--- a/Quot/Examples/SigmaEx.thy	Thu Feb 04 18:09:20 2010 +0100
+++ b/Quot/Examples/SigmaEx.thy	Fri Feb 05 10:32:21 2010 +0100
@@ -75,6 +75,8 @@
 
 end
 
+
+
 lemma tolift:
 "\<forall> fvar.
  \<forall> fobj\<in>Respects (op = ===> list_rel (prod_rel (op =) alpha_method) ===> op =).
@@ -85,18 +87,16 @@
  \<forall> fpar\<in>Respects (op = ===> op = ===> alpha_method ===> op =).
  \<forall> fsgm\<in>Respects (op = ===> (op = ===> alpha_obj) ===> op =).
 
- Bex1
-   (Respects (prod_rel (alpha_obj ===> op =)
+ Ex1 (\<lambda>x.
+(x \<in> (Respects (prod_rel (alpha_obj ===> op =)
      (prod_rel (list_rel (prod_rel (op =) alpha_method) ===> op =)
        (prod_rel ((prod_rel (op =) alpha_method) ===> op =)
          (alpha_method ===> op =)
        )
-     )
-   ))
+     )))) \<and>
 (\<lambda> (hom_o\<Colon>robj \<Rightarrow> 'a, hom_d\<Colon>(char list \<times> rmethod) list \<Rightarrow> 'b, hom_e\<Colon>char list \<times> rmethod \<Rightarrow> 'c, hom_m\<Colon>rmethod \<Rightarrow> 'd).
 
-
- (\<forall>x. hom_o (rVar x) = fvar x) \<and>
+((\<forall>x. hom_o (rVar x) = fvar x) \<and>
  (\<forall>d. hom_o (rObj d) = fobj (hom_d d) d) \<and>
  (\<forall>a l. hom_o (rInv a l) = fnvk (hom_o a) a l) \<and>
  (\<forall>a l m. hom_o (rUpd a l m) = fupd (hom_o a) (hom_m m) a l m) \<and>
@@ -104,14 +104,25 @@
  (hom_d [] = fnil) \<and>
  (\<forall>l m. hom_e (l, m) = fpar (hom_m m) l m) \<and>
  (\<forall>x a. hom_m (rSig x a) = fsgm (\<lambda>y. hom_o ([(x, y)] \<bullet> a)) (\<lambda>y. [(x, y)] \<bullet> a))
-)"
+)) x) "
 sorry
 
-syntax
+lemma test_to: "Ex1 (\<lambda>x. (x \<in> (Respects alpha_obj)) \<and> P x)"
+ML_prf {* prop_of (#goal (Isar.goal ())) *}
+sorry
+lemma test_tod: "Ex1 (P :: obj \<Rightarrow> bool)"
+apply (lifting test_to)
+done
+
+
+
+
+(*syntax
   "_expttrn"        :: "pttrn => bool => bool"      ("(3\<exists>\<exists> _./ _)" [0, 10] 10)
 
 translations
   "\<exists>\<exists> x. P"   == "Ex (%x. P)"
+*)
 
 lemma rvar_rsp[quot_respect]: "(op = ===> alpha_obj) rVar rVar"
   by (simp add: a1)
@@ -129,7 +140,7 @@
 
   
 lemma bex1_bex1reg: "(\<exists>!x\<in>Respects R. P x) \<longrightarrow> (Bex1_rel R (\<lambda>x. P x))"
-apply (simp add: Bex1_def Ex1_def Bex1_rel_def in_respects)
+apply (simp add: Ex1_def Bex1_rel_def in_respects)
 apply clarify
 apply auto
 apply (rule bexI)
@@ -154,8 +165,6 @@
 apply (lifting tolift)
 done
 
-done
-
 lemma tolift':
 "\<forall> fvar.
  \<forall> fobj\<in>Respects (op = ===> list_rel (prod_rel (op =) alpha_method) ===> op =).

--- a/Quot/QuotBase.thy	Thu Feb 04 18:09:20 2010 +0100
+++ b/Quot/QuotBase.thy	Fri Feb 05 10:32:21 2010 +0100
@@ -434,9 +434,9 @@
 
 lemma bex1_rsp:
   assumes a: "(R ===> (op =)) f g"
-  shows "(Bex1 (Respects R) f = Bex1 (Respects R) g)"
+  shows "Ex1 (\<lambda>x. x \<in> Respects R \<and> f x) = Ex1 (\<lambda>x. x \<in> Respects R \<and> g x)"
   using a 
-by (simp add: Ex1_def Bex1_def in_respects) auto
+by (simp add: Ex1_def in_respects) auto
 
 (* 3 lemmas needed for cleaning of quantifiers *)
 lemma all_prs:
@@ -536,7 +536,7 @@
 done
 
 lemma bex1_bexeq_reg: "(\<exists>!x\<in>Respects R. P x) \<longrightarrow> (Bex1_rel R (\<lambda>x. P x))"
-  apply (simp add: Bex1_def Ex1_def Bex1_rel_def in_respects)
+  apply (simp add: Ex1_def Bex1_rel_def in_respects)
   apply clarify
   apply auto
   apply (rule bexI)

--- a/Quot/quotient_tacs.ML	Thu Feb 04 18:09:20 2010 +0100
+++ b/Quot/quotient_tacs.ML	Fri Feb 05 10:32:21 2010 +0100
@@ -139,7 +139,7 @@
   0. preliminary simplification step according to
      ball_reg_eqv bex_reg_eqv babs_reg_eqv ball_reg_eqv_range bex_reg_eqv_range
 
-  1. eliminating simple Ball/Bex/Bex1 instances (ball_reg_right bex_reg_left)
+  1. eliminating simple Ball/Bex instances (ball_reg_right bex_reg_left)
 
   2. monos
 
@@ -354,17 +354,6 @@
     (Const(@{const_name Bex},_) $ (Const (@{const_name Respects}, _) $ _) $ _)
       => rtac @{thm fun_rel_id} THEN' quot_true_tac ctxt unlam
 
-| Const (@{const_name "op ="},_) $
-    (Const(@{const_name Bex1},_) $ (Const (@{const_name Respects}, _) $ _) $ _) $
-    (Const(@{const_name Bex1},_) $ (Const (@{const_name Respects}, _) $ _) $ _)
-      => rtac @{thm bex1_rsp} THEN' dtac @{thm QT_ex1}
-
-(* TODO: Check why less _ are needed then in EX/ALL cases *)
-| (Const (@{const_name fun_rel}, _) $ _ $ _) $
-    (Const(@{const_name Bex1},_) $ (Const (@{const_name Respects}, _) $ _)) $
-    (Const(@{const_name Bex1},_) $ (Const (@{const_name Respects}, _) $ _))
-      => rtac @{thm fun_rel_id} THEN' quot_true_tac ctxt unlam
-
 | (Const (@{const_name fun_rel}, _) $ _ $ _) $
     (Const(@{const_name Bex1_rel},_) $ _) $ (Const(@{const_name Bex1_rel},_) $ _)
       => rtac @{thm bexeq_rsp} THEN' quotient_tac ctxt

--- a/Quot/quotient_term.ML	Thu Feb 04 18:09:20 2010 +0100
+++ b/Quot/quotient_term.ML	Fri Feb 05 10:32:21 2010 +0100
@@ -389,7 +389,6 @@
 val mk_babs = Const (@{const_name Babs}, dummyT)
 val mk_ball = Const (@{const_name Ball}, dummyT)
 val mk_bex  = Const (@{const_name Bex}, dummyT)
-val mk_bex1 = Const (@{const_name Bex1}, dummyT)
 val mk_bex1_rel = Const (@{const_name Bex1_rel}, dummyT)
 val mk_resp = Const (@{const_name Respects}, dummyT)
 
@@ -474,6 +473,24 @@
          else mk_bex $ (mk_resp $ equiv_relation ctxt (qnt_typ ty, qnt_typ ty')) $ subtrm
        end
 
+  | (Const (@{const_name "Ex1"}, ty) $ 
+      (Abs (n, _,
+        (Const (@{const_name "op &"}, _) $ 
+          (Const (@{const_name "op :"}, _) $ _ $ (Const (@{const_name "Respects"}, _) $ resrel)) $ 
+          (t $ _)
+        )
+      )), Const (@{const_name "Ex1"}, ty') $ t') =>
+       let
+         val t = incr_boundvars (~1) t
+         val subtrm = apply_subt (regularize_trm ctxt) (t, t')
+         val needrel = equiv_relation_chk ctxt (qnt_typ ty, qnt_typ ty')
+         val _ = tracing "bla"
+       in
+         if resrel <> needrel
+         then term_mismatch "regularize (Bex1)" ctxt resrel needrel
+         else mk_bex1_rel $ resrel $ subtrm
+       end
+
   | (Const (@{const_name "Ex1"}, ty) $ t, Const (@{const_name "Ex1"}, ty') $ t') =>
        let
          val subtrm = apply_subt (regularize_trm ctxt) (t, t')
@@ -514,17 +531,6 @@
          else mk_bex1_rel $ resrel $ subtrm
        end
 
-  | (Const (@{const_name "Bex1"}, ty) $ (Const (@{const_name "Respects"}, _) $ resrel) $ t, 
-     Const (@{const_name "Ex1"}, ty') $ t') =>
-       let
-         val subtrm = apply_subt (regularize_trm ctxt) (t, t')
-         val needrel = equiv_relation_chk ctxt (qnt_typ ty, qnt_typ ty')
-       in
-         if resrel <> needrel
-         then term_mismatch "regularize (Bex1)" ctxt resrel needrel
-         else mk_bex1_rel $ resrel $ subtrm
-       end
-
   | (* equalities need to be replaced by appropriate equivalence relations *) 
     (Const (@{const_name "op ="}, ty), Const (@{const_name "op ="}, ty')) =>
          if ty = ty' then rtrm