Theorems · Theorem · logic and foundations
Ordinal.lift_card_sInf_compl_le
∀ (s : Set Ordinal.{u}), Cardinal.lift.{u + 1, u} (sInf sᶜ).card ≤ Cardinal.mk ↑s- Defined in
- Mathlib.SetTheory.Ordinal.Family
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.Elemstatement and proof · cited by 7,166
- Compl.complstatement and proof · cited by 2,925
- Cardinalstatement and proof · cited by 2,598
- Ordinalstatement and proof · cited by 1,688
- Cardinal.mkstatement and proof · cited by 942
- InfSet.sInfstatement and proof · cited by 935
- Cardinal.liftstatement · cited by 583
- Ordinal.cardstatement · cited by 122
- Cardinal.mk_le_mk_of_subsetproof · cited by 37
- Cardinal.mk_Iio_ordinalproof · cited by 8
- Set.not_notMemproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Ordinal.card_sInf_range_compl_le_liftproof · cited by 2