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Theorems · Theorem · order theory

Set.InjOn.injective

∀ {α : Type u_1} {β : Type u_2} {s : Set α} {f : α → β}, Set.InjOn f s → Function.Injective (s.domRestrict f)

Alias of the forward direction of Set.injOn_iff_injective.

Defined in
Mathlib.Data.Set.Restrict
Cited by
6 results in Mathlib
Foundations
Depth 8 from the axioms · uses no axioms
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Around this declaration

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

ContinuousOn.strictMonoOn_of_injOn_Icc · cited by 2ContinuousOn.strictMonoOn…Function.Embedding.min_injective · cited by 2Embedding.min_injectiveSet.exists_injOn_iff_injective · cited by 1Set.exists_injOn_iff_inje…Continuous.strictMonoOn_of_inj_rigidity · cited by 1Continuous.strictMonoOn_o…ContinuousOn.strictMonoOn_of_injOn_Ioo · cited by 0ContinuousOn.strictMonoOn…Filter.map_inf' · cited by 0Filter.map_inf'Set · cited by 53352SetSet.Elem · cited by 7166Set.ElemSet.InjOn · cited by 543Set.InjOnSet.domRestrict · cited by 383Set.domRestrictSet.injOn_iff_injective · cited by 20Set.injOn_iff_injectiveInjOn.injectiveCITED BYCITES

Cites5

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

Cited by6

Results whose statement or proof uses this declaration.