Theorems · Theorem · order theory
Set.eq_preimage_iff_image_eq
∀ {α : Type u} {β : Type v} {f : α → β}, Function.Bijective f → ∀ {s : Set α} {t : Set β}, s = f ⁻¹' t ↔ f '' s = t- Defined in
- Mathlib.Data.Set.Image
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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 · cited by 4,946
- Function.Bijectivestatement and proof · cited by 863
- Function.Surjective.image_preimageproof · cited by 16
- Set.image_eq_imageproof · cited by 8
Cited by5
Results whose statement or proof uses this declaration.
- Equiv.eq_preimage_iff_image_eqproof · cited by 6
- ZSpan.measure_fundamentalDomainproof · cited by 4
- AlgebraicGeometry.PresheafedSpace.GlueData.ι_image_preimage_eqproof · cited by 3
- PrimeSpectrum.isHomeomorph_comapproof · cited by 1
- TopCat.GlueData.preimage_image_eq_image'proof · cited by 1