Theorems · Theorem · order theory
Set.InjOn.image_eq_image_iff
∀ {α : Type u_1} {β : Type u_2} {s s₁ s₂ : Set α} {f : α → β},
Set.InjOn f s → s₁ ⊆ s → s₂ ⊆ s → (f '' s₁ = f '' s₂ ↔ s₁ = s₂)- Defined in
- Mathlib.Data.Set.Function
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses propext, 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 · cited by 5,609
- Set.InjOnstatement and proof · cited by 543
- Set.InjOn.eq_iffproof · cited by 25
- Set.InjOn.imageproof · cited by 1
Cited by8
Results whose statement or proof uses this declaration.
- Matroid.IsBasis.mapproof · cited by 6
- Matroid.map_isBase_iffproof · cited by 5
- Matroid.cRk_map_image_liftproof · cited by 1
- Matroid.map_dep_iffproof · cited by 1
- Matroid.map_image_indep_iffproof · cited by 1
- Matroid.map_image_isBase_iffproof · cited by 1
- Matroid.map_isBasis_iffproof · cited by 1
- Finset.image_eq_image_iff_of_injOnproof · cited by 0