Theorems · Theorem · order theory
Set.Finite.of_injOn
∀ {α : Type u} {β : Type v} {f : α → β} {s : Set α} {t : Set β}, Set.MapsTo f s t → Set.InjOn f s → t.Finite → s.Finite- Defined in
- Mathlib.Data.Set.Finite.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.Finitestatement and proof · cited by 1,814
- Set.MapsTostatement and proof · cited by 732
- Set.InjOnstatement and proof · cited by 543
- Set.Finite.subsetproof · cited by 285
- Set.image_subset_iffproof · cited by 203
- Set.Finite.of_finite_imageproof · cited by 20
Cited by7
Results whose statement or proof uses this declaration.
- Set.VAddAntidiagonal.finite_of_finiteproof · cited by 5
- Set.SMulAntidiagonal.finite_of_finite_fstproof · cited by 4
- Set.BijOn.finite_iff_finiteproof · cited by 3
- PowerSeries.exist_eq_span_eq_ncard_of_X_notMemproof · cited by 2
- Function.HasFiniteSupport.comp_of_injectiveproof · cited by 2
- Ring.HasFiniteQuotients.finite_cardQuot_heightOneSpectrum_leproof · cited by 1
- Function.HasFiniteMulSupport.comp_of_injectiveproof · cited by 1