Theorems · Theorem · order theory
Function.Injective.preimage_image
∀ {α : Type u_1} {β : Type u_2} {f : α → β}, Function.Injective f → ∀ (s : Set α), f ⁻¹' f '' s = s- Defined in
- Mathlib.Data.Set.Image
- Cited by
- 30 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.imagestatement · cited by 5,609
- Set.preimagestatement · cited by 4,946
- Set.preimage_image_eqproof · cited by 87
Cited by30
Results whose statement or proof uses this declaration.
- MeasurableEmbedding.comap_applyproof · cited by 20
- MeasurableEmbedding.measurableSet_imageproof · cited by 18
- MeasurableEmbedding.map_applyproof · cited by 16
- Equiv.preimage_imageproof · cited by 9
- MeasurableEmbedding.comap_eqproof · cited by 4
- ContinuousMapZero.adjoin_id_denseproof · cited by 3
- TopologicalSpace.Compacts.isClopen_singleton_botproof · cited by 3
- Topology.IsClosedEmbedding.of_compproof · cited by 3
- IsAntichain.image_relEmbedding_iffproof · cited by 3
- IsChain.image_relEmbedding_iffproof · cited by 3
- DiscreteTopology.of_continuous_injectiveproof · cited by 2
- MeasurableEmbedding.mutuallySingular_mapproof · cited by 2