Theorems · Theorem · general algebraic systems
DFinsupp.single_eq_of_ne
∀ {ι : Type u} {β : ι → Type v} [inst : (i : ι) → Zero (β i)] [inst_1 : DecidableEq ι] {i i' : ι} {b : β i},
i' ≠ i → (fun₀ | i => b) i' = 0- Defined in
- Mathlib.Data.DFinsupp.Defs
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 25 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.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- DFinsuppstatement · cited by 694
- DFinsupp.singlestatement · cited by 113
Cited by12
Results whose statement or proof uses this declaration.
- DirectSum.of_eq_of_neproof · cited by 9
- MultilinearMap.dfinsuppFamily_singleproof · cited by 2
- DFinsupp.single_eq_single_iffproof · cited by 2
- DFinsupp.erase_eq_sub_singleproof · cited by 1
- DFinsupp.sigmaCurry_singleproof · cited by 1
- DFinsupp.Lex.acc_singleproof · cited by 1
- DFinsupp.comapDomain_singleproof · cited by 0
- DFinsupp.single_tsubproof · cited by 0
- OrthogonalFamily.projection_directSum_coeAddHomproof · cited by 0
- DFinsupp.extendWith_single_zeroproof · cited by 0
- DFinsupp.extendWith_zeroproof · cited by 0
- DFinsupp.sigmaUncurry_singleproof · cited by 0