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Theorems · Theorem · order theory

Order.IsSuccLimit.iSup_Iio

∀ {α : Type u_2} [inst : ConditionallyCompleteLinearOrderBot α] {x : α}, Order.IsSuccLimit x → ⨆ a, ↑a = x
Defined in
Mathlib.Order.SuccPred.CompleteLinearOrder
Cited by
1 results in Mathlib
Foundations
Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
ConditionallyCompleteLinearOrderBot
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Around this declaration

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

Order.IsNormal.apply_of_isSuccLimit · cited by 7IsNormal.apply_of_isSuccL…Set · cited by 53352SetSet.Elem · cited by 7166Set.ElemiSup · cited by 2415iSupSet.Iio · cited by 1166Set.IioOrder.IsSuccLimit · cited by 255Order.IsSuccLimitConditionallyCompleteLinearOrderBot · cited by 84ConditionallyCompleteLine…Order.IsSuccLimit.isSuccPrelimit · cited by 37IsSuccLimit.isSuccPrelimitOrder.IsSuccPrelimit.iSup_Iio · cited by 1IsSuccPrelimit.iSup_IioIsSuccLimit.iSup_IioCITED BYCITES

Cites8

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.