Theorems · Theorem · group theory
AddSubmonoid.multiset_sum_mem
∀ {M : Type u_4} [inst : AddCommMonoid M] (S : AddSubmonoid M) (m : Multiset M), (∀ a ∈ m, a ∈ S) → m.sum ∈ SSum of a multiset of elements in an AddSubmonoid of an AddCommMonoid is
in the AddSubmonoid.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommMonoidstatement and proof · cited by 12,281
- Multisetstatement and proof · cited by 2,627
- AddSubmonoidstatement and proof · cited by 1,178
- Multiset.sumstatement · cited by 388
- multiset_sum_memproof · cited by 10
Cited by2
Results whose statement or proof uses this declaration.
- AddSubmonoid.sum_memproof · cited by 9
- convex_multiset_sumproof · cited by 0