Theorems · Theorem · general algebraic systems
DFinsupp.sum_single
∀ {ι : Type u} {β : ι → Type v} [inst : DecidableEq ι] [inst_1 : (i : ι) → AddCommMonoid (β i)]
[inst_2 : (i : ι) → (x : β i) → Decidable (x ≠ 0)] {f : Π₀ (i : ι), β i}, f.sum DFinsupp.single = f- Defined in
- Mathlib.Data.DFinsupp.BigOperators
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- AddCommMonoidstatement and proof · cited by 12,281
- AddMonoidHomproof · cited by 3,230
- DFinsuppstatement and proof · cited by 694
- DFunLike.congr_funproof · cited by 288
- DFinsupp.singlestatement · cited by 113
- AddMonoidHom.idproof · cited by 107
- DFinsupp.sumstatement · cited by 64
- DFinsupp.singleAddHomproof · cited by 17
- DFinsupp.sumAddHom_applyproof · cited by 16
- DFinsupp.liftAddHomproof · cited by 11
- DFinsupp.liftAddHom_applyproof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- MultilinearMap.dfinsupp_extproof · cited by 2
- Pi.counit_comp_dFinsuppCoeFnLinearMapproof · cited by 1
- DirectSum.sum_support_ofproof · cited by 1
- Pi.comul_comp_dFinsuppCoeFnLinearMapproof · cited by 1