Theorems · Theorem · order theory
Order.isPredPrelimit_iff_pred_ne
∀ {α : Type u_1} {a : α} [inst : PartialOrder α] [inst_1 : PredOrder α] [NoMinOrder α],
Order.IsPredPrelimit a ↔ ∀ (b : α), Order.pred b ≠ a- Defined in
- Mathlib.Order.SuccPred.Limit
- Cited by
- 1 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PartialOrderstatement and proof · cited by 6,410
- PredOrderstatement and proof · cited by 334
- Order.predstatement · cited by 273
- NoMinOrderstatement and proof · cited by 247
- Order.IsPredPrelimitstatement · cited by 93
- Order.IsPredPrelimit.pred_neproof · cited by 3
- Order.isPredPrelimit_of_pred_neproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Order.not_isPredPrelimit_iff_mem_range_predproof · cited by 0