Theorems · Theorem · order theory
Set.Finite.surjOn_iff_bijOn_of_mapsTo
∀ {α : Type u} {s : Set α} {f : α → α}, s.Finite → Set.MapsTo f s s → (Set.SurjOn f s s ↔ Set.BijOn f s s)- Defined in
- Mathlib.Data.Set.Finite.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
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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.SurjOnstatement and proof · cited by 186
- Set.BijOnstatement · cited by 168
- Set.BijOn.surjOnproof · cited by 31
- 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
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