Theorems · Theorem · general algebraic systems
DFinsupp.sumZeroHom_single
∀ {ι : Type u} {γ : Type w} {β : ι → Type v} [inst : DecidableEq ι] [inst_1 : (i : ι) → Zero (β i)]
[inst_2 : AddCommMonoid γ] (φ : (i : ι) → ZeroHom (β i) γ) (i : ι) (x : β i),
((DFinsupp.sumZeroHom φ) fun₀ | i => x) = (φ i) x- Defined in
- Mathlib.Data.DFinsupp.BigOperators
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqZeroAddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Finsetproof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- Finset.sumproof · cited by 5,195
- DFinsuppstatement · cited by 694
- Pi.singleproof · cited by 518
- Finset.sum_singletonproof · cited by 251
- ZeroHomstatement and proof · cited by 161
- Pi.single_eq_sameproof · cited by 144
- DFinsupp.singlestatement · cited by 113
- Multiset.toFinset_singletonproof · cited by 9
- DFinsupp.sumZeroHomstatement · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- DFinsupp.sumAddHom_singleproof · cited by 17