Theorems · Theorem · order theory
Set.Finite.of_finite_image
∀ {α : Type u} {β : Type v} {s : Set α} {f : α → β}, (f '' s).Finite → Set.InjOn f s → s.Finite- Defined in
- Mathlib.Data.Set.Finite.Basic
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Set.imagestatement and proof · cited by 5,609
- Finiteproof · cited by 3,029
- Set.Finitestatement and proof · cited by 1,814
- Set.InjOnstatement and proof · cited by 543
- Function.Bijective.injectiveproof · cited by 115
- Set.MapsTo.restrictproof · cited by 57
- Set.Finite.to_subtypeproof · cited by 44
- Set.BijOn.mapsToproof · cited by 42
- Finite.of_injectiveproof · cited by 32
- Set.InjOn.bijOn_imageproof · cited by 20
Cited by20
Results whose statement or proof uses this declaration.
- Set.Finite.preimageproof · cited by 16
- Set.finite_image_iffproof · cited by 16
- Set.Finite.of_injOnproof · cited by 7
- Polynomial.mahlerMeasure_mulproof · cited by 5
- WellFoundedGT.finite_ne_bot_of_iSupIndepproof · cited by 5
- Set.countable_ofPred_finite_subsetproof · cited by 5
- Polynomial.bUnion_roots_finiteproof · cited by 3
- NumberField.FinitePlace.hasFiniteMulSupport_intproof · cited by 3
- Finset.exists_subset_injOn_image_eq_of_surjOnproof · cited by 3
- Ideal.finite_setOfPred_absNorm_eqproof · cited by 3
- PrimeSpectrum.finite_setOfPred_isMinproof · cited by 2
- PowerSeries.exist_eq_span_eq_ncard_of_X_notMemproof · cited by 2