equal
deleted
inserted
replaced
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))" |