Theorems · Definition · group theory
Multiset.noncommFold
{α : Type u_3} →
(op : α → α → α) →
[assoc : Std.Associative op] → (s : Multiset α) → ({x | x ∈ s}.Pairwise fun x y => op x y = op y x) → α → αFold of a s : Multiset α with an associative op : α → α → α, given a proofs that op
is commutative on all elements x ∈ s.
- Defined in
- Mathlib.Data.Finset.NoncommProd
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Std.Associative
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Multisetstatement and proof · cited by 2,627
- Set.Pairwisestatement and proof · cited by 321
- Multiset.noncommFoldrproof · cited by 5
Cited by7
Results whose statement or proof uses this declaration.
- Multiset.noncommProdproof · cited by 23
- Multiset.noncommSumproof · cited by 18
- Multiset.noncommFold_coestatement · cited by 4
- Multiset.noncommFold_consstatement · cited by 0
- Multiset.noncommFold_emptystatement · cited by 0
- Multiset.noncommFold_eq_foldstatement · cited by 0
- Multiset.noncommFold.congr_simpstatement and proof · cited by 0