Theorems · Theorem · group theory
AddSubmonoid.noncommSum_mem
∀ {M : Type u_1} [inst : AddMonoid M] (S : AddSubmonoid M) {ι : Type u_4} (t : Finset ι) (f : ι → M)
(comm : (↑t).Pairwise (Function.onFun AddCommute f)), (∀ c ∈ t, f c ∈ S) → t.noncommSum f comm ∈ S- Cited by
- 3 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- AddMonoidstatement and proof · cited by 2,864
- AddSubmonoidstatement and proof · cited by 1,178
- Multiset.mapproof · cited by 876
- Function.onFunstatement and proof · cited by 570
- Finset.valproof · cited by 438
- Set.Pairwisestatement and proof · cited by 321
- AddCommutestatement and proof · cited by 185
- Multiset.mem_mapproof · cited by 72
- Finset.noncommSumstatement · cited by 24
- Finset.noncommSum_lemmaproof · cited by 10
Cited by3
Results whose statement or proof uses this declaration.
- AddSubgroup.noncommSum_memproof · cited by 2
- AddSubmonoid.iSup_map_singleproof · cited by 1
- AddMonoidHom.noncommPiCoprod_mrangeproof · cited by 0