Theorems · Theorem · order theory
Set.InjOn.bijOn_image
∀ {α : Type u_1} {β : Type u_2} {s : Set α} {f : α → β}, Set.InjOn f s → Set.BijOn f s (f '' s)- Defined in
- Mathlib.Data.Set.Function
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.InjOnstatement and proof · cited by 543
- Set.BijOnstatement · cited by 168
- Set.mapsTo_imageproof · cited by 71
- Set.Subset.reflproof · cited by 66
- Set.BijOn.mkproof · cited by 5
Cited by21
Results whose statement or proof uses this declaration.
- Set.Finite.of_finite_imageproof · cited by 20
- Equiv.bijOn_imageproof · cited by 2
- threeAPFree_imageproof · cited by 2
- threeGPFree_imageproof · cited by 2
- Set.InjOn.toPartialEquivproof · cited by 2
- Subgroup.properlyDiscontinuousSMul_iffproof · cited by 2
- AddSubgroup.properlyDiscontinuousVAdd_iffproof · cited by 2
- Matroid.Indep.exists_bijOn_of_mapproof · cited by 1
- IsAddFreimanIso.addRothNumber_congrproof · cited by 1
- Set.BijOn.subset_leftproof · cited by 1
- Besicovitch.exists_closedBall_covering_tsum_measure_leproof · cited by 1
- Set.Finite.exists_bijOn_of_encard_eqproof · cited by 0