Mathlib Map

Theorems · Theorem

Pi.map_injective

∀ {ι : Sort u_1} {α : ι → Sort u_2} {β : ι → Sort u_3} [∀ (i : ι), Nonempty (α i)] {f : (i : ι) → α i → β i},
  Function.Injective (Pi.map f) ↔ ∀ (i : ι), Function.Injective (f i)
Defined in
Mathlib.Logic.Function.Basic
Cited by
5 results in Mathlib
Foundations
Depth 13 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Nonempty
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Pi.isAddLeftRegular_iff · cited by 1Pi.isAddLeftRegular_iffPi.isAddRightRegular_iff · cited by 1Pi.isAddRightRegular_iffPi.isSMulRegular_iff · cited by 0Pi.isSMulRegular_iffPi.isLeftRegular_iff · cited by 0Pi.isLeftRegular_iffPi.isRightRegular_iff · cited by 0Pi.isRightRegular_iffFunction.update · cited by 502Function.updateFunction.update_self · cited by 201Function.update_selfPi.map · cited by 60Pi.mapFunction.Injective.piMap · cited by 5Injective.piMapPi.map_update · cited by 1Pi.map_updatePi.map_injectiveCITED BYCITES

Cites5

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.