Theorems · Theorem · order theory
Set.preimage_image_eq
∀ {α : Type u_1} {β : Type u_2} {f : α → β} (s : Set α), Function.Injective f → f ⁻¹' f '' s = s- Defined in
- Mathlib.Data.Set.Image
- Cited by
- 87 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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 and proof · cited by 5,609
- Set.preimagestatement and proof · cited by 4,946
- Set.Subset.antisymmproof · cited by 213
- Set.subset_preimage_imageproof · cited by 44
Cited by87
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.preimage_image_eqproof · cited by 37
- Function.Injective.image_injectiveproof · cited by 33
- Function.Injective.preimage_imageproof · cited by 30
- Topology.IsClosedEmbedding.isClosed_iff_image_isClosedproof · cited by 13
- Filter.comap_mapproof · cited by 12
- Set.image_eq_imageproof · cited by 8
- Topology.IsClosedEmbedding.of_continuous_injective_isClosedMapproof · cited by 7
- Topology.IsOpenEmbedding.isOpen_iff_image_isOpenproof · cited by 7
- MulAction.isPreprimitive_congrproof · cited by 6
- isOpenMap_sigmaMkproof · cited by 5
- MeasureTheory.MeasurePreserving.setLIntegral_comp_embproof · cited by 5
- AddAction.isPreprimitive_congrproof · cited by 4