Theorems · Theorem · group theory
finsum_eq_finsetSum_of_support_subset
∀ {α : Type u_1} {M : Type u_5} [inst : AddCommMonoid M] (f : α → M) {s : Finset α},
Function.support f ⊆ ↑s → ∑ᶠ (i : α), f i = ∑ i ∈ s, f i- Defined in
- Mathlib.Algebra.BigOperators.Finprod
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 76 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.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Finsetstatement and proof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- SetLike.coestatement and proof · cited by 8,199
- Finset.sumstatement · cited by 5,195
- Function.supportstatement and proof · cited by 610
- SetLike.mem_coeproof · cited by 302
- finsumstatement · cited by 286
- Set.Finite.subsetproof · cited by 285
- Finset.finite_toSetproof · cited by 210
- Set.Finite.coe_toFinsetproof · cited by 124
- Finset.coe_subsetproof · cited by 93
Cited by3
Results whose statement or proof uses this declaration.
- finsum_le_finsum'proof · cited by 1
- finsum_eq_finset_sum_of_support_subsetproof · cited by 0
- finsum_sum_filterproof · cited by 0