Theorems · Theorem · order theory
Order.IsPredPrelimit.isMax_of_noMin
∀ {α : Type u_1} {a : α} [inst : Preorder α] [inst_1 : PredOrder α] [IsPredArchimedean α] [NoMinOrder α],
Order.IsPredPrelimit a → IsMax a- Defined in
- Mathlib.Order.SuccPred.Limit
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- le_rflproof · cited by 1,558
- Nat.iterateproof · cited by 740
- IsMaxstatement · cited by 372
- PredOrderstatement and proof · cited by 334
- Order.predproof · cited by 273
- NoMinOrderstatement and proof · cited by 247
- Order.IsPredPrelimitstatement and proof · cited by 93
- Function.iterate_succ_apply'proof · cited by 72
- IsPredArchimedeanstatement and proof · cited by 66
- LE.le.exists_pred_iterateproof · cited by 6
- Order.not_isPredPrelimit_predproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Order.isPredPrelimit_iff_of_noMinproof · cited by 1
- Order.not_isPredLimit_of_noMinproof · cited by 1