Theorems · Theorem · group theory
finsum_eq_sum_of_fintype
∀ {α : Type u_1} {M : Type u_5} [inst : AddCommMonoid M] [inst_1 : Fintype α] (f : α → M), ∑ᶠ (i : α), f i = ∑ i, f i- Defined in
- Mathlib.Algebra.BigOperators.Finprod
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoidFintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Fintypestatement and proof · cited by 7,736
- Finset.sumstatement · cited by 5,195
- Finset.univstatement · cited by 3,473
- Function.supportproof · cited by 610
- Set.Finite.toFinsetproof · cited by 351
- finsumstatement · cited by 286
- Set.toFiniteproof · cited by 174
- Finset.subset_univproof · cited by 60
- finsum_eq_sum_of_support_toFinset_subsetproof · cited by 5
Cited by8
Results whose statement or proof uses this declaration.
- map_finsetSumproof · cited by 2
- MulAction.IsPreprimitive.of_card_ltproof · cited by 1
- IsOpenMap.enatCard_connectedComponents_le_encard_preimage_singletonproof · cited by 1
- finsum_mem_iUnionproof · cited by 1
- AddAction.IsPreprimitive.of_card_ltproof · cited by 0
- Group.card_center_add_sum_card_noncenter_eq_cardproof · cited by 0
- Group.sum_card_conj_classes_eq_cardproof · cited by 0
- Module.rankAtStalk_piproof · cited by 0