Theorems · Theorem · order theory
Order.not_isPredPrelimit_iff_mem_range_pred
∀ {α : Type u_1} {a : α} [inst : PartialOrder α] [inst_1 : PredOrder α] [NoMinOrder α],
¬Order.IsPredPrelimit a ↔ a ∈ Set.range Order.pred- Defined in
- Mathlib.Order.SuccPred.Limit
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- PartialOrderstatement and proof · cited by 6,410
- Set.rangestatement and proof · cited by 4,705
- PredOrderstatement and proof · cited by 334
- Order.predstatement and proof · cited by 273
- NoMinOrderstatement and proof · cited by 247
- Set.mem_rangeproof · cited by 102
- Order.IsPredPrelimitstatement · cited by 93
- not_ne_iffproof · cited by 30
- Order.isPredPrelimit_iff_pred_neproof · cited by 1
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