Theorems · Theorem · group theory
Multiset.noncommFold_coe
∀ {α : Type u_3} (op : α → α → α) [assoc : Std.Associative op] (l : List α)
(comm : {x | x ∈ ↑l}.Pairwise fun x y => op x y = op y x) (a : α),
Multiset.noncommFold op (↑l) comm a = List.foldr op a l- Defined in
- Mathlib.Data.Finset.NoncommProd
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 21 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.
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
- Multisetstatement · cited by 2,627
- Set.Pairwisestatement and proof · cited by 321
- Multiset.ofListstatement and proof · cited by 290
- Multiset.noncommFoldstatement · cited by 5
- Multiset.noncommFoldr_coeproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- Multiset.noncommProd_coeproof · cited by 12
- Multiset.noncommSum_coeproof · cited by 11
- Multiset.noncommFold_consproof · cited by 0
- Multiset.noncommFold_eq_foldproof · cited by 0