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Theorems · Theorem · general algebraic systems

Pi.single_injective

∀ {ι : Type u_1} {M : ι → Type u_6} [inst : (i : ι) → Zero (M i)] [inst_1 : DecidableEq ι] (i : ι),
  Function.Injective (Pi.single i)
Defined in
Mathlib.Algebra.Notation.Pi.Basic
Cited by
5 results in Mathlib
Foundations
Depth 9 from the axioms · uses no axioms
Assumes
ZeroDecidableEq
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

DFinsupp.single_injective · cited by 4DFinsupp.single_injectiveRestrictedProduct.single_injective · cited by 1RestrictedProduct.single_…Pi.single_inj · cited by 0Pi.single_injstrongRankCondition_iff_forall_zero_lt_finrank · cited by 0strongRankCondition_iff_f…LinearMap.ker_single · cited by 0LinearMap.ker_singlePi.single · cited by 518Pi.singleFunction.update_injective · cited by 8Function.update_injectivePi.single_injectiveCITED BYCITES

Cites2

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

Cited by5

Results whose statement or proof uses this declaration.