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Theorems · Theorem · order theory

Function.Injective.subsingleton_image_iff

∀ {α : Type u_1} {β : Type u_2} {f : α → β},
  Function.Injective f → ∀ {s : Set α}, (f '' s).Subsingleton ↔ s.Subsingleton
Defined in
Mathlib.Data.Set.Image
Cited by
4 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.

AddAction.IsTrivialBlock.vadd · cited by 1IsTrivialBlock.vaddMulAction.IsTrivialBlock.smul · cited by 1IsTrivialBlock.smulSimpleGraph.isClique_map_image_iff · cited by 0SimpleGraph.isClique_map_…WithTop.denselyOrdered_set_iff_subsingleton · cited by 0WithTop.denselyOrdered_se…Set · cited by 53352SetSet.image · cited by 5609Set.imageSet.Subsingleton · cited by 276Set.SubsingletonSet.Subsingleton.image · cited by 14Subsingleton.imageSet.subsingleton_of_image · cited by 3Set.subsingleton_of_imageInjective.subsingleton_image_…CITED BYCITES

Cites5

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Cited by4

Results whose statement or proof uses this declaration.