Theorems · Theorem · group theory

multiset_sum_mem

∀ {B : Type u_3} {S : B} {M : Type u_4} [inst : AddCommMonoid M] [inst_1 : SetLike B M] [AddSubmonoidClass B M]
  (m : Multiset M), (∀ a ∈ m, a ∈ S) → m.sum ∈ S

Sum of a multiset of elements in an AddSubmonoid of an AddCommMonoid is in the AddSubmonoid.

Defined in

Mathlib.Algebra.Group.Submonoid.BigOperators

Cited by

10 results in Mathlib

Foundations

Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidSetLikeAddSubmonoidClass