Theorems · Theorem · logic and foundations
Finite.card_eq_zero_of_surjective
∀ {α : Type u_1} {β : Type u_2} {f : α → β}, Function.Surjective f → Nat.card β = 0 → Nat.card α = 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 94 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finiteproof · cited by 3,029
- Nat.cardstatement and proof · cited by 844
- IsEmptyproof · cited by 759
- Infiniteproof · cited by 352
- finite_or_infiniteproof · cited by 50
- Nat.card_eq_zero_of_infiniteproof · cited by 46
- Function.isEmptyproof · cited by 15
- Nat.card_of_isEmptyproof · cited by 6
- Finite.card_eq_zero_iffproof · cited by 2
- Infinite.of_surjectiveproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Finite.card_eq_zero_of_injectiveproof · cited by 1