Theorems · Theorem · ring theory
Finset.mul_sum
∀ {ι : Type u_1} {R : Type u_4} [inst : NonUnitalNonAssocSemiring R] (s : Finset ι) (f : ι → R) (a : R),
a * ∑ i ∈ s, f i = ∑ i ∈ s, a * f i- Defined in
- Mathlib.Algebra.BigOperators.Ring.Finset
- Cited by
- 196 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.mulLeftproof · cited by 23
Cited by196
Results whose statement or proof uses this declaration.
- Matrix.det_mulproof · cited by 51
- Matrix.dotProduct_mulVecproof · cited by 19
- Commute.add_powproof · cited by 12
- Matrix.toLinearMap₂'_apply'proof · cited by 10
- MulChar.sum_eq_zero_of_ne_oneproof · cited by 9
- MeasureTheory.SimpleFunc.map_lintegralproof · cited by 7
- Algebra.FormallyUnramified.finite_of_freeproof · cited by 7
- Polynomial.eval₂_smulproof · cited by 5
- Matrix.posSemidef_iff_dotProduct_mulVecproof · cited by 5
- geom_sum_succproof · cited by 5
- gaussSum_mulShiftproof · cited by 5
- hasStrictFDerivAt_list_prod'proof · cited by 4