Theorems · Definition · combinatorics
Multiset.foldr
{α : Type u_1} → {β : Type v} → (f : α → β → β) → [LeftCommutative f] → β → Multiset α → βfoldr f H b s is the lift of the list operation foldr f b l,
which folds f over the multiset. It is well defined when f is left-commutative,
that is, f a₁ (f a₂ b) = f a₂ (f a₁ b).
- Defined in
- Mathlib.Data.Multiset.MapFold
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses propext
- Assumes
- LeftCommutative
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Multisetstatement and proof · cited by 2,627
- LeftCommutativestatement and proof · cited by 20
- List.Perm.foldr_eqproof · cited by 1
Cited by22
Results whose statement or proof uses this declaration.
- Multiset.prodproof · cited by 528
- Multiset.sumproof · cited by 388
- Multiset.foldproof · cited by 38
- Finset.sum_disjiUnionproof · cited by 10
- Finset.prod_disjiUnionproof · cited by 6
- Multiset.noncommFoldrproof · cited by 5
- Multiset.foldr_consstatement · cited by 4
- Multiset.foldr_swapstatement · cited by 3
- Multiset.coe_foldr_swapstatement and proof · cited by 2
- Polynomial.natDegree_multiset_sum_lestatement · cited by 2
- Multiset.foldr_inductionstatement · cited by 2
- Multiset.foldr_induction'statement and proof · cited by 2