Theorems · Theorem · order theory
Order.isPredLimit_iff
∀ {α : Type u_1} [inst : Preorder α] (a : α), Order.IsPredLimit a ↔ ¬IsMax a ∧ Order.IsPredPrelimit a- Defined in
- Mathlib.Order.SuccPred.Limit
- Cited by
- 10 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
- IsMaxstatement and proof · cited by 372
- Order.IsPredPrelimitstatement and proof · cited by 93
- Order.IsPredLimitstatement and proof · cited by 60
- Order.IsPredLimit.casesOnproof · cited by 1
Cited by10
Results whose statement or proof uses this declaration.
- csInf_mem_of_not_isPredLimitproof · cited by 3
- PredOrder.nhds_of_isMaxproof · cited by 2
- WithBot.isPredLimit_iffproof · cited by 1
- Order.isPredPrelimit_iff_isPredLimit_of_not_isMaxproof · cited by 1
- Order.isPredLimit_toDual_iffproof · cited by 1
- Order.not_isPredLimit_iffproof · cited by 1
- AccPt.isPredLimitproof · cited by 0
- Order.isMax_or_mem_range_pred_or_isPredLimitproof · cited by 0
- Order.isPredLimit_iff_of_orderTopproof · cited by 0
- Order.IsPredLimit.withBotCoeproof · cited by 0