Theorems · Theorem · combinatorics
Finite.of_injective
∀ {α : Sort u_4} {β : Sort u_5} [Finite β] (f : α → β), Function.Injective f → Finite α- Defined in
- Mathlib.Data.Fintype.EquivFin
- Cited by
- 32 results in Mathlib
- Foundations
- Depth 62 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Equivproof · cited by 8,337
- Set.Elemproof · cited by 7,166
- Set.rangeproof · cited by 4,705
- Equiv.symmproof · cited by 3,681
- Finitestatement and proof · cited by 3,029
- Equiv.injectiveproof · cited by 464
- Equiv.ofInjectiveproof · cited by 64
- Finite.exists_equiv_finproof · cited by 23
- Finite.of_equivproof · cited by 20
Cited by32
Results whose statement or proof uses this declaration.
- Set.Finite.of_finite_imageproof · cited by 20
- Finite.of_surjectiveproof · cited by 14
- Infinite.of_injectiveproof · cited by 10
- IsGaloisGroup.card_eq_finrankproof · cited by 10
- not_injective_infinite_finiteproof · cited by 7
- Ideal.finite_factorsproof · cited by 7
- RootPairing.setOfPred_root_add_zsmul_eq_Icc_of_linearIndependentproof · cited by 5
- FiniteField.nonempty_algHom_of_finrank_dvdproof · cited by 3
- Finite.of_injective_finite_rangeproof · cited by 3
- SSet.finite_of_monoproof · cited by 3
- NumberField.hermiteTheorem.finite_of_finite_generating_setproof · cited by 2
- Setoid.IsPartition.ncard_eq_finsumproof · cited by 2