Theorems · Theorem · general algebraic systems
DFinsupp.finsetSum_apply
∀ {ι : Type u} {β : ι → Type v} {α : Type u_1} [inst : (i : ι) → AddCommMonoid (β i)] (s : Finset α)
(g : α → Π₀ (i : ι), β i) (i : ι), (∑ a ∈ s, g a) i = ∑ a ∈ s, (g a) i- Defined in
- Mathlib.Data.DFinsupp.BigOperators
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 30 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.
- DFunLike.coestatement · cited by 62,936
- Finsetstatement and proof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- Finset.sumstatement · cited by 5,195
- DFinsuppstatement and proof · cited by 694
- map_sumproof · cited by 455
- DFinsupp.evalAddMonoidHomproof · cited by 7
Cited by7
Results whose statement or proof uses this declaration.
- DirectSum.coe_mul_applyproof · cited by 3
- PiTensorProduct.ofDFinsuppEquiv_tprod_applyproof · cited by 2
- MultilinearMap.freeDFinsuppEquiv_singleproof · cited by 2
- DirectSum.sum_applyproof · cited by 1
- Ideal.homogeneous_spanproof · cited by 1
- DirectSum.completeOrthogonalIdempotents_idempotentproof · cited by 0
- DFinsupp.finset_sum_applyproof · cited by 0