Theorems · Theorem · group theory
Multiset.noncommProd_add
∀ {α : Type u_3} [inst : Monoid α] (s t : Multiset α) (comm : {x | x ∈ s + t}.Pairwise Commute),
(s + t).noncommProd comm = s.noncommProd ⋯ * t.noncommProd ⋯- Defined in
- Mathlib.Data.Finset.NoncommProd
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Monoidstatement and proof · cited by 3,887
- Multisetstatement and proof · cited by 2,627
- Commutestatement and proof · cited by 639
- Set.Pairwisestatement and proof · cited by 321
- Multiset.ofListproof · cited by 290
- Set.Pairwise.monostatement and proof · cited by 55
- Multiset.subset_of_lestatement and proof · cited by 27
- Multiset.noncommProdstatement · cited by 23
- Multiset.noncommProd_coeproof · cited by 12
- Multiset.le_add_rightstatement and proof · cited by 9
- Multiset.le_add_leftstatement and proof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- Finset.sum_pow_of_commuteproof · cited by 1