Mathlib Map

Theorems · Theorem

Prod.map_injective

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {δ : Type u_4} [Nonempty α] [Nonempty β] {f : α → γ} {g : β → δ},
  Function.Injective (Prod.map f g) ↔ Function.Injective f ∧ Function.Injective g
Defined in
Mathlib.Data.Prod.Basic
Cited by
7 results in Mathlib
Foundations
Depth 7 from the axioms · uses Classical.choice
Assumes
NonemptyNonempty
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Around this declaration

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

Prod.isAddLeftRegular_mk · cited by 2Prod.isAddLeftRegular_mkProd.isAddRightRegular_mk · cited by 2Prod.isAddRightRegular_mkProd.isLeftRegular_mk · cited by 1Prod.isLeftRegular_mkProd.isRightRegular_mk · cited by 1Prod.isRightRegular_mkProd.map_bijective · cited by 0Prod.map_bijectiveLinearMap.separatingLeft_dualProd · cited by 0LinearMap.separatingLeft_…Prod.isSMulRegular_iff · cited by 0Prod.isSMulRegular_iffFunction.Injective.prodMap · cited by 9Injective.prodMapProd.map_injectiveCITED BYCITES

Cites1

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

Cited by7

Results whose statement or proof uses this declaration.