Mathlib Map

Theorems · Theorem · order theory

Order.IsPredLimit.pred_ne

∀ {α : Type u_1} {a : α} [inst : Preorder α] [inst_1 : PredOrder α] [NoMinOrder α],
  Order.IsPredLimit a → ∀ (b : α), Order.pred b ≠ a
Defined in
Mathlib.Order.SuccPred.Limit
Cited by
1 results in Mathlib
Foundations
Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PreorderPredOrderNoMinOrder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Order.not_isPredLimit_pred · cited by 0Order.not_isPredLimit_predPreorder · cited by 7952PreorderPredOrder · cited by 334PredOrderOrder.pred · cited by 273Order.predNoMinOrder · cited by 247NoMinOrderOrder.IsPredLimit · cited by 60Order.IsPredLimitOrder.IsPredLimit.isPredPrelimit · cited by 23IsPredLimit.isPredPrelimitOrder.IsPredPrelimit.pred_ne · cited by 3IsPredPrelimit.pred_neIsPredLimit.pred_neCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.