Theorems · Theorem · general algebraic systems
DFinsupp.single_zero
∀ {ι : Type u} {β : ι → Type v} [inst : (i : ι) → Zero (β i)] [inst_1 : DecidableEq ι] (i : ι), (fun₀ | i => 0) = 0- Defined in
- Mathlib.Data.DFinsupp.Defs
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- ZeroDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFinsuppstatement · cited by 694
- DFunLike.coe_injectiveproof · cited by 161
- DFinsupp.singlestatement and proof · cited by 113
- Pi.single_zeroproof · cited by 10
Cited by8
Results whose statement or proof uses this declaration.
- DFinsupp.sum_single_indexproof · cited by 5
- DFinsupp.inductionproof · cited by 5
- DFinsupp.single_eq_zeroproof · cited by 3
- DFinsupp.single_eq_single_iffproof · cited by 2
- Pi.counit_comp_dFinsuppCoeFnLinearMapproof · cited by 1
- Pi.comul_comp_dFinsuppCoeFnLinearMapproof · cited by 1
- DFinsupp.Lex.acc_singleproof · cited by 1
- DFinsupp.prod_single_indexproof · cited by 0