src/HOL/IOA/NTP/Multiset.ML

--- a/src/HOL/IOA/NTP/Multiset.ML	Wed Oct 04 13:11:57 1995 +0100
+++ b/src/HOL/IOA/NTP/Multiset.ML	Wed Oct 04 13:12:14 1995 +0100
@@ -14,13 +14,13 @@
 
 goal Multiset.thy 
      "count (addm M x) y = (if y=x then Suc(count M y) else count M y)";
-  by (asm_simp_tac (arith_ss addsimps 
+  by (asm_simp_tac (!simpset addsimps 
                     [Multiset.count_def,Multiset.countm_nonempty_def]
                     setloop (split_tac [expand_if])) 1);
 qed "count_addm_simp";
 
 goal Multiset.thy "count M y <= count (addm M x) y";
-  by (simp_tac (arith_ss addsimps [count_addm_simp]
+  by (simp_tac (!simpset addsimps [count_addm_simp]
                          setloop (split_tac [expand_if])) 1);
   by (rtac impI 1);
   by (rtac (le_refl RS (leq_suc RS mp)) 1);
@@ -29,31 +29,31 @@
 goalw Multiset.thy [Multiset.count_def] 
      "count (delm M x) y = (if y=x then pred(count M y) else count M y)";
   by (res_inst_tac [("M","M")] Multiset.induction 1);
-  by (asm_simp_tac (arith_ss 
+  by (asm_simp_tac (!simpset 
                    addsimps [Multiset.delm_empty_def,Multiset.countm_empty_def]
                    setloop (split_tac [expand_if])) 1);
-  by (asm_full_simp_tac (arith_ss 
+  by (asm_full_simp_tac (!simpset 
                          addsimps [Multiset.delm_nonempty_def,
                                    Multiset.countm_nonempty_def]
                          setloop (split_tac [expand_if])) 1);
   by (safe_tac HOL_cs);
-  by (asm_full_simp_tac HOL_ss 1);
+  by (Asm_full_simp_tac 1);
 qed "count_delm_simp";
 
 goal Multiset.thy "!!M. (!x. P(x) --> Q(x)) ==> (countm M P <= countm M Q)";
   by (res_inst_tac [("M","M")] Multiset.induction 1);
-  by (simp_tac (arith_ss addsimps [Multiset.countm_empty_def]) 1);
-  by (simp_tac (arith_ss addsimps[Multiset.countm_nonempty_def]) 1);
+  by (simp_tac (!simpset addsimps [Multiset.countm_empty_def]) 1);
+  by (simp_tac (!simpset addsimps[Multiset.countm_nonempty_def]) 1);
   by (etac (less_eq_add_cong RS mp RS mp) 1);
-  by (asm_full_simp_tac (arith_ss addsimps [le_eq_less_or_eq]
+  by (asm_full_simp_tac (!simpset addsimps [le_eq_less_or_eq]
                                   setloop (split_tac [expand_if])) 1);
 qed "countm_props";
 
 goal Multiset.thy "!!P. ~P(obj) ==> countm M P = countm (delm M obj) P";
   by (res_inst_tac [("M","M")] Multiset.induction 1);
-  by (simp_tac (arith_ss addsimps [Multiset.delm_empty_def,
+  by (simp_tac (!simpset addsimps [Multiset.delm_empty_def,
                                    Multiset.countm_empty_def]) 1);
-  by (asm_simp_tac (arith_ss addsimps[Multiset.countm_nonempty_def,
+  by (asm_simp_tac (!simpset addsimps[Multiset.countm_nonempty_def,
                                       Multiset.delm_nonempty_def]
                              setloop (split_tac [expand_if])) 1);
 qed "countm_spurious_delm";
@@ -61,10 +61,10 @@
 
 goal Multiset.thy "!!P. P(x) ==> 0<count M x --> 0<countm M P";
   by (res_inst_tac [("M","M")] Multiset.induction 1);
-  by (simp_tac (arith_ss addsimps 
+  by (simp_tac (!simpset addsimps 
                           [Multiset.delm_empty_def,Multiset.count_def,
                            Multiset.countm_empty_def]) 1);
-  by (asm_simp_tac (arith_ss addsimps 
+  by (asm_simp_tac (!simpset addsimps 
                        [Multiset.count_def,Multiset.delm_nonempty_def,
                         Multiset.countm_nonempty_def]
                     setloop (split_tac [expand_if])) 1);
@@ -73,10 +73,10 @@
 goal Multiset.thy
    "!!P. P(x) ==> 0<count M x --> countm (delm M x) P = pred (countm M P)";
   by (res_inst_tac [("M","M")] Multiset.induction 1);
-  by (simp_tac (arith_ss addsimps 
+  by (simp_tac (!simpset addsimps 
                           [Multiset.delm_empty_def,
                            Multiset.countm_empty_def]) 1);
-  by (asm_simp_tac (arith_ss addsimps 
+  by (asm_simp_tac (!simpset addsimps 
                       [eq_sym_conv,count_addm_simp,Multiset.delm_nonempty_def,
                        Multiset.countm_nonempty_def,pos_count_imp_pos_countm,
                        suc_pred_id]