Theorems · Theorem · order theory
Set.image_injective
∀ {α : Type u} {β : Type v} {f : α → β}, Function.Injective (Set.image f) ↔ Function.Injective f- Defined in
- Mathlib.Data.Set.Image
- Cited by
- 15 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.
Cites5
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.image_singletonproof · cited by 174
- Function.Injective.image_injectiveproof · cited by 33
- Set.singleton_eq_singleton_iffproof · cited by 13
Cited by15
Results whose statement or proof uses this declaration.
- Subalgebra.map_injectiveproof · cited by 5
- IsTranscendenceBasis.of_compproof · cited by 2
- Topology.IsOpenEmbedding.quasiSoberproof · cited by 2
- Set.ncard_le_ncard_image_add_one_iffproof · cited by 1
- Topology.IsClosedEmbedding.quasiSoberproof · cited by 1
- Topology.IsOpenEmbedding.functor_obj_injectiveproof · cited by 1
- AlgebraicGeometry.Scheme.Hom.isLocallyConstructible_imageproof · cited by 1
- NonUnitalStarSubalgebra.map_injectiveproof · cited by 0
- NonUnitalSubalgebra.map_injectiveproof · cited by 0
- LinearIndependent.maximal_iffproof · cited by 0
- exteriorPower.ιMulti_family_spanproof · cited by 0
- AlgebraicIndependent.isTranscendenceBasis_iffproof · cited by 0