Theorems · Theorem · group theory
Finset.sum_erase_eq_sub
∀ {ι : Type u_1} {G : Type u_3} {s : Finset ι} [inst : AddCommGroup G] [inst_1 : DecidableEq ι] {f : ι → G} {a : ι},
a ∈ s → ∑ x ∈ s.erase a, f x = ∑ x ∈ s, f x - f a- Cited by
- 6 results in Mathlib
- Foundations
- Depth 59 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.
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
- AddCommGroupstatement and proof · cited by 12,871
- Finset.sumstatement and proof · cited by 5,195
- Finset.erasestatement · cited by 455
- eq_sub_iff_add_eqproof · cited by 65
- Finset.sum_erase_addproof · cited by 13
Cited by6
Results whose statement or proof uses this declaration.
- eigenvalue_mem_ballproof · cited by 1
- Affine.Simplex.inv_height_eq_sum_mul_inv_distproof · cited by 1
- IsVisible.of_convexHull_of_posproof · cited by 1
- PointedCone.IsFaceOf.mem_of_sum_memproof · cited by 1
- NumberField.Units.dirichletUnitTheorem.unitLattice_span_eq_topproof · cited by 0
- Finset.exists_subset_addSpan_card_le_of_forall_addDissociatedproof · cited by 0