Theorems · Theorem · logic and foundations
Nat.card_eq
∀ (α : Type u_4), Nat.card α = if x : Finite α then Fintype.card α else 0
- 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.
- Fintypeproof · cited by 7,736
- Finitestatement and proof · cited by 3,029
- Fintype.cardstatement and proof · cited by 1,386
- Nat.cardstatement · cited by 844
- Infiniteproof · cited by 352
- Fintype.ofFinitestatement and proof · cited by 255
- Nat.card_eq_fintype_cardproof · cited by 200
- finite_or_infiniteproof · cited by 50
- Nat.card_eq_zero_of_infiniteproof · cited by 46
- not_finite_iff_infiniteproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.Quotient.index_eq_zeroproof · cited by 1