Theorems · Theorem · logic and foundations
Ordinal.card_iSup_Iio_le_sum_card
∀ {o : Ordinal.{u}} (f : ↑(Set.Iio o) → Ordinal.{max u v}), (⨆ a, f a).card ≤ Cardinal.sum fun i => (f i.toOrd).card- Defined in
- Mathlib.SetTheory.Cardinal.Ordinal
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.Elemstatement and proof · cited by 7,166
- Cardinalstatement · cited by 2,598
- iSupstatement · cited by 2,415
- Ordinalstatement and proof · cited by 1,688
- Set.Iiostatement and proof · cited by 1,166
- OrderIso.symmproof · cited by 475
- Ordinal.ToTypestatement and proof · cited by 143
- Ordinal.cardstatement and proof · cited by 122
- RelIso.toEquivproof · cited by 113
- Cardinal.sumstatement · cited by 58
- Equiv.iSup_compproof · cited by 14
- Ordinal.ToType.mkproof · cited by 10
Cited by1
Results whose statement or proof uses this declaration.
- Ordinal.card_iSup_Iio_le_card_mul_iSupproof · cited by 0