Theorems · Theorem · logic and foundations
Finite.one_lt_card_iff_nontrivial
∀ {α : Type u_1} [Finite α], 1 < Nat.card α ↔ Nontrivial α- Defined in
- Mathlib.SetTheory.Cardinal.NatCard
- Cited by
- 11 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
- Nontrivialstatement and proof · cited by 2,416
- Nat.cardstatement · cited by 844
- Fintype.ofFiniteproof · cited by 255
- Nat.card_eq_fintype_cardproof · cited by 200
Cited by11
Results whose statement or proof uses this declaration.
- Finite.one_lt_cardproof · cited by 12
- isCyclic_of_prime_cardproof · cited by 3
- alternatingGroup.card_of_card_eq_fourproof · cited by 2
- IsPGroup.nontrivial_iff_cardproof · cited by 2
- alternatingGroup.isCoatom_stabilizer_singletonproof · cited by 1
- isSimpleAddGroup_of_prime_cardproof · cited by 1
- isSimpleGroup_of_prime_cardproof · cited by 1
- isAddCyclic_of_prime_cardproof · cited by 1
- not_isAddCyclic_iff_exponent_eq_primeproof · cited by 0
- Set.powersetCard.nontrivial_iffproof · cited by 0
- not_isCyclic_iff_exponent_eq_primeproof · cited by 0