Theorems · Definition · logic and foundations
Set.BijOn
{α : Type u} → {β : Type v} → (α → β) → Set α → Set β → Propf is bijective from s to t if f is injective on s and f '' s = t.
- Defined in
- Mathlib.Data.Set.Operations
- Cited by
- 168 results in Mathlib
- Foundations
- Depth 7 from the axioms, rests on 19 definitions · uses no axioms
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.MapsToproof · cited by 732
- Set.InjOnproof · cited by 543
- Set.SurjOnproof · cited by 186
Cited by177
Results whose statement or proof uses this declaration.
- Set.BijOn.injOnstatement and proof · cited by 42
- Set.BijOn.mapsTostatement and proof · cited by 42
- Equiv.Perm.IsCycleOnproof · cited by 41
- Set.BijOn.surjOnstatement and proof · cited by 31
- Set.BijOn.image_eqstatement and proof · cited by 30
- Set.InjOn.bijOn_imagestatement · cited by 20
- IsAddFreimanIso.bijOnstatement · cited by 14
- IsMulFreimanIso.bijOnstatement · cited by 13
- SimpleGraph.ConnectedComponent.Representsproof · cited by 10
- Set.InvOn.bijOnstatement · cited by 9
- PartialEquiv.bijOnstatement · cited by 6
- Set.BijOn.compstatement and proof · cited by 6