Theorems · Theorem · logic and foundations
Ordinal.card_iSup_le_lift
∀ {ι : Type u} {c : Cardinal.{v}} {f : ι → Ordinal.{v}},
Cardinal.lift.{v, u} (Cardinal.mk ι) ≤ Cardinal.lift.{u, v} c → (∀ (i : ι), (f i).card ≤ c) → (⨆ i, f i).card ≤ c- Defined in
- Mathlib.SetTheory.Cardinal.Ordinal
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LE.le.transproof · cited by 3,151
- Cardinalstatement and proof · cited by 2,598
- iSupstatement and proof · cited by 2,415
- Ordinalstatement and proof · cited by 1,688
- Cardinal.mkstatement and proof · cited by 942
- Cardinal.liftstatement and proof · cited by 583
- Cardinal.aleph0proof · cited by 521
- mul_le_mul'proof · cited by 274
- Ordinal.cardstatement and proof · cited by 122
- Cardinal.lift_leproof · cited by 78
- ciSup_le'proof · cited by 39
- Cardinal.lt_aleph0proof · cited by 19
Cited by3
Results whose statement or proof uses this declaration.
- Ordinal.card_iSup_Iio_le_of_liftproof · cited by 1
- Ordinal.card_sSup_leproof · cited by 0
- Ordinal.card_iSup_leproof · cited by 0