Theorems · Theorem · logic and foundations
Ordinal.preOmega_natCast
∀ (n : ℕ), Ordinal.preOmega ↑n = ↑n
- Defined in
- Mathlib.SetTheory.Cardinal.Aleph
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Ordinalstatement · cited by 1,688
- OrderEmbeddingstatement · cited by 619
- LE.le.antisymm'proof · cited by 104
- Nat.cast_ltproof · cited by 80
- Order.lt_succproof · cited by 45
- Eq.trans_ltproof · cited by 34
- Ordinal.preOmegastatement and proof · cited by 31
- Ordinal.isInitial_natCastproof · cited by 4
- Ordinal.not_bddAbove_isInitialproof · cited by 3
- Ordinal.le_preOmega_selfproof · cited by 2
- Ordinal.preOmega_zeroproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Ordinal.preOmega_omega0proof · cited by 4
- Cardinal.preAleph_natCastproof · cited by 3
- Ordinal.preOmega_ofNatproof · cited by 0