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Theorems · Theorem · logic and foundations

Ordinal.sSup_lt_of_lt_cof

∀ {s : Set Ordinal.{u}} {a : Ordinal.{u}},
  Cardinal.mk ↑s < (Ordinal.lift.{u + 1, u} a).cof → (∀ i ∈ s, i < a) → sSup s < a
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.

Cardinal.sSup_lt_of_lt_cof_ord · cited by 0Cardinal.sSup_lt_of_lt_co…Set · cited by 53352SetSet.Elem · cited by 7166Set.ElemCardinal · cited by 2598CardinalOrdinal · cited by 1688OrdinalSupSet.sSup · cited by 954SupSet.sSupCardinal.mk · cited by 942Cardinal.mkLE.le.trans_lt · cited by 795le.trans_ltOrdinal.cof · cited by 125Ordinal.cofOrdinal.lift · cited by 86Ordinal.liftOrdinal.sSup_add_one_lt_of_lt_cof · cited by 2Ordinal.sSup_add_one_lt_o…Ordinal.sSup_le_sSup_add_one · cited by 2Ordinal.sSup_le_sSup_add_…Ordinal.sSup_lt_of_lt_cofCITED BYCITES

Cites11

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Cited by1

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