Theorems · Theorem · logic and foundations
Ordinal.isSuccPrelimit_type_lt_iff
∀ {α : Type u} [inst : LinearOrder α] [inst_1 : WellFoundedLT α],
Order.IsSuccPrelimit (Ordinal.type fun x1 x2 => x1 < x2) ↔ NoMaxOrder α- Defined in
- Mathlib.SetTheory.Ordinal.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrderWellFoundedLT
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.
- LinearOrderstatement and proof · cited by 8,572
- Ordinalstatement · cited by 1,688
- WellFoundedLTstatement and proof · cited by 491
- IsMaxproof · cited by 372
- NoMaxOrderstatement · cited by 340
- Ordinal.typestatement and proof · cited by 207
- IsWellOrderstatement · cited by 171
- not_iff_notproof · cited by 159
- Order.IsSuccPrelimitstatement and proof · cited by 157
- Order.not_isSuccPrelimit_iff_mem_range_succproof · cited by 4
- Ordinal.type_lt_mem_range_succ_iffproof · cited by 3
- noMaxOrder_iffproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- Cardinal.mul_eq_selfproof · cited by 13
- Cardinal.noMaxOrderproof · cited by 3
- Cardinal.lt_power_cof_ordproof · cited by 2
- Ordinal.cof_eq'proof · cited by 0
- Ordinal.isSuccPrelimit_type_ltproof · cited by 0