Theorems · Theorem · order theory
Order.isPredPrelimit_iff_lt_pred
∀ {α : Type u_1} {b : α} [inst : PartialOrder α] [inst_1 : PredOrder α],
Order.IsPredPrelimit b ↔ ∀ (a : α), b < a → b < Order.pred a- Defined in
- Mathlib.Order.SuccPred.Limit
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PartialOrderPredOrder
Around this declaration
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Cites6
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
- Order.IsPredPrelimitstatement and proof · cited by 93
- Order.IsPredPrelimit.lt_predproof · cited by 4
- Order.isPredPrelimit_of_lt_predproof · cited by 1
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