Theorems · Theorem · group theory
Finset.sum_add_distrib
∀ {ι : Type u_1} {M : Type u_4} {s : Finset ι} [inst : AddCommMonoid M] {f g : ι → M},
∑ x ∈ s, (f x + g x) = ∑ x ∈ s, f x + ∑ x ∈ s, g x- Cited by
- 131 results in Mathlib
- Foundations
- Depth 17 from the axioms, rests on 92 definitions · 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 and proof · cited by 5,195
- zero_addproof · cited by 2,366
- Finset.foldproof · cited by 46
- Finset.fold_op_distribproof · cited by 2
Cited by131
Results whose statement or proof uses this declaration.
- HasSum.addproof · cited by 23
- Finsupp.sum_addproof · cited by 18
- Finsupp.sum_add_indexproof · cited by 18
- Commute.add_powproof · cited by 12
- HasSum.nat_add_negproof · cited by 10
- add_dotProductproof · cited by 7
- dotProduct_addproof · cited by 6
- Finset.sum_affineCombinationLineMapWeightsproof · cited by 5
- HasSum.nat_add_neg_add_oneproof · cited by 5
- AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eqproof · cited by 4
- affineIndependent_iff_indicator_eq_of_affineCombination_eqproof · cited by 4
- dist_sum_sum_le_of_leproof · cited by 4