Theorems · Theorem · logic and foundations
Finite.card_eq_zero_of_injective
∀ {α : Type u_1} {β : Type u_2} [Nonempty α] {f : α → β}, Function.Injective f → Nat.card α = 0 → Nat.card β = 0NB: Nat.card is defined to be 0 for infinite types.
- Defined in
- Mathlib.SetTheory.Cardinal.NatCard
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Nonempty
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nat.cardstatement and proof · cited by 844
- Function.invFun_surjectiveproof · cited by 8
- Finite.card_eq_zero_of_surjectiveproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Finite.card_eq_zero_of_embeddingproof · cited by 4