Theorems · Theorem · logic and foundations
Ordinal.card_le_nat
∀ {o : Ordinal.{u_1}} {n : ℕ}, o.card ≤ ↑n ↔ o ≤ ↑n- Defined in
- Mathlib.SetTheory.Ordinal.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Cardinalstatement · cited by 2,598
- Ordinalstatement and proof · cited by 1,688
- Ordinal.cardstatement · cited by 122
- le_iff_le_iff_lt_iff_ltproof · cited by 25
- Ordinal.nat_lt_cardproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- Ordinal.card_iSup_le_liftproof · cited by 3
- Ordinal.card_le_oneproof · cited by 0
- Ordinal.card_le_ofNatproof · cited by 0