Theorems · Definition · group theory

Set.addCommMonoid

{α : Type u_2} → [AddCommMonoid α] → AddCommMonoid (Set α)

Set α is an AddCommMonoid under pointwise operations if α is.

Defined in: Mathlib.Algebra.Group.Pointwise.Set.Basic
Cited by: 25 results in Mathlib
Foundations: Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AddCommMonoid

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Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Setstatement and proof · cited by 53,352
AddCommMonoidstatement and proof · cited by 12,281
AddMonoidproof · cited by 2,864
AddCommSemigroupproof · cited by 178
Set.addMonoidproof · cited by 18
Set.addCommSemigroupproof · cited by 0

Cited by25

Results whose statement or proof uses this declaration.

Set.mem_finsetSumstatement · cited by 4
Set.image_finsetSum_pistatement · cited by 2
parallelepiped_eq_sum_segmentstatement · cited by 2
Set.image_multiset_sumstatement · cited by 1
Set.multiset_sum_mem_multiset_sumstatement · cited by 1
Set.multiset_sum_subset_multiset_sumstatement · cited by 1
Set.finsetSum_mem_finsetSumstatement · cited by 1
Set.finsetSum_singletonstatement · cited by 1
Set.finsetSum_subset_finsetSumstatement · cited by 1
convex_sumstatement · cited by 1
convexHull_sumstatement · cited by 1
Set.image_finsetSumstatement · cited by 1