Theorems · Theorem · group theory
DirectSum.sum_univ_of
∀ {ι : Type v} {β : ι → Type w} [inst : (i : ι) → AddCommMonoid (β i)] [inst_1 : DecidableEq ι] [inst_2 : Fintype ι]
(x : DirectSum ι fun i => β i), ∑ i, (DirectSum.of β i) (x i) = x- Defined in
- Mathlib.Algebra.DirectSum.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- DFunLike.coestatement and proof · cited by 62,936
- AddCommMonoidstatement and proof · cited by 12,281
- Fintypestatement and proof · cited by 7,736
- Finset.sumstatement · cited by 5,195
- Finset.univstatement and proof · cited by 3,473
- AddMonoidHomstatement · cited by 3,230
- Finset.sum_congrproof · cited by 2,323
- DFinsuppstatement · cited by 694
- DirectSumstatement and proof · cited by 446
- DirectSum.ofstatement and proof · cited by 122
- Finset.sum_dite_eq'proof · cited by 21
- DirectSum.extproof · cited by 13
Cited by1
Results whose statement or proof uses this declaration.
- AdicCompletion.sum_comp_sumInvproof · cited by 0