Theorems · Theorem · combinatorics
Fintype.bijective_iff_injective_and_card
∀ {α : Type u_1} {β : Type u_2} [inst : Fintype α] [inst_1 : Fintype β] (f : α → β),
Function.Bijective f ↔ Function.Injective f ∧ Fintype.card α = Fintype.card β- Defined in
- Mathlib.Data.Fintype.EquivFin
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- Fintype.cardstatement and proof · cited by 1,386
- Function.Bijectivestatement and proof · cited by 863
- Fintype.equivOfCardEqproof · cited by 23
- Function.Injective.surjective_of_finiteproof · cited by 2
- Fintype.card_of_bijectiveproof · cited by 2
Cited by11
Results whose statement or proof uses this declaration.
- Nat.bijective_iff_injective_and_cardproof · cited by 3
- Submodule.exists_smith_normal_form_of_rank_eqproof · cited by 2
- isSquare_of_charTwo'proof · cited by 1
- Finpartition.IsEquipartition.exists_partPreservingEquivproof · cited by 1
- Equiv.Perm.eq_top_of_isMultiplyPretransitiveproof · cited by 1
- Configuration.HasLines.exists_bijective_of_card_eqproof · cited by 1
- CategoryTheory.PreGaloisCategory.isIso_of_mono_of_eq_card_fiberproof · cited by 1
- FixedPoints.toAlgHom_bijectiveproof · cited by 1
- Matrix.IsDetpBalanced.submatrix_of_card_leproof · cited by 1
- ZMod.castHom_bijectiveproof · cited by 0
- AddChar.doubleDualEmb_bijectiveproof · cited by 0