Theorems · Theorem · group theory
AddSubgroup.list_sum_mem
∀ {G : Type u_1} [inst : AddGroup G] (K : AddSubgroup G) {l : List G}, (∀ x ∈ l, x ∈ K) → l.sum ∈ KSum of a list of elements in an AddSubgroup is in the AddSubgroup.
- Defined in
- Mathlib.Algebra.Group.Subgroup.Finite
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
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- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- list_sum_memproof · cited by 10
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