Theorems · Theorem · group theory
AddSubgroup.multiset_sum_mem
∀ {G : Type u_3} [inst : AddCommGroup G] (K : AddSubgroup G) (g : Multiset G), (∀ a ∈ g, a ∈ K) → g.sum ∈ KSum of a multiset of elements in an AddSubgroup of an AddCommGroup is in
the AddSubgroup.
- Defined in
- Mathlib.Algebra.Group.Subgroup.Finite
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommGroup
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Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommGroupstatement and proof · cited by 12,871
- AddSubgroupstatement and proof · cited by 3,232
- Multisetstatement and proof · cited by 2,627
- Multiset.sumstatement · cited by 388
- multiset_sum_memproof · cited by 10
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