Theorems · Theorem · logic and foundations
Ordinal.isSuccPrelimit_iff_omega0_dvd
∀ {a : Ordinal.{u_4}}, Order.IsSuccPrelimit a ↔ Ordinal.omega0 ∣ a- Defined in
- Mathlib.SetTheory.Ordinal.Arithmetic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LT.lt.leproof · cited by 2,189
- le_antisymmproof · cited by 2,068
- le_reflproof · cited by 2,061
- Ordinalstatement and proof · cited by 1,688
- le_of_ltproof · cited by 1,175
- add_le_addproof · cited by 666
- le_imp_le_of_le_of_leproof · cited by 576
- Ordinal.omega0statement and proof · cited by 197
- Order.IsSuccPrelimitstatement and proof · cited by 157
- Order.succ_le_iffproof · cited by 20
- Ordinal.lt_omega0proof · cited by 15
- Ordinal.omega0_ne_zeroproof · cited by 10
Cited by2
Results whose statement or proof uses this declaration.
- ONote.repr_opow_aux₂proof · cited by 1
- Ordinal.isSuccLimit_iff_omega0_dvdproof · cited by 0