Theorems · Theorem · order theory
Set.image_subset_range
∀ {α : Type u_1} {β : Type u_2} (f : α → β) (s : Set α), f '' s ⊆ Set.range f- Defined in
- Mathlib.Data.Set.Image
- Cited by
- 76 results in Mathlib
- Foundations
- Depth 17 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.rangestatement · cited by 4,705
- Set.image_univproof · cited by 322
- Set.subset_univproof · cited by 228
- Set.image_monoproof · cited by 197
Cited by76
Results whose statement or proof uses this declaration.
- MeasurableEmbedding.comap_applyproof · cited by 20
- Finsupp.mapDomain_of_notMem_rangeproof · cited by 7
- LinearMap.map_le_rangeproof · cited by 7
- Set.SurjOn.subset_rangeproof · cited by 6
- HahnSeries.embDomain_of_notMem_rangeproof · cited by 6
- Fin.image_addNat_Ioiproof · cited by 5
- WellFoundedGT.finite_ne_bot_of_iSupIndepproof · cited by 5
- Fin.image_addNat_Iccproof · cited by 4
- Fin.image_addNat_Iocproof · cited by 4
- Fin.image_addNat_Iooproof · cited by 4
- MeasureTheory.Measure.addHaar_image_linearMapproof · cited by 4
- Fin.image_natAdd_Ioiproof · cited by 4