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Theorems · Theorem · logic and foundations

Function.Injective.bijective_of_nat_card_le

∀ {α : Type u_1} {β : Type u_2} [Finite β] {f : α → β},
  Function.Injective f → Nat.card β ≤ Nat.card α → Function.Bijective f
Defined in
Mathlib.SetTheory.Cardinal.Finite
Cited by
1 results in Mathlib
Foundations
Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Finite
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

FiniteField.bijective_frobeniusAlgHom_pow · cited by 2FiniteField.bijective_fro…Finite · cited by 3029FiniteFunction.Bijective · cited by 863Function.BijectiveNat.card · cited by 844Nat.cardLE.le.antisymm · cited by 507le.antisymmNat.card_le_card_of_injective · cited by 19Nat.card_le_card_of_injec…Nat.bijective_iff_injective_and_card · cited by 3Nat.bijective_iff_injecti…Injective.bijective_of_nat_ca…CITED BYCITES

Cites6

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Cited by1

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