Theorems · Theorem · order theory
Order.not_isPredLimit_iff
∀ {α : Type u_1} {a : α} [inst : Preorder α], ¬Order.IsPredLimit a ↔ IsMax a ∨ ¬Order.IsPredPrelimit a- Defined in
- Mathlib.Order.SuccPred.Limit
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Preorder
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.
- Preorderstatement and proof · cited by 7,952
- IsMaxstatement and proof · cited by 372
- Order.IsPredPrelimitstatement and proof · cited by 93
- not_and_orproof · cited by 82
- Order.IsPredLimitstatement · cited by 60
- Order.isPredLimit_iffproof · cited by 10
Cited by1
Results whose statement or proof uses this declaration.
- PredOrder.isOpen_singleton_iffproof · cited by 2