IOA/example/Multiset.ML

 *)
 
 goalw Multiset.thy [Multiset.count_def, Multiset.countm_empty_def]
    "count({|},x) = 0";
  by (rtac refl 1);
-val count_empty = result();
+qed "count_empty";
 
 goal Multiset.thy 
      "count(addm(M,x),y) = if(y=x,Suc(count(M,y)),count(M,y))";
   by (asm_simp_tac (arith_ss addsimps 
                     [Multiset.count_def,Multiset.countm_nonempty_def]
                     setloop (split_tac [expand_if])) 1);
-val count_addm_simp = result();
+qed "count_addm_simp";
 
 goal Multiset.thy "count(M,y) <= count(addm(M,x),y)";
   by (simp_tac (arith_ss addsimps [count_addm_simp]
                          setloop (split_tac [expand_if])) 1);
   by (rtac impI 1);
   by (rtac (le_refl RS (leq_suc RS mp)) 1);
-val count_leq_addm = result();
+qed "count_leq_addm";
 
 goalw Multiset.thy [Multiset.count_def] 
      "count(delm(M,x),y) = if(y=x,pred(count(M,y)),count(M,y))";
   by (res_inst_tac [("M","M")] Multiset.induction 1);
   by (asm_simp_tac (arith_ss 

                          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);
-val count_delm_simp = result();
+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 (etac (less_eq_add_cong RS mp RS mp) 1);
   by (asm_full_simp_tac (arith_ss addsimps [le_eq_less_or_eq]
                                   setloop (split_tac [expand_if])) 1);
-val countm_props = result();
+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,
                                    Multiset.countm_empty_def]) 1);
   by (asm_simp_tac (arith_ss addsimps[Multiset.countm_nonempty_def,
                                       Multiset.delm_nonempty_def]
                              setloop (split_tac [expand_if])) 1);
-val countm_spurious_delm = result();
+qed "countm_spurious_delm";
 
 
 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 

                            Multiset.countm_empty_def]) 1);
   by (asm_simp_tac (arith_ss addsimps 
                        [Multiset.count_def,Multiset.delm_nonempty_def,
                         Multiset.countm_nonempty_def]
                     setloop (split_tac [expand_if])) 1);
-val pos_count_imp_pos_countm = standard(result() RS mp);
+val pos_count_imp_pos_countm = store_thm("pos_count_imp_pos_countm", standard(result() RS mp));
 
 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 (asm_simp_tac (arith_ss addsimps 
                       [eq_sym_conv,count_addm_simp,Multiset.delm_nonempty_def,
                        Multiset.countm_nonempty_def,pos_count_imp_pos_countm,
                        suc_pred_id]
                     setloop (split_tac [expand_if])) 1);
-val countm_done_delm = result();
+qed "countm_done_delm";