Theorems · Theorem · combinatorics
Multiset.fold_cons_left
∀ {α : Type u_1} (op : α → α → α) [hc : Std.Commutative op] [ha : Std.Associative op] (b a : α) (s : Multiset α),
Multiset.fold op b (a ::ₘ s) = op a (Multiset.fold op b s)- Defined in
- Mathlib.Data.Multiset.Fold
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Quot.sound
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.
- Multisetstatement · cited by 2,627
- Multiset.consstatement · cited by 313
- Multiset.foldstatement · cited by 38
- Multiset.foldr_consproof · cited by 4
Cited by14
Results whose statement or proof uses this declaration.
- Finset.fold_insertproof · cited by 11
- Multiset.fold_addproof · cited by 9
- Multiset.gcd_consproof · cited by 7
- Finset.fold_consproof · cited by 6
- Multiset.lcm_consproof · cited by 6
- Multiset.inf_consproof · cited by 5
- Multiset.fold_dedup_idemproof · cited by 4
- Multiset.gcd_dedupproof · cited by 4
- Multiset.sup_consproof · cited by 3
- Multiset.lcm_dedupproof · cited by 3
- Multiset.fold_cons_rightproof · cited by 2
- Multiset.fold_bindproof · cited by 1