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Theorems · Theorem · logic and foundations

Ordinal.le_cof_iff_lsub

Deprecated since 2026-03-21Use Order.le_cof_iff instead.

∀ {o : Ordinal.{u}} {a : Cardinal.{u}},
  a ≤ o.cof ↔ ∀ {ι : Type u} (f : ι → Ordinal.{u}), Ordinal.lsub f = o → a ≤ Cardinal.mk ι
Defined in
Mathlib.SetTheory.Cardinal.Cofinality.Ordinal
Cited by
1 results in Mathlib
Foundations
Depth 93 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.le_cof_iff_blsub · cited by 0Ordinal.le_cof_iff_blsubSet.ofPred · cited by 6101Set.ofPredCardinal · cited by 2598CardinalOrdinal · cited by 1688OrdinalCardinal.mk · cited by 942Cardinal.mkOrdinal.cof · cited by 125Ordinal.cofOrdinal.lsub · cited by 43Ordinal.lsubOrdinal.cof_lsub_def_nonempty · cited by 3Ordinal.cof_lsub_def_none…Ordinal.cof_eq_sInf_lsub · cited by 2Ordinal.cof_eq_sInf_lsuble_csInf_iff'' · cited by 1le_csInf_iff''Ordinal.le_cof_iff_lsubCITED BYCITES

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Cited by1

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