Theorems · Theorem · group theory
finsum_zero
∀ {M : Type u_2} {α : Sort u_4} [inst : AddCommMonoid M], ∑ᶠ (x : α), 0 = 0- Defined in
- Mathlib.Algebra.BigOperators.Finprod
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- SetLike.coeproof · cited by 8,199
- Function.supportproof · cited by 610
- finsumstatement · cited by 286
- Finset.sum_emptyproof · cited by 45
- Set.mem_empty_iff_falseproof · cited by 32
- Function.support_fun_zeroproof · cited by 6
- finsum_eq_sum_plift_of_support_subsetproof · cited by 5
Cited by18
Results whose statement or proof uses this declaration.
- tsum_zeroproof · cited by 63
- finsum_eq_zero_of_forall_eq_zeroproof · cited by 7
- MeromorphicOn.circleAverage_log_normproof · cited by 3
- HahnSeries.SummableFamily.smul_hsumproof · cited by 2
- Function.locallyFinsuppWithin.logCounting_eval_zeroproof · cited by 2
- finsum_mulproof · cited by 2
- finsum_of_isEmptyproof · cited by 2
- finsum_mem_emptyproof · cited by 2
- exists_contMDiffMap_zero_one_of_isClosedproof · cited by 2
- finsum_mem_zeroproof · cited by 1
- finsum_oneproof · cited by 1
- SmoothPartitionOfUnity.exists_pos_of_memproof · cited by 1