Theorems · Theorem · combinatorics
Finite.injective_iff_surjective
∀ {α : Type u_1} [Finite α] {f : α → α}, Function.Injective f ↔ Function.Surjective f- Defined in
- Mathlib.Data.Fintype.Card
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Finite
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.
- Finitestatement and proof · cited by 3,029
- Function.surjInvproof · cited by 63
- Function.injective_surjInvproof · cited by 14
- Function.rightInverse_surjInvproof · cited by 11
- Finite.surjective_of_injectiveproof · cited by 3
Cited by9
Results whose statement or proof uses this declaration.
- SimpleGraph.chromaticNumber_topproof · cited by 4
- Algebra.IsAlgebraic.algHom_bijectiveproof · cited by 3
- Finite.injective_iff_surjective_of_equivproof · cited by 2
- SimplexCategory.isIso_iff_of_epiproof · cited by 2
- SimplexCategory.isIso_iff_of_monoproof · cited by 1
- ax_grothendieck_of_locally_finiteproof · cited by 1
- Set.Finite.injOn_iff_bijOn_of_mapsToproof · cited by 1
- Set.Finite.surjOn_iff_bijOn_of_mapsToproof · cited by 0
- Function.injective_iff_periodicPts_eq_univproof · cited by 0