Theorems · Theorem · order theory
Set.image_subset_iff
∀ {α : Type u_1} {β : Type u_2} {s : Set α} {t : Set β} {f : α → β}, f '' s ⊆ t ↔ s ⊆ f ⁻¹' timage and preimage are a Galois connection
- Defined in
- Mathlib.Data.Set.Image
- Cited by
- 203 results in Mathlib
- Foundations
- Depth 8 from the axioms, rests on 25 definitions · uses propext, 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.forall_mem_imageproof · cited by 65
Cited by203
Results whose statement or proof uses this declaration.
- Set.image_preimage_subsetproof · cited by 75
- Ideal.map_le_iff_le_comapproof · cited by 60
- Submodule.map_le_iff_le_comapproof · cited by 49
- Ideal.map_spanproof · cited by 43
- IsPreconnected.imageproof · cited by 24
- ContDiffWithinAt.compproof · cited by 18
- Set.mapsTo_iff_image_subsetproof · cited by 18
- Filter.prod_map_map_eqproof · cited by 17
- Filter.map_principalproof · cited by 17
- Set.image_preimageproof · cited by 16
- MeasureTheory.SimpleFunc.inductionproof · cited by 14
- Subgroup.map_le_iff_le_comapproof · cited by 13
Showing the 200 most cited of 203.