Theorems · Theorem · logic and foundations
Ordinal.zero_or_succ_or_isSuccLimit
∀ (o : Ordinal.{u_4}), o = 0 ∨ o ∈ Set.range Order.succ ∨ Order.IsSuccLimit o- Defined in
- Mathlib.SetTheory.Ordinal.Arithmetic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.rangestatement · cited by 4,705
- Ordinalstatement and proof · cited by 1,688
- Order.succstatement · cited by 633
- Order.IsSuccLimitstatement and proof · cited by 255
- Order.succ_eq_add_oneproof · cited by 115
- bot_eq_zero'proof · cited by 92
- Order.isMin_or_mem_range_succ_or_isSuccLimitproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- Cardinal.isSingular_aleph_iffproof · cited by 2
- Ordinal.cof_addproof · cited by 2
- Ordinal.isSuccLimit_opow_leftproof · cited by 1
- Ordinal.isSuccLimit_mul_leftproof · cited by 1
- Ordinal.mul_lt_omega0_opowproof · cited by 1