Theorems · Theorem · group theory
Finset.sum_multiset_count_of_subset
∀ {M : Type u_4} [inst : AddCommMonoid M] [inst_1 : DecidableEq M] (m : Multiset M) (s : Finset M),
m.toFinset ⊆ s → m.sum = ∑ i ∈ s, Multiset.count i m • i- Cited by
- 1 results in Mathlib
- Foundations
- Depth 80 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- Finset.sumstatement · cited by 5,195
- Multisetstatement and proof · cited by 2,627
- Finset.sum_congrproof · cited by 2,323
- Multiset.sumstatement · cited by 388
- Multiset.countstatement · cited by 302
- Multiset.ofListproof · cited by 290
- Multiset.toFinsetstatement and proof · cited by 230
- Quot.induction_onproof · cited by 36
- Multiset.coe_countproof · cited by 23
- Finset.sum_list_count_of_subsetproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Finset.val_sum_eq_sum_count_nsmulproof · cited by 0