Theorems · Theorem · group theory
Finset.sum_indicator_subset
∀ {ι : Type u_1} {β : Type u_4} [inst : AddCommMonoid β] (f : ι → β) {s t : Finset ι},
s ⊆ t → ∑ i ∈ t, (↑s).indicator f i = ∑ i ∈ s, f iSumming an indicator function over a possibly larger Finset is the same as
summing the original function over the original finset.
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, 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
- SetLike.coestatement · cited by 8,199
- Finset.sumstatement · cited by 5,195
- Set.indicatorstatement · cited by 723
- Finset.sum_indicator_subset_of_eq_zeroproof · cited by 3
Cited by11
Results whose statement or proof uses this declaration.
- affineIndependent_iff_eq_of_fintype_affineCombination_eqproof · cited by 5
- eq_affineCombination_of_mem_affineSpanproof · cited by 4
- affineIndependent_iff_indicator_eq_of_affineCombination_eqproof · cited by 4
- AffineIndependent.affineCombination_mem_shift_iffproof · cited by 3
- Finset.sum_centroidWeightsIndicatorproof · cited by 3
- sum_eq_tsum_indicatorproof · cited by 2
- Affine.Simplex.convexHull_eq_closedInteriorproof · cited by 1
- AffineIndependent.exists_affineCombination_eq_smul_eq_of_fintypeproof · cited by 1
- Set.infinite_iff_tendsto_sum_indicator_atTopproof · cited by 1
- Affine.Simplex.sum_centroidWeightsWithCircumcenterproof · cited by 1
- affineIndependent_iff_of_fintypeproof · cited by 1