Theorems · Theorem · order theory
Set.image_preimage_eq_iff
∀ {α : Type u_1} {β : Type u_2} {f : α → β} {s : Set β}, f '' f ⁻¹' s = s ↔ s ⊆ Set.range f- Defined in
- Mathlib.Data.Set.Image
- Cited by
- 23 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 · cited by 4,705
Cited by23
Results whose statement or proof uses this declaration.
- Function.Injective.tprod_eqproof · cited by 6
- Function.Injective.tsum_eqproof · cited by 6
- Finset.image_val_attachFinproof · cited by 5
- Cardinal.mk_preimage_of_subset_range_liftproof · cited by 3
- Set.subset_range_iff_exists_image_eqproof · cited by 3
- SimpleGraph.isClique_map_iff_of_nontrivialproof · cited by 2
- NumberField.mixedEmbedding.normAtAllPlaces_image_preimage_of_nonnegproof · cited by 2
- MeasureTheory.Measure.InnerRegularWRT.comapproof · cited by 2
- AddSubmonoid.FG.map_injectiveproof · cited by 1
- Submonoid.FG.map_injectiveproof · cited by 1
- SimpleGraph.Subgraph.image_coe_edgeSet_coeproof · cited by 1
- Matroid.restrictSubtype_indep_iff_of_subsetproof · cited by 1