Theorems · Theorem · group theory
Finset.sum_sdiff
∀ {ι : Type u_1} {M : Type u_4} {s₁ s₂ : Finset ι} [inst : AddCommMonoid M] {f : ι → M} [inst_1 : DecidableEq ι],
s₁ ⊆ s₂ → ∑ x ∈ s₂ \ s₁, f x + ∑ x ∈ s₁, f x = ∑ x ∈ s₂, f x- Cited by
- 16 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoidDecidableEq
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
- Finset.sum_unionproof · cited by 40
- Finset.sdiff_disjointproof · cited by 20
- Finset.sdiff_union_of_subsetproof · cited by 12
Cited by16
Results whose statement or proof uses this declaration.
- Finset.sum_subset_zero_on_sdiffproof · cited by 7
- cauchySeq_finset_iff_sum_vanishingproof · cited by 5
- Affine.Triangle.dist_orthocenter_reflection_circumcenterproof · cited by 3
- MvPowerSeries.coeff_eq_zero_of_constantCoeff_nilpotentproof · cited by 2
- BoxIntegral.integrable_of_bounded_and_ae_continuousWithinAtproof · cited by 2
- Finset.weightedVSubOfPoint_sdiffproof · cited by 2
- Finset.sum_involutionproof · cited by 2
- Finset.sum_sdiff_sub_sum_sdiffproof · cited by 2
- Nat.eq_properDivisors_of_subset_of_sum_eq_sumproof · cited by 2
- affineCombination_mem_affineSpan_imageproof · cited by 2
- Group.nat_card_center_add_sum_card_noncenter_eq_cardproof · cited by 1
- FiniteField.sum_pow_lt_card_sub_oneproof · cited by 1