Theorems · Theorem · group theory
finsum_def
∀ {α : Type u_1} {M : Type u_5} [inst : AddCommMonoid M] (f : α → M) [inst_1 : Decidable (Function.HasFiniteSupport f)],
∑ᶠ (i : α), f i = if h : Function.HasFiniteSupport f then ∑ i ∈ Set.Finite.toFinset h, f i else 0- Defined in
- Mathlib.Algebra.BigOperators.Finprod
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoidDecidable
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- AddCommMonoidstatement and proof · cited by 12,281
- Finset.sumstatement · cited by 5,195
- Set.preimageproof · cited by 4,946
- Set.Finiteproof · cited by 1,814
- Function.supportstatement and proof · cited by 610
- Set.Finite.toFinsetstatement and proof · cited by 351
- finsumstatement and proof · cited by 286
- Equiv.surjectiveproof · cited by 198
- Function.HasFiniteSupportstatement and proof · cited by 113
- Finset.Subset.reflproof · cited by 29
- Equiv.pliftproof · cited by 23
Cited by8
Results whose statement or proof uses this declaration.
- finsum_eq_sumproof · cited by 17
- finsum_of_infinite_supportproof · cited by 10
- Setoid.IsPartition.ncard_eq_finsumproof · cited by 2
- finsum_mulproof · cited by 2
- Commute.isNilpotent_finsumproof · cited by 1
- Real.log_finprodproof · cited by 1
- mul_finsumproof · cited by 1
- finsum_applyproof · cited by 0