Theorems · Theorem · order theory
Order.IsPredPrelimit.pred_ne
∀ {α : Type u_1} {a : α} [inst : Preorder α] [inst_1 : PredOrder α] [NoMinOrder α],
Order.IsPredPrelimit a → ∀ (b : α), Order.pred b ≠ a- Defined in
- Mathlib.Order.SuccPred.Limit
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PreorderPredOrderNoMinOrder
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.
- Preorderstatement and proof · cited by 7,952
- PredOrderstatement and proof · cited by 334
- Order.predstatement and proof · cited by 273
- NoMinOrderstatement and proof · cited by 247
- Order.IsPredPrelimitstatement and proof · cited by 93
- not_isMinproof · cited by 42
- Order.IsPredPrelimit.isMinproof · cited by 7
Cited by3
Results whose statement or proof uses this declaration.
- Order.not_isPredPrelimit_predproof · cited by 1
- Order.isPredPrelimit_iff_pred_neproof · cited by 1
- Order.IsPredLimit.pred_neproof · cited by 1