Theorems · Theorem · group theory
Finset.sum_eq_multiset_sum
∀ {ι : Type u_1} {M : Type u_3} [inst : AddCommMonoid M] (s : Finset ι) (f : ι → M),
∑ x ∈ s, f x = (Multiset.map f s.val).sum- Cited by
- 5 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Quot.sound
- Assumes
- AddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Multiset.mapstatement · cited by 876
- Finset.valstatement · cited by 438
- Multiset.sumstatement · cited by 388
Cited by5
Results whose statement or proof uses this declaration.
- Multiset.prod_X_add_C_eq_sum_esymmproof · cited by 3
- Nat.sum_divisors_filter_squarefreeproof · cited by 1
- trace_eq_sum_embeddings_genproof · cited by 1
- FiniteField.sum_subgroup_pow_eq_zeroproof · cited by 0
- Multiset.sup_powerset_lenproof · cited by 0