Theorems · Theorem · order theory
Order.isSuccLimit_iff
∀ {α : Type u_1} [inst : Preorder α] (a : α), Order.IsSuccLimit a ↔ ¬IsMin a ∧ Order.IsSuccPrelimit a- Defined in
- Mathlib.Order.SuccPred.Limit
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- IsMinstatement and proof · cited by 277
- Order.IsSuccLimitstatement and proof · cited by 255
- Order.IsSuccPrelimitstatement and proof · cited by 157
- Order.IsSuccLimit.casesOnproof · cited by 1
Cited by9
Results whose statement or proof uses this declaration.
- csSup_mem_of_not_isSuccLimitproof · cited by 3
- SuccOrder.nhds_of_isMinproof · cited by 2
- Order.isSuccLimit_iff_of_orderBotproof · cited by 2
- WithBot.isSuccPrelimit_iffproof · cited by 1
- AccPt.isSuccLimitproof · cited by 1
- Order.isMin_or_mem_range_succ_or_isSuccLimitproof · cited by 1
- Order.not_isSuccLimit_iffproof · cited by 1
- Order.isPredLimit_toDual_iffproof · cited by 1
- Order.IsSuccLimit.withBotCoeproof · cited by 0