Theorems · Theorem · group theory
Finset.sum_multiset_count
∀ {M : Type u_4} [inst : AddCommMonoid M] [inst_1 : DecidableEq M] (s : Multiset M),
s.sum = ∑ m ∈ s.toFinset, Multiset.count m s • m- Cited by
- 3 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoidDecidableEq
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
- Finset.sumstatement and proof · cited by 5,195
- Multisetstatement and proof · cited by 2,627
- Finset.sum_congrproof · cited by 2,323
- Multiset.mapproof · cited by 876
- Multiset.sumstatement and proof · cited by 388
- Multiset.countstatement and proof · cited by 302
- Multiset.toFinsetstatement and proof · cited by 230
- Multiset.map_idproof · cited by 20
- Finset.sum_multiset_map_countproof · cited by 10
Cited by3
Results whose statement or proof uses this declaration.
- Multiset.bell_mul_eqproof · cited by 2
- Nat.bell_eq_sum_eraseproof · cited by 1
- Nat.Partition.toFinsuppAntidiag_mem_finsuppAntidiagproof · cited by 1