Theorems · Theorem · order theory
Order.mem_range_pred_of_not_isPredPrelimit
∀ {α : Type u_1} {a : α} [inst : PartialOrder α] [inst_1 : PredOrder α],
¬Order.IsPredPrelimit a → a ∈ Set.range Order.predSee not_isPredPrelimit_iff_pred_eq for a version that states that a is a predecessor of a
value other than itself.
- Defined in
- Mathlib.Order.SuccPred.Limit
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PartialOrderPredOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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 · cited by 4,705
- PredOrderstatement and proof · cited by 334
- IsMinproof · cited by 277
- Order.predstatement and proof · cited by 273
- Order.IsPredPrelimitstatement and proof · cited by 93
- Order.not_isPredPrelimit_iff_pred_eqproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Order.mem_range_pred_or_isPredPrelimitproof · cited by 1