adapt to changes in RBT_Impl

--- a/src/HOL/Imperative_HOL/ex/SatChecker.thy	Fri Apr 13 11:45:30 2012 +0200
+++ b/src/HOL/Imperative_HOL/ex/SatChecker.thy	Fri Apr 13 12:49:33 2012 +0200
@@ -675,21 +675,21 @@
 primrec tres_thm :: "(ClauseId, Clause) RBT_Impl.rbt \<Rightarrow> Lit \<times> ClauseId \<Rightarrow> Clause \<Rightarrow> Clause Heap"
 where
   "tres_thm t (l, j) cli =
-  (case (RBT_Impl.lookup t j) of 
+  (case (rbt_lookup t j) of 
      None \<Rightarrow> raise (''MiniSatChecked.res_thm: No resolvant clause in thms array for Conflict step.'')
    | Some clj \<Rightarrow> res_thm' l cli clj)"
 
 fun tdoProofStep :: " ProofStep \<Rightarrow> ((ClauseId, Clause) RBT_Impl.rbt * Clause list) \<Rightarrow> ((ClauseId, Clause) RBT_Impl.rbt * Clause list) Heap"
 where
   "tdoProofStep (Conflict saveTo (i, rs)) (t, rcl) =
-     (case (RBT_Impl.lookup t i) of
+     (case (rbt_lookup t i) of
        None \<Rightarrow> raise (''MiniSatChecked.doProofStep: No starting clause in thms array for Conflict step.'')
      | Some cli \<Rightarrow> do {
                       result \<leftarrow> foldM (tres_thm t) rs cli;
-                      return ((RBT_Impl.insert saveTo result t), rcl)
+                      return ((rbt_insert saveTo result t), rcl)
                    })"
-| "tdoProofStep (Delete cid) (t, rcl) = return ((RBT_Impl.delete cid t), rcl)"
-| "tdoProofStep (Root cid clause) (t, rcl) = return (RBT_Impl.insert cid (sort clause) t, (remdups(sort clause)) # rcl)"
+| "tdoProofStep (Delete cid) (t, rcl) = return ((rbt_delete cid t), rcl)"
+| "tdoProofStep (Root cid clause) (t, rcl) = return (rbt_insert cid (sort clause) t, (remdups(sort clause)) # rcl)"
 | "tdoProofStep (Xstep cid1 cid2) (t, rcl) = raise ''MiniSatChecked.doProofStep: Xstep constructor found.''"
 | "tdoProofStep (ProofDone b) (t, rcl) = raise ''MiniSatChecked.doProofStep: ProofDone constructor found.''"
 
@@ -698,7 +698,7 @@
   "tchecker n p i =
   do {
      rcs \<leftarrow> foldM (tdoProofStep) p (RBT_Impl.Empty, []);
-     (if (RBT_Impl.lookup (fst rcs) i) = Some [] then return (snd rcs) 
+     (if (rbt_lookup (fst rcs) i) = Some [] then return (snd rcs) 
                 else raise(''No empty clause''))
   }"
 

--- a/src/HOL/Quotient_Examples/Lift_RBT.thy	Fri Apr 13 11:45:30 2012 +0200
+++ b/src/HOL/Quotient_Examples/Lift_RBT.thy	Fri Apr 13 12:49:33 2012 +0200
@@ -37,16 +37,16 @@
 
 setup_lifting type_definition_rbt
 
-lift_definition lookup :: "('a\<Colon>linorder, 'b) rbt \<Rightarrow> 'a \<rightharpoonup> 'b" is "RBT_Impl.lookup" 
+lift_definition lookup :: "('a\<Colon>linorder, 'b) rbt \<Rightarrow> 'a \<rightharpoonup> 'b" is "rbt_lookup" 
 by simp
 
 lift_definition empty :: "('a\<Colon>linorder, 'b) rbt" is RBT_Impl.Empty 
 by (simp add: empty_def)
 
-lift_definition insert :: "'a\<Colon>linorder \<Rightarrow> 'b \<Rightarrow> ('a, 'b) rbt \<Rightarrow> ('a, 'b) rbt" is "RBT_Impl.insert" 
+lift_definition insert :: "'a\<Colon>linorder \<Rightarrow> 'b \<Rightarrow> ('a, 'b) rbt \<Rightarrow> ('a, 'b) rbt" is "rbt_insert" 
 by simp
 
-lift_definition delete :: "'a\<Colon>linorder \<Rightarrow> ('a, 'b) rbt \<Rightarrow> ('a, 'b) rbt" is "RBT_Impl.delete" 
+lift_definition delete :: "'a\<Colon>linorder \<Rightarrow> ('a, 'b) rbt \<Rightarrow> ('a, 'b) rbt" is "rbt_delete" 
 by simp
 
 lift_definition entries :: "('a\<Colon>linorder, 'b) rbt \<Rightarrow> ('a \<times> 'b) list" is RBT_Impl.entries
@@ -55,10 +55,10 @@
 lift_definition keys :: "('a\<Colon>linorder, 'b) rbt \<Rightarrow> 'a list" is RBT_Impl.keys 
 by simp
 
-lift_definition bulkload :: "('a\<Colon>linorder \<times> 'b) list \<Rightarrow> ('a, 'b) rbt" is "RBT_Impl.bulkload" 
+lift_definition bulkload :: "('a\<Colon>linorder \<times> 'b) list \<Rightarrow> ('a, 'b) rbt" is "rbt_bulkload" 
 by simp
 
-lift_definition map_entry :: "'a \<Rightarrow> ('b \<Rightarrow> 'b) \<Rightarrow> ('a\<Colon>linorder, 'b) rbt \<Rightarrow> ('a, 'b) rbt" is RBT_Impl.map_entry 
+lift_definition map_entry :: "'a \<Rightarrow> ('b \<Rightarrow> 'b) \<Rightarrow> ('a\<Colon>linorder, 'b) rbt \<Rightarrow> ('a, 'b) rbt" is rbt_map_entry 
 by simp
 
 lift_definition map :: "('a \<Rightarrow> 'b \<Rightarrow> 'b) \<Rightarrow> ('a\<Colon>linorder, 'b) rbt \<Rightarrow> ('a, 'b) rbt" is RBT_Impl.map
@@ -80,11 +80,11 @@
 (* TODO: obtain the following lemmas by lifting existing theorems. *)
 
 lemma lookup_RBT:
-  "is_rbt t \<Longrightarrow> lookup (RBT t) = RBT_Impl.lookup t"
+  "is_rbt t \<Longrightarrow> lookup (RBT t) = rbt_lookup t"
   by (simp add: lookup_def RBT_inverse)
 
 lemma lookup_impl_of:
-  "RBT_Impl.lookup (impl_of t) = lookup t"
+  "rbt_lookup (impl_of t) = lookup t"
   by (simp add: lookup_def)
 
 lemma entries_impl_of:
@@ -101,11 +101,11 @@
 
 lemma lookup_insert [simp]:
   "lookup (insert k v t) = (lookup t)(k \<mapsto> v)"
-  by (simp add: insert_def lookup_RBT lookup_insert lookup_impl_of)
+  by (simp add: insert_def lookup_RBT rbt_lookup_rbt_insert lookup_impl_of)
 
 lemma lookup_delete [simp]:
   "lookup (delete k t) = (lookup t)(k := None)"
-  by (simp add: delete_def lookup_RBT RBT_Impl.lookup_delete lookup_impl_of restrict_complement_singleton_eq)
+  by (simp add: delete_def lookup_RBT rbt_lookup_rbt_delete lookup_impl_of restrict_complement_singleton_eq)
 
 lemma map_of_entries [simp]:
   "map_of (entries t) = lookup t"
@@ -113,19 +113,19 @@
 
 lemma entries_lookup:
   "entries t1 = entries t2 \<longleftrightarrow> lookup t1 = lookup t2"
-  by (simp add: entries_def lookup_def entries_lookup)
+  by (simp add: entries_def lookup_def entries_rbt_lookup)
 
 lemma lookup_bulkload [simp]:
   "lookup (bulkload xs) = map_of xs"
-  by (simp add: bulkload_def lookup_RBT RBT_Impl.lookup_bulkload)
+  by (simp add: bulkload_def lookup_RBT rbt_lookup_rbt_bulkload)
 
 lemma lookup_map_entry [simp]:
   "lookup (map_entry k f t) = (lookup t)(k := Option.map f (lookup t k))"
-  by (simp add: map_entry_def lookup_RBT RBT_Impl.lookup_map_entry lookup_impl_of)
+  by (simp add: map_entry_def lookup_RBT rbt_lookup_rbt_map_entry lookup_impl_of)
 
 lemma lookup_map [simp]:
   "lookup (map f t) k = Option.map (f k) (lookup t k)"
-  by (simp add: map_def lookup_RBT RBT_Impl.lookup_map lookup_impl_of)
+  by (simp add: map_def lookup_RBT rbt_lookup_map lookup_impl_of)
 
 lemma fold_fold:
   "fold f t = List.fold (prod_case f) (entries t)"
@@ -140,7 +140,7 @@
   by (simp add: rbt_eq_iff is_empty_def impl_of_empty split: rbt.split)
 
 lemma RBT_lookup_empty [simp]: (*FIXME*)
-  "RBT_Impl.lookup t = Map.empty \<longleftrightarrow> t = RBT_Impl.Empty"
+  "rbt_lookup t = Map.empty \<longleftrightarrow> t = RBT_Impl.Empty"
   by (cases t) (auto simp add: fun_eq_iff)
 
 lemma lookup_empty_empty [simp]:
@@ -149,7 +149,7 @@
 
 lemma sorted_keys [iff]:
   "sorted (keys t)"
-  by (simp add: keys_def RBT_Impl.keys_def sorted_entries)
+  by (simp add: keys_def RBT_Impl.keys_def rbt_sorted_entries)
 
 lemma distinct_keys [iff]:
   "distinct (keys t)"