diff -r f04b33ce250f -r a4dc62a46ee4 IOA/example/Multiset.ML
--- a/IOA/example/Multiset.ML	Tue Oct 24 14:59:17 1995 +0100
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,84 +0,0 @@
-(*  Title:      HOL/IOA/example/Multiset.ML
-    ID:         $Id$
-    Author:     Tobias Nipkow & Konrad Slind
-    Copyright   1994  TU Muenchen
-
-Axiomatic multisets.
-Should be done as a subtype and moved to a global place.
-*)
-
-goalw Multiset.thy [Multiset.count_def, Multiset.countm_empty_def]
-   "count({|},x) = 0";
- by (rtac refl 1);
-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);
-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);
-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_empty_def,Multiset.countm_empty_def]
-                   setloop (split_tac [expand_if])) 1);
-  by (asm_full_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);
-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);
-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);
-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.delm_empty_def,Multiset.count_def,
-                           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 = 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 
-                          [Multiset.delm_empty_def,
-                           Multiset.countm_empty_def]) 1);
-  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);
-qed "countm_done_delm";