Theorems · Theorem · order theory
Order.IsPredLimit.not_isMax
∀ {α : Type u_1} [inst : Preorder α] {a : α}, Order.IsPredLimit a → ¬IsMax aPredecessor limits aren't maximal.
- Defined in
- Mathlib.Order.SuccPred.Limit
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 3 from the axioms · uses no axioms
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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 · cited by 372
- Order.IsPredLimitstatement and proof · cited by 60
Cited by11
Results whose statement or proof uses this declaration.
- PredOrder.isOpen_singleton_iffproof · cited by 2
- IsMax.not_isPredLimitproof · cited by 1
- Order.IsPredLimit.top_ltproof · cited by 1
- Order.not_isPredLimit_of_isPredArchimedeanproof · cited by 1
- Order.not_isPredLimit_of_noMinproof · cited by 1
- PredOrder.isOpen_iffproof · cited by 0
- PredOrder.colimitRecOn_of_isPredLimitproof · cited by 0
- Order.IsPredLimit.nonempty_Ioiproof · cited by 0
- Order.isPredLimitRecOn_of_isPredLimitproof · cited by 0
- Order.IsPredLimit.subtypeValproof · cited by 0
- Order.IsPredLimit.withBotCoeproof · cited by 0