src/HOL/UNITY/Follows.thy
changeset 61169 4de9ff3ea29a
parent 61076 bdc1e2f0a86a
child 62430 9527ff088c15
equal deleted inserted replaced
61168:dcdfb6355a05 61169:4de9ff3ea29a
   177 
   177 
   178 definition less_eq_multiset :: "'a multiset \<Rightarrow> 'a multiset \<Rightarrow> bool" where
   178 definition less_eq_multiset :: "'a multiset \<Rightarrow> 'a multiset \<Rightarrow> bool" where
   179    "(M'::'a multiset) \<le> M \<longleftrightarrow> M' #<=# M"
   179    "(M'::'a multiset) \<le> M \<longleftrightarrow> M' #<=# M"
   180 
   180 
   181 instance
   181 instance
   182   by default (auto simp add: less_eq_multiset_def less_multiset_def multiset_order.less_le_not_le add.commute multiset_order.add_right_mono)
   182   by standard (auto simp add: less_eq_multiset_def less_multiset_def multiset_order.less_le_not_le add.commute multiset_order.add_right_mono)
   183 end
   183 end
   184 
   184 
   185 lemma increasing_union: 
   185 lemma increasing_union: 
   186     "[| F \<in> increasing f;  F \<in> increasing g |]  
   186     "[| F \<in> increasing f;  F \<in> increasing g |]  
   187      ==> F \<in> increasing (%s. (f s) + (g s :: ('a::order) multiset))"
   187      ==> F \<in> increasing (%s. (f s) + (g s :: ('a::order) multiset))"