Theorems · Theorem · group theory
DirectSum.sum_apply
∀ {ι : Type v} {β : ι → Type w} [inst : (i : ι) → AddCommMonoid (β i)] {α : Type u_1} (s : Finset α)
(g : α → DirectSum ι fun i => β i) (i : ι), (∑ a ∈ s, g a) i = ∑ a ∈ s, (g a) i- Defined in
- Mathlib.Algebra.DirectSum.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 31 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 · cited by 694
- DirectSumstatement and proof · cited by 446
- DFinsupp.finsetSum_applyproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- DirectSum.sum_univ_ofproof · cited by 1