Theorems · Theorem · order theory
Set.Finite.injOn_iff_bijOn_of_mapsTo
∀ {α : Type u} {s : Set α} {f : α → α}, s.Finite → Set.MapsTo f s s → (Set.InjOn f s ↔ Set.BijOn f s s)- Defined in
- Mathlib.Data.Set.Finite.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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.Elemproof · cited by 7,166
- Finiteproof · cited by 3,029
- Set.Finitestatement and proof · cited by 1,814
- Set.MapsTostatement and proof · cited by 732
- Set.InjOnstatement and proof · cited by 543
- Set.BijOnstatement · cited by 168
- Set.BijOn.injOnproof · cited by 42
- Set.finite_coe_iffproof · cited by 21
- Finite.injective_iff_surjectiveproof · cited by 9
- Set.MapsTo.restrict_injproof · cited by 4
- Set.MapsTo.restrict_surjective_iffproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- LinearEquiv.isOfFinOrder_of_finite_of_span_eq_top_of_mapsToproof · cited by 1