Theorems · Theorem · logic and foundations
Finite.card_le_one_iff_subsingleton
∀ {α : Type u_1} [Finite α], Nat.card α ≤ 1 ↔ Subsingleton α- Defined in
- Mathlib.SetTheory.Cardinal.NatCard
- Cited by
- 6 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.
Cites5
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
Cited by6
Results whose statement or proof uses this declaration.
- Set.powersetCard.isPretransitive_alternatingGroupproof · cited by 1
- alternatingGroup.exponent_kleinFour_of_card_eq_fourproof · cited by 1
- AddSubgroup.eq_bot_of_card_leproof · cited by 1
- Subgroup.eq_bot_of_card_leproof · cited by 1
- modularCyclotomicCharacter.idproof · cited by 0
- SpecialLinearGroup.center_eq_bot_of_finrank_le_oneproof · cited by 0