Theorems · Theorem · group theory
Finset.sum_sub_distrib
∀ {ι : Type u_1} {G : Type u_5} {s : Finset ι} [inst : SubtractionCommMonoid G] (f g : ι → G),
∑ x ∈ s, (f x - g x) = ∑ x ∈ s, f x - ∑ x ∈ s, g x- Cited by
- 84 results in Mathlib
- Foundations
- Depth 15 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_subproof · cited by 3
Cited by84
Results whose statement or proof uses this declaration.
- linearIndependent_iff'proof · cited by 22
- affineCombination_mem_affineSpanproof · cited by 12
- Finsupp.sum_subproof · cited by 9
- HasFDerivAtFilter.fun_sumproof · cited by 4
- affineIndependent_iff_indicator_eq_of_affineCombination_eqproof · cited by 4
- ProbabilityTheory.HasGaussianLaw.iIndepFun_of_covariance_strongDualproof · cited by 3
- MeasureTheory.martingalePart_eq_sumproof · cited by 3
- ZMod.differentiableAt_LFunctionproof · cited by 3
- linearIndependent_monoidHomproof · cited by 3
- Affine.Simplex.sOppSide_affineSpan_faceOpposite_of_pos_of_negproof · cited by 3
- Affine.Simplex.sSameSide_affineSpan_faceOpposite_of_sign_eqproof · cited by 3
- AffineIndependent.affineCombination_mem_shift_iffproof · cited by 3