--- 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";