Theorems · Theorem · logic and foundations
Finite.card_pos_iff
∀ {α : Type u_1} [Finite α], 0 < Nat.card α ↔ Nonempty α- Defined in
- Mathlib.SetTheory.Cardinal.NatCard
- 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.
Cites6
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
- Nat.cardstatement · cited by 844
- Fintype.ofFiniteproof · cited by 255
- Nat.card_eq_fintype_cardproof · cited by 200
- Fintype.card_pos_iffproof · cited by 31
Cited by3
Results whose statement or proof uses this declaration.
- Finite.card_posproof · cited by 6
- IsPGroup.exists_fixed_point_of_prime_dvd_card_of_fixed_pointproof · cited by 1
- commProb_posproof · cited by 0