Theorems · Definition · group theory
Multiset.noncommSum
{α : Type u_3} → [inst : AddMonoid α] → (s : Multiset α) → {x | x ∈ s}.Pairwise AddCommute → αSum of a s : Multiset α with [AddMonoid α], given a proof that + commutes
on all elements x ∈ s.
- Defined in
- Mathlib.Data.Finset.NoncommProd
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 21 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.ofPredstatement and proof · cited by 6,101
- AddMonoidstatement and proof · cited by 2,864
- Multisetstatement and proof · cited by 2,627
- Set.Pairwisestatement and proof · cited by 321
- AddCommutestatement and proof · cited by 185
- Multiset.noncommFoldproof · cited by 5
Cited by19
Results whose statement or proof uses this declaration.
- Finset.noncommSumproof · cited by 24
- Multiset.noncommSum_coestatement · cited by 11
- Finset.noncommSum_congrproof · cited by 5
- Finset.map_noncommSumproof · cited by 3
- Finset.noncommSum_consproof · cited by 3
- AddSubmonoid.multiset_noncommSum_memstatement · cited by 2
- Multiset.noncommSum_addCommutestatement · cited by 1
- Multiset.noncommSum_consstatement · cited by 1
- Multiset.noncommSum_cons'statement · cited by 1
- Multiset.noncommSum_eq_card_nsmulstatement · cited by 1
- Multiset.noncommSum_inductionstatement · cited by 1
- Multiset.map_noncommSumstatement · cited by 1