Mathlib Map

Theorems · Theorem · order theory

Function.Injective.codRestrict

∀ {α : Type u_1} {ι : Sort u_5} {f : ι → α} {s : Set α} (h : ∀ (x : ι), f x ∈ s),
  Function.Injective f → Function.Injective (Set.codRestrict f s h)

Alias of the reverse direction of Set.injective_codRestrict.

Defined in
Mathlib.Data.Set.Restrict
Cited by
5 results in Mathlib
Foundations
Depth 10 from the axioms · uses propext, Quot.sound
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Set.MapsTo.countable_of_injOn · cited by 5MapsTo.countable_of_injOnIsDenseEmbedding.subtype · cited by 3IsDenseEmbedding.subtypeFinite.of_injective_finite_range · cited by 3Finite.of_injective_finit…Pairwise.countable_of_isOpen_disjoint · cited by 1Pairwise.countable_of_isO…Submodule.finiteQuotient_iff · cited by 1Submodule.finiteQuotient_…Set · cited by 53352SetSet.Elem · cited by 7166Set.ElemSet.codRestrict · cited by 48Set.codRestrictSet.injective_codRestrict · cited by 10Set.injective_codRestrictInjective.codRestrictCITED BYCITES

Cites4

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.