Theorems · Theorem · combinatorics
Fintype.sum_eq_zero
∀ {α : Type u_1} {M : Type u_4} [inst : Fintype α] [inst_1 : AddCommMonoid M] (f : α → M),
(∀ (a : α), f a = 0) → ∑ a, f a = 0- Defined in
- Mathlib.Data.Fintype.BigOperators
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeAddCommMonoid
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.
- AddCommMonoidstatement and proof · cited by 12,281
- Fintypestatement and proof · cited by 7,736
- Finset.sumstatement · cited by 5,195
- Finset.univstatement and proof · cited by 3,473
- Finset.sum_eq_zeroproof · cited by 139
Cited by7
Results whose statement or proof uses this declaration.
- AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eq_zeroproof · cited by 3
- CategoryTheory.SimplicialObject.Splitting.comp_PInfty_eq_zero_iffproof · cited by 2
- RootPairing.exists_coroot_neproof · cited by 1
- PowerBasis.dim_le_natDegree_of_rootproof · cited by 1
- Fin.sum_truncproof · cited by 1
- extDerivWithin_apply_vectorField_of_pairwise_commuteproof · cited by 1
- MvPolynomial.sum_eval_eq_zeroproof · cited by 1