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Theorems · Theorem · order theory

IsMax.isPredPrelimit

∀ {α : Type u_1} {a : α} [inst : Preorder α], IsMax a → Order.IsPredPrelimit a
Defined in
Mathlib.Order.SuccPred.Limit
Cited by
5 results in Mathlib
Foundations
Depth 8 from the axioms · uses no axioms
Assumes
Preorder
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Around this declaration

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

Order.isPredPrelimit_iff_isMax · cited by 2Order.isPredPrelimit_iff_…Order.isPredPrelimit_iff_of_noMin · cited by 1Order.isPredPrelimit_iff_…PredOrder.colimitRecOn_isMax · cited by 0PredOrder.colimitRecOn_is…Order.isPredLimitRecOn_of_isMax · cited by 0Order.isPredLimitRecOn_of…Order.isPredPrelimit_top · cited by 0Order.isPredPrelimit_topPreorder · cited by 7952PreorderIsMax · cited by 372IsMaxCovBy · cited by 290CovByOrder.IsPredPrelimit · cited by 93Order.IsPredPrelimitCovBy.lt · cited by 51CovBy.ltnot_isMax_of_lt · cited by 6not_isMax_of_ltIsMax.isPredPrelimitCITED BYCITES

Cites6

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

Cited by5

Results whose statement or proof uses this declaration.