Theorems · Definition · group theory
Multiset.noncommProd
{α : Type u_3} → [inst : Monoid α] → (s : Multiset α) → {x | x ∈ s}.Pairwise Commute → αProduct of a s : Multiset α with [Monoid α], given a proof that * commutes
on all elements x ∈ s.
- Defined in
- Mathlib.Data.Finset.NoncommProd
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 21 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.
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
- 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.noncommFoldproof · cited by 5
Cited by24
Results whose statement or proof uses this declaration.
- Finset.noncommProdproof · cited by 44
- Finset.noncommProd_congrproof · cited by 13
- Multiset.noncommProd_coestatement · cited by 12
- Multiset.noncommProd.congr_simpstatement and proof · cited by 9
- Finset.map_noncommProdproof · cited by 5
- Finset.noncommProd_consproof · cited by 4
- Submonoid.multiset_noncommProd_memstatement · cited by 2
- Multiset.mul_noncommProd_erasestatement · cited by 2
- Multiset.noncommProd_commutestatement · cited by 2
- Multiset.noncommProd_eq_pow_cardstatement · cited by 2
- Finset.noncommProd_erase_mulproof · cited by 2
- Multiset.noncommProd_addstatement · cited by 1