Theorems · Theorem · combinatorics
Multiset.sum_join
∀ {α : Type u_1} [inst : AddCommMonoid α] {S : Multiset (Multiset α)}, S.join.sum = (Multiset.map Multiset.sum S).sum- Defined in
- Mathlib.Data.Multiset.Bind
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommMonoidstatement and proof · cited by 12,281
- Multisetstatement and proof · cited by 2,627
- Multiset.mapstatement and proof · cited by 876
- Multiset.sumstatement and proof · cited by 388
- Multiset.map_consproof · cited by 93
- Multiset.sum_consproof · cited by 45
- Multiset.inductionproof · cited by 31
- Multiset.joinstatement and proof · cited by 21
- Multiset.sum_addproof · cited by 10
- Multiset.join_consproof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- Multiset.sum_bindproof · cited by 2