Theorems · Theorem · logic and foundations
Ordinal.card_nat
∀ (n : ℕ), (↑n).card = ↑n
- Defined in
- Mathlib.SetTheory.Ordinal.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Cardinalstatement · cited by 2,598
- Nat.cast_zeroproof · cited by 1,870
- Ordinalstatement · cited by 1,688
- Ordinal.cardstatement and proof · cited by 122
- Nat.cast_succproof · cited by 99
- Ordinal.card_addproof · cited by 6
- Ordinal.card_oneproof · cited by 6
- Ordinal.card_zeroproof · cited by 4
Cited by6
Results whose statement or proof uses this declaration.
- Cardinal.ord_natCastproof · cited by 6
- Ordinal.isInitial_natCastproof · cited by 4
- Cardinal.preAleph_natCastproof · cited by 3
- Ordinal.card_opow_le_of_omega0_le_rightproof · cited by 2
- Ordinal.card_opow_leproof · cited by 1
- Ordinal.card_ofNatproof · cited by 0