Theorems · Theorem · order theory
Order.isSuccPrelimit_iff_succ_lt
∀ {α : Type u_1} {b : α} [inst : PartialOrder α] [inst_1 : SuccOrder α],
Order.IsSuccPrelimit b ↔ ∀ a < b, Order.succ a < b- Defined in
- Mathlib.Order.SuccPred.Limit
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PartialOrderSuccOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PartialOrderstatement and proof · cited by 6,410
- Order.succstatement · cited by 633
- SuccOrderstatement and proof · cited by 574
- Order.IsSuccPrelimitstatement and proof · cited by 157
- Order.IsSuccPrelimit.succ_ltproof · cited by 7
- Order.isSuccPrelimit_of_succ_ltproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- Ordinal.isSuccLimit_omega0proof · cited by 9
- Ordinal.isSuccLimit_of_isPrincipal_addproof · cited by 4
- Ordinal.isSuccLimit_subproof · cited by 2
- Ordinal.iSup_typein_limitproof · cited by 1