Theorems · Theorem · order theory
Set.image_preimage_eq_of_subset
∀ {α : Type u_1} {β : Type u_2} {f : α → β} {s : Set β}, s ⊆ Set.range f → f '' f ⁻¹' s = s- Defined in
- Mathlib.Data.Set.Image
- Cited by
- 41 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.
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 and proof · cited by 4,705
Cited by42
Results whose statement or proof uses this declaration.
- Fin.image_addNat_Iciproof · cited by 6
- Fin.image_addNat_Ioiproof · cited by 5
- Fin.image_natAdd_Iciproof · cited by 5
- Fin.image_addNat_Iccproof · cited by 4
- Fin.image_addNat_Iocproof · cited by 4
- Fin.image_addNat_Iooproof · cited by 4
- Fin.image_natAdd_Ioiproof · cited by 4
- Topology.IsInducing.isCompact_preimage_iffproof · cited by 3
- Fin.image_addNat_Icoproof · cited by 3
- TopologicalSpace.Compacts.closure_finite_subsetsproof · cited by 3
- Fin.image_natAdd_Iccproof · cited by 3
- Fin.image_natAdd_Iocproof · cited by 3