Theorems · Theorem · order theory
Function.Surjective.image_preimage
∀ {α : Type u_1} {β : Type u_2} {f : α → β}, Function.Surjective f → ∀ (s : Set β), f '' f ⁻¹' s = s- Defined in
- Mathlib.Data.Set.Image
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 15 from the axioms · 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.image_preimage_eqproof · cited by 38
Cited by16
Results whose statement or proof uses this declaration.
- IsOpenMap.isQuotientMapproof · cited by 10
- Equiv.image_preimageproof · cited by 8
- Set.Finite.of_preimageproof · cited by 6
- Set.eq_preimage_iff_image_eqproof · cited by 5
- Set.preimage_eq_iff_eq_imageproof · cited by 5
- Function.Surjective.nonempty_preimageproof · cited by 4
- IsClosedMap.isQuotientMapproof · cited by 3
- Function.Surjective.image_surjectiveproof · cited by 3
- PrimeSpectrum.comap_isInducing_of_surjectiveproof · cited by 2
- MeasureTheory.OuterMeasure.comap_ofFunctionproof · cited by 2
- IsOpenMap.of_compproof · cited by 2
- ContinuousAffineEquiv.image_preimageproof · cited by 1