Theorems · Definition · general algebraic systems
DFinsupp.single
{ι : Type u} → {β : ι → Type v} → [inst : (i : ι) → Zero (β i)] → [DecidableEq ι] → (i : ι) → β i → Π₀ (i : ι), β iThe function single i b : Π₀ i, β i sends i to b
and all other points to 0.
- Defined in
- Mathlib.Data.DFinsupp.Defs
- Cited by
- 113 results in Mathlib
- Foundations
- Depth 21 from the axioms, rests on 93 definitions · uses propext, Quot.sound
- Assumes
- ZeroDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Cited by116
Results whose statement or proof uses this declaration.
- DFinsupp.single_applystatement · cited by 35
- DFinsupp.lsingleproof · cited by 23
- DFinsupp.singleAddHomproof · cited by 17
- DFinsupp.sumAddHom_singlestatement · cited by 17
- DFinsupp.single_eq_of_nestatement · cited by 12
- DFinsupp.single_eq_samestatement · cited by 11
- Finsupp.toDFinsupp_singlestatement · cited by 10
- DFinsupp.mapRange_singlestatement · cited by 8
- DFinsupp.single_zerostatement and proof · cited by 8
- DFinsupp.toFinsupp_singlestatement · cited by 8
- DirectSum.IsInternal.collectedBasis_coeproof · cited by 6
- Submodule.iSup_eq_range_dfinsupp_lsumproof · cited by 6