Theorems · Theorem · group theory
Fintype.sum_subset
∀ {M : Type u_4} {ι : Type u_7} [inst : Fintype ι] [inst_1 : AddCommMonoid M] {s : Finset ι} {f : ι → M},
(∀ (i : ι), f i ≠ 0 → i ∈ s) → ∑ i ∈ s, f i = ∑ i, f i- Cited by
- 4 results in Mathlib
- Foundations
- Depth 68 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- Fintypestatement and proof · cited by 7,736
- Finset.sumstatement · cited by 5,195
- Finset.univstatement · cited by 3,473
- Finset.mem_univproof · cited by 361
- Finset.sum_subsetproof · cited by 79
- Finset.subset_univproof · cited by 60
- not_imp_commproof · cited by 56
Cited by4
Results whose statement or proof uses this declaration.
- exists_continuous_sum_one_of_isOpen_isCompactproof · cited by 1
- IsVisible.mem_convexHull_isVisibleproof · cited by 1
- Finset.addEnergy_eq_sum_sqproof · cited by 0
- Finset.mulEnergy_eq_sum_sqproof · cited by 0