Theorems · Theorem · group theory
Finset.sum_neg_distrib
∀ {ι : Type u_1} {G : Type u_5} {s : Finset ι} [inst : SubtractionCommMonoid G] (f : ι → G),
∑ x ∈ s, -f x = -∑ x ∈ s, f x- Cited by
- 65 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
- Assumes
- SubtractionCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- SubtractionCommMonoidstatement and proof · cited by 79
- Multiset.sum_map_negproof · cited by 2
Cited by65
Results whose statement or proof uses this declaration.
- RootPairing.Base.exists_root_eq_sum_intproof · cited by 7
- dotProduct_negproof · cited by 6
- Orientation.eq_or_eq_neg_of_isEmptyproof · cited by 6
- groupCohomology.comp_d₀₁_eqproof · cited by 6
- groupHomology.comp_d₁₀_eqproof · cited by 6
- groupHomology.comp_d₃₂_eqproof · cited by 6
- neg_dotProductproof · cited by 5
- RootPairing.Base.height_reflectionPerm_selfproof · cited by 4
- Matrix.trace_negproof · cited by 4
- dist_sum_sum_le_of_leproof · cited by 4
- LieAlgebra.Basis.iSupIndep_rootSpaceproof · cited by 3
- MeasureTheory.SimpleFunc.setToSimpleFunc_negproof · cited by 3