Theorems · Theorem · order theory
Order.not_isSuccPrelimit_iff_mem_range_succ
∀ {α : Type u_1} {a : α} [inst : PartialOrder α] [inst_1 : SuccOrder α] [NoMaxOrder α],
¬Order.IsSuccPrelimit a ↔ a ∈ Set.range Order.succ- Defined in
- Mathlib.Order.SuccPred.Limit
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- PartialOrderstatement and proof · cited by 6,410
- Set.rangestatement and proof · cited by 4,705
- Order.succstatement and proof · cited by 633
- SuccOrderstatement and proof · cited by 574
- NoMaxOrderstatement and proof · cited by 340
- Order.IsSuccPrelimitstatement · cited by 157
Cited by4
Results whose statement or proof uses this declaration.
- Ordinal.isSuccPrelimit_type_lt_iffproof · cited by 5
- Ordinal.one_lt_cof_iffproof · cited by 4
- Cardinal.isStrongPrelimit_preBethproof · cited by 1
- Order.not_isSuccPrelimit_iff'proof · cited by 0