Theorems · Theorem · logic and foundations
Cardinal.ord_natCast
∀ (n : ℕ), (↑n).ord = ↑n
- Defined in
- Mathlib.SetTheory.Ordinal.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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_oneproof · cited by 2,501
- Ordinalstatement · cited by 1,688
- LE.le.trans_ltproof · cited by 795
- Nat.cast_addproof · cited by 586
- LE.le.antisymmproof · cited by 507
- zero_leproof · cited by 382
- Eq.geproof · cited by 375
- Cardinal.ordstatement and proof · cited by 266
- Cardinal.ord_leproof · cited by 10
- Ordinal.card_natproof · cited by 6
- LT.lt.succ_leproof · cited by 5
Cited by6
Results whose statement or proof uses this declaration.
- Ordinal.isInitial_natCastproof · cited by 4
- Ordinal.nat_le_cardproof · cited by 4
- Cardinal.ord_oneproof · cited by 4
- Cardinal.le_ord_iff_card_le_of_lt_aleph0proof · cited by 1
- Cardinal.ord_ofNatproof · cited by 0
- Cardinal.ord_natproof · cited by 0