Theorems · Theorem · logic and foundations
Nat.bijective_iff_injective_and_card
∀ {α : Type u_1} {β : Type u_2} [Finite β] (f : α → β),
Function.Bijective f ↔ Function.Injective f ∧ Nat.card α = Nat.card β- Defined in
- Mathlib.SetTheory.Cardinal.Finite
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 93 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypeproof · cited by 7,736
- Finitestatement and proof · cited by 3,029
- Fintype.cardproof · cited by 1,386
- Function.Bijectivestatement and proof · cited by 863
- Nat.cardstatement and proof · cited by 844
- Fintype.ofFiniteproof · cited by 255
- Nat.card_eq_fintype_cardproof · cited by 200
- Fintype.bijective_iff_injective_and_cardproof · cited by 11
- Fintype.ofInjectiveproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- IntermediateField.fixingSubgroup_fixedFieldproof · cited by 3
- Subgroup.isComplement'_of_card_mul_and_disjointproof · cited by 2
- Function.Injective.bijective_of_nat_card_leproof · cited by 1