equal
deleted
inserted
replaced
2327 if "\<And>i. i \<in># K \<Longrightarrow> f i \<le> g i" |
2327 if "\<And>i. i \<in># K \<Longrightarrow> f i \<le> g i" |
2328 using that by (induction K) (simp_all add: add_mono) |
2328 using that by (induction K) (simp_all add: add_mono) |
2329 |
2329 |
2330 end |
2330 end |
2331 |
2331 |
2332 context ordered_cancel_comm_monoid_diff |
2332 context cancel_comm_monoid_add |
2333 begin |
2333 begin |
2334 |
2334 |
2335 lemma sum_mset_diff: |
2335 lemma sum_mset_diff: |
2336 "sum_mset (M - N) = sum_mset M - sum_mset N" if "N \<subseteq># M" for M N :: "'a multiset" |
2336 "sum_mset (M - N) = sum_mset M - sum_mset N" if "N \<subseteq># M" for M N :: "'a multiset" |
2337 using that by (auto simp add: subset_mset.le_iff_add) |
2337 using that by (auto simp add: subset_mset.le_iff_add) |