equal
deleted
inserted
replaced
3456 instance |
3456 instance |
3457 by standard (simp add: equal_multiset_def) |
3457 by standard (simp add: equal_multiset_def) |
3458 |
3458 |
3459 end |
3459 end |
3460 |
3460 |
3461 lemma [code]: "sum_mset (mset xs) = sum_list xs" |
3461 declare sum_mset_sum_list [code] |
3462 by (induct xs) simp_all |
|
3463 |
3462 |
3464 lemma [code]: "prod_mset (mset xs) = fold times xs 1" |
3463 lemma [code]: "prod_mset (mset xs) = fold times xs 1" |
3465 proof - |
3464 proof - |
3466 have "\<And>x. fold times xs x = prod_mset (mset xs) * x" |
3465 have "\<And>x. fold times xs x = prod_mset (mset xs) * x" |
3467 by (induct xs) (simp_all add: ac_simps) |
3466 by (induct xs) (simp_all add: ac_simps) |