Theorems · Theorem · group theory
Finset.sum_sdiff_eq_sub
∀ {ι : Type u_1} {G : Type u_3} {s₁ s₂ : Finset ι} [inst : AddCommGroup G] [inst_1 : DecidableEq ι] {f : ι → G},
s₁ ⊆ s₂ → ∑ x ∈ s₂ \ s₁, f x = ∑ x ∈ s₂, f x - ∑ x ∈ s₁, f x- Cited by
- 1 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommGroupDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- AddCommGroupstatement and proof · cited by 12,871
- Finset.sumstatement and proof · cited by 5,195
- eq_sub_iff_add_eqproof · cited by 65
- Finset.sum_sdiffproof · cited by 16
Cited by1
Results whose statement or proof uses this declaration.
- jacobiSum_eq_sum_sdiffproof · cited by 1