Theorems · Theorem · logic and foundations
Function.Surjective.bijective_of_nat_card_le
∀ {α : Type u_1} {β : Type u_2} [Finite α] {f : α → β},
Function.Surjective f → Nat.card α ≤ Nat.card β → 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
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.
- Finitestatement and proof · cited by 3,029
- Function.Bijectivestatement · cited by 863
- Nat.cardstatement and proof · cited by 844
- LE.le.antisymmproof · cited by 507
- Nat.card_le_card_of_surjectiveproof · cited by 11
- Nat.bijective_iff_surjective_and_cardproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.IsAlgebraic.isTranscendenceBasis_of_lift_le_trdeg_of_finiteproof · cited by 2