apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 3 *) (* Ball-Ball *)
-apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *)
-apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 2 *) (* lam-lam-elim for R = (===>) *)
-apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* B *) (* Cong *)
-apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* B *) (* Cong *)
-apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 8 *) (* = reflexivity arising from cong *)
-apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* A *) (* application if type needs lifting *)
-apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *)
-apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* E *) (* R x y assumptions *)
-apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *)
-apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* D *) (* reflexivity of basic relations *)
-apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* B *) (* Cong *)
-apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* B *) (* Cong *)
-apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 8 *) (* = reflexivity arising from cong *)
-apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* B *) (* Cong *)
-apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 8 *) (* = reflexivity arising from cong *)
-apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* C *) (* = and extensionality *)
-apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 3 *) (* Ball-Ball *)
-apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *)
-apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 2 *) (* lam-lam-elim for R = (===>) *) 
-apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* B *) (* Cong *)
-apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* B *) (* Cong *)
-apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 8 *) (* = reflexivity arising from cong *)
-apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* A *) (* application if type needs lifting *)
-apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *)
-apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* E *) (* R x y assumptions *)
-apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *)
-apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* E *) (* R x y assumptions *)
-apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* A *) (* application if type needs lifting *)
-apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *)
-apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* E *) (* R x y assumptions *)
-apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *)
-apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* A *) (* application if type needs lifting *)
-apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* A *) (* application if type needs lifting *)
-apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 7 *) (* respectfulness *)
-apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 8 *) (* = reflexivity arising from cong *)
-apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *)
-apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* E *) (* R x y assumptions *)
-apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* A *) (* application if type needs lifting *)
-apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *)
-apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* E *) (* R x y assumptions *)
-apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* 9 *) (* Rep-Abs-elim - can be complex Rep-Abs *)
-apply(tactic {* inj_repabs_tac_fset @{context} 1*}) (* E *) (* R x y assumptions *)
+apply(tactic {* inj_repabs_tac_fset @{context} 1*})+
 done
 
 lemma list_induct_part: