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Theorems · Theorem · logic and foundations

Ordinal.cof_iSup_Iio

∀ {a : Ordinal.{u_1}} {f : ↑(Set.Iio a) → Ordinal.{u_1}}, StrictMono f → Order.IsSuccPrelimit a → (⨆ i, f i).cof = a.cof
Defined in
Mathlib.SetTheory.Cardinal.Cofinality.Ordinal
Cited by
1 results in Mathlib
Foundations
Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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

Ordinal.cof_map_of_isNormal · cited by 7Ordinal.cof_map_of_isNorm…Set · cited by 53352SetSet.Elem · cited by 7166Set.ElemCardinal · cited by 2598CardinaliSup · cited by 2415iSupOrdinal · cited by 1688OrdinalSet.Iio · cited by 1166Set.IioStrictMono · cited by 706StrictMonoOrder.IsSuccPrelimit · cited by 157Order.IsSuccPrelimitOrdinal.cof · cited by 125Ordinal.cofOrdinal.cof_iSup_Iio_add_one · cited by 2Ordinal.cof_iSup_Iio_add_…Ordinal.iSup_Iio_add_one · cited by 2Ordinal.iSup_Iio_add_oneOrdinal.cof_iSup_IioCITED BYCITES

Cites11

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Cited by1

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