Theorems · Theorem · logic and foundations
Ordinal.isSuccLimit_iff
∀ {o : Ordinal.{u_4}}, Order.IsSuccLimit o ↔ o ≠ 0 ∧ Order.IsSuccPrelimit o- Defined in
- Mathlib.SetTheory.Ordinal.Arithmetic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ordinalstatement and proof · cited by 1,688
- Order.IsSuccLimitstatement · cited by 255
- Order.IsSuccPrelimitstatement · cited by 157
- Order.isSuccLimit_iff_of_orderBotproof · cited by 2
Cited by6
Results whose statement or proof uses this declaration.
- Ordinal.isSuccLimit_omega0proof · cited by 9
- Ordinal.one_lt_cof_iffproof · cited by 4
- Ordinal.isSuccLimit_of_isPrincipal_addproof · cited by 4
- Ordinal.isSuccLimit_subproof · cited by 2
- Cardinal.isStrongLimit_preBethproof · cited by 1
- Ordinal.isSuccLimit_iff_omega0_dvdproof · cited by 0