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Theorems · Theorem · order theory

IsLUB.isSuccLimit_of_notMem

∀ {α : Type u_1} {a : α} [inst : LinearOrder α] {s : Set α}, IsLUB s a → s.Nonempty → a ∉ s → Order.IsSuccLimit a
Defined in
Mathlib.Order.SuccPred.Limit
Cited by
2 results in Mathlib
Foundations
Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
LinearOrder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Order.IsNormal.map_isLUB · cited by 3IsNormal.map_isLUBIsLUB.mem_of_not_isSuccLimit · cited by 0IsLUB.mem_of_not_isSuccLi…Set · cited by 53352SetLinearOrder · cited by 8572LinearOrderSet.Nonempty · cited by 2627Set.NonemptyIsLUB · cited by 280IsLUBOrder.IsSuccLimit · cited by 255Order.IsSuccLimitLE.le.eq_or_lt · cited by 220le.eq_or_ltLT.lt.not_isMin · cited by 8lt.not_isMinIsLUB.isSuccPrelimit_of_notMem · cited by 2IsLUB.isSuccPrelimit_of_n…IsLUB.isSuccLimit_of_notMemCITED BYCITES

Cites8

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

Cited by2

Results whose statement or proof uses this declaration.