Theorems · Theorem · group theory
Finset.sum_inter_add_sum_sdiff
∀ {ι : Type u_1} {M : Type u_3} [inst : AddCommMonoid M] [inst_1 : DecidableEq ι] (s t : Finset ι) (f : ι → M),
∑ x ∈ s ∩ t, f x + ∑ x ∈ s \ t, f x = ∑ x ∈ s, f x- Cited by
- 5 results in Mathlib
- Foundations
- Depth 82 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_congrproof · cited by 2,323
- Finset.piecewiseproof · cited by 64
- Finset.sum_piecewiseproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- Finset.sum_eq_add_sum_sdiff_singletonproof · cited by 3
- AffineIndependent.inf_affineSpan_eq_affineSpan_interproof · cited by 2
- Finset.affineCombination_apply_eq_lineMap_sumproof · cited by 1
- Finset.sum_Ico_le_sumproof · cited by 1
- Finset.sum_le_sum_Iocproof · cited by 1