Lemmas about `multiset.sum` and `multiset.prod` requiring extra algebra imports #

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theorem multiset.dvd_prod {α : Type u_2} [comm_monoid α] {s : multiset α} {a : α} :

a ∈ s → a ∣ s.prod

theorem multiset.sum_eq_zero_iff {α : Type u_2} [canonically_ordered_add_monoid α] {m : multiset α} :

m.sum = 0 ↔ ∀ (x : α), x ∈ m → x = 0

theorem multiset.prod_eq_one_iff {α : Type u_2} [canonically_ordered_monoid α] {m : multiset α} :

m.prod = 1 ↔ ∀ (x : α), x ∈ m → x = 1

theorem commute.multiset_sum_right {α : Type u_2} [non_unital_non_assoc_semiring α] (s : multiset α) (a : α) (h : ∀ (b : α), b ∈ s → commute a b) :

theorem commute.multiset_sum_left {α : Type u_2} [non_unital_non_assoc_semiring α] (s : multiset α) (b : α) (h : ∀ (a : α), a ∈ s → commute a b) :

Lemmas about multiset.sum and multiset.prod requiring extra algebra imports #