Theorems · Theorem · group theory
Finset.sum_empty
∀ {ι : Type u_1} {M : Type u_3} {f : ι → M} [inst : AddCommMonoid M], ∑ x ∈ ∅, f x = 0- Cited by
- 45 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
- Assumes
- AddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- Finset.sumstatement · cited by 5,195
Cited by45
Results whose statement or proof uses this declaration.
- finsum_zeroproof · cited by 18
- Commute.add_powproof · cited by 12
- Finset.sum_Ico_eq_sum_rangeproof · cited by 10
- Finset.sum_range_zeroproof · cited by 9
- xInTermsOfW_zeroproof · cited by 7
- sum_mul_eq_sub_sub_integral_mulproof · cited by 4
- HahnSeries.coeff_mul_single_addproof · cited by 3
- meromorphicOrderAt_prodproof · cited by 3
- AddMonoidAlgebra.supDegree_prod_leproof · cited by 3
- Finset.nonempty_of_sum_ne_zeroproof · cited by 3
- Commute.geom_sum₂_mul_addproof · cited by 3
- Finset.sum_of_isEmptyproof · cited by 3