Theorems · Theorem · group theory
finsum_eq_sum
∀ {α : Type u_1} {M : Type u_5} [inst : AddCommMonoid M] (f : α → M) (hf : Function.HasFiniteSupport f),
∑ᶠ (i : α), f i = ∑ i ∈ Set.Finite.toFinset hf, f i- Defined in
- Mathlib.Algebra.BigOperators.Finprod
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 82 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.
Cites7
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
- Finset.sumstatement and proof · cited by 5,195
- Function.supportstatement · cited by 610
- Set.Finite.toFinsetstatement and proof · cited by 351
- finsumstatement · cited by 286
- Function.HasFiniteSupportstatement and proof · cited by 113
- finsum_defproof · cited by 8
Cited by17
Results whose statement or proof uses this declaration.
- HahnSeries.SummableFamily.coeff_hsum_eq_sumproof · cited by 4
- MvPowerSeries.rescale_eq_substproof · cited by 3
- MeromorphicAt.finsumproof · cited by 2
- MvPowerSeries.truncTotal_subst_eq_truncTotal_subst_sumproof · cited by 2
- CircleIntegrable.finsumproof · cited by 2
- MvPowerSeries.rename_eq_substproof · cited by 2
- HahnSeries.SummableFamily.coeff_smulproof · cited by 2
- tsum_le_of_sum_le'proof · cited by 2
- HahnSeries.SummableFamily.support_hsum_subsetproof · cited by 1
- MvPolynomial.sum_weightedHomogeneousComponentproof · cited by 1
- IntervalIntegrable.finsumproof · cited by 1
- Topology.IsInducing.summable_iff_tsum_comp_mem_rangeproof · cited by 1