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Theorems · Theorem · general algebraic systems

Finsupp.single_injective

∀ {α : Type u_1} {M : Type u_5} [inst : Zero M] (a : α), Function.Injective (Finsupp.single a)

Finsupp.single a b is injective in b. For the statement that it is injective in a, see Finsupp.single_left_injective

Defined in
Mathlib.Data.Finsupp.Single
Cited by
9 results in Mathlib
Foundations
Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Zero
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

PowerSeries.coeff_mul · cited by 29PowerSeries.coeff_mulCardinal.mk_finsupp_lift_of_infinite · cited by 6Cardinal.mk_finsupp_lift_…Finsupp.single_eq_single_iff · cited by 6Finsupp.single_eq_single_…PowerSeries.hasSum_eval₂ · cited by 2PowerSeries.hasSum_eval₂Finsupp.antidiagonal_single · cited by 2Finsupp.antidiagonal_sing…SkewMonoidAlgebra.single_injective · cited by 2SkewMonoidAlgebra.single_…LinearIndependent.smul_left_injective · cited by 1LinearIndependent.smul_le…Module.Basis.isScalarTower_of_nonempty · cited by 0Basis.isScalarTower_of_no…Finsupp.ker_lsingle · cited by 0Finsupp.ker_lsingleDFunLike.coe · cited by 62936DFunLike.coeFinsupp · cited by 5255FinsuppFinsupp.single · cited by 943Finsupp.singleFinsupp.single_eq_same · cited by 171Finsupp.single_eq_sameFinsupp.single_injectiveCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by9

Results whose statement or proof uses this declaration.