Theorems · Theorem · ring theory
Finset.sum_mul
∀ {ι : Type u_1} {R : Type u_4} [inst : NonUnitalNonAssocSemiring R] (s : Finset ι) (f : ι → R) (a : R),
(∑ i ∈ s, f i) * a = ∑ i ∈ s, f i * a- Defined in
- Mathlib.Algebra.BigOperators.Ring.Finset
- Cited by
- 112 results in Mathlib
- Foundations
- Depth 16 from the axioms, rests on 122 definitions · uses propext, Quot.sound
- Assumes
- NonUnitalNonAssocSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Finset.sumstatement · cited by 5,195
- NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
- map_sumproof · cited by 455
- AddMonoidHom.mulRightproof · cited by 20
Cited by112
Results whose statement or proof uses this declaration.
- Complex.exp_addproof · cited by 55
- Finset.sum_divproof · cited by 20
- Matrix.dotProduct_mulVecproof · cited by 19
- Finset.sum_mul_sumproof · cited by 13
- LinearMap.toMatrix₂_compl₁₂proof · cited by 7
- Algebra.FormallyUnramified.finite_of_freeproof · cited by 7
- LinearMap.toMatrix₂'_compl₁₂proof · cited by 6
- gaussSum_mul_gaussSum_eq_cardproof · cited by 4
- Finsupp.sum_mulproof · cited by 4
- Finset.expect_mulproof · cited by 3
- dotProduct_assocproof · cited by 3
- ProbabilityTheory.iIndepFun.hasGaussianLawproof · cited by 3