Theorems · Theorem · logic and foundations
Nat.card_eq_zero_of_infinite
∀ {α : Type u_1} [Infinite α], Nat.card α = 0- Defined in
- Mathlib.SetTheory.Cardinal.Finite
- Cited by
- 46 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Infinite
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 · cited by 844
- Infinitestatement and proof · cited by 352
- Cardinal.mk_toNat_of_infiniteproof · cited by 1
Cited by46
Results whose statement or proof uses this declaration.
- orderOf_dvd_natCardproof · cited by 14
- Nat.card_zmodproof · cited by 13
- Set.Infinite.ncardproof · cited by 12
- IsGaloisGroup.card_eq_finrankproof · cited by 10
- Nat.card_unitsproof · cited by 6
- addOrderOf_dvd_natCardproof · cited by 6
- Set.powersetCard.cardproof · cited by 5
- Configuration.HasLines.pointCount_le_lineCountproof · cited by 4
- Nat.card_image_of_injOnproof · cited by 3
- DihedralGroup.nat_cardproof · cited by 3
- Projectivization.cardproof · cited by 3
- MulAction.IsPreprimitive.isMultiplyPreprimitiveproof · cited by 2