Theorems · Theorem · group theory
Multiset.noncommProd_coe
∀ {α : Type u_3} [inst : Monoid α] (l : List α) (comm : {x | x ∈ ↑l}.Pairwise Commute), (↑l).noncommProd comm = l.prod- Defined in
- Mathlib.Data.Finset.NoncommProd
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 23 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.
Cites8
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 · cited by 2,627
- Commutestatement and proof · cited by 639
- Set.Pairwisestatement and proof · cited by 321
- Multiset.ofListstatement and proof · cited by 290
- Multiset.noncommProdstatement · cited by 23
- Multiset.noncommFold_coeproof · cited by 4
Cited by12
Results whose statement or proof uses this declaration.
- Multiset.noncommProd_eq_pow_cardproof · cited by 2
- Submonoid.multiset_noncommProd_memproof · cited by 2
- Finset.noncommProd_toFinsetproof · cited by 2
- Multiset.mul_noncommProd_eraseproof · cited by 2
- Multiset.noncommProd_commuteproof · cited by 2
- Multiset.noncommProd_eq_prodproof · cited by 1
- Multiset.noncommProd_inductionproof · cited by 1
- Finset.noncommProd_union_of_disjointproof · cited by 1
- Multiset.map_noncommProdproof · cited by 1
- Multiset.noncommProd_addproof · cited by 1
- Multiset.noncommProd_consproof · cited by 1
- Multiset.noncommProd_cons'proof · cited by 1