Theorems · Theorem · order theory
Set.image_preimage_eq_inter_range
∀ {α : Type u_1} {β : Type u_2} {f : α → β} {t : Set β}, f '' f ⁻¹' t = t ∩ Set.range f- Defined in
- Mathlib.Data.Set.Image
- Cited by
- 121 results in Mathlib
- Foundations
- Depth 16 from the axioms, rests on 74 definitions · uses propext, Classical.choice, 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.rangestatement · cited by 4,705
Cited by121
Results whose statement or proof uses this declaration.
- MeasurableEmbedding.map_applyproof · cited by 16
- MeasurableEmbedding.map_comapproof · cited by 8
- Finset.image_preimageproof · cited by 8
- AddSubgroup.map_comap_eqproof · cited by 5
- IsLocallyClosed.imageproof · cited by 5
- Subgroup.map_comap_eqproof · cited by 5
- Submodule.fg_of_fg_map_injectiveproof · cited by 5
- AlgebraicGeometry.IsAffineOpen.fromSpec_image_zeroLocusproof · cited by 4
- TopologicalSpace.IsOpenCover.isOpen_iff_coe_preimageproof · cited by 4
- WithTop.image_coe_Iicproof · cited by 4
- WithTop.image_coe_Iioproof · cited by 4
- AlgebraicGeometry.Scheme.IdealSheafData.le_support_iff_le_vanishingIdealproof · cited by 4