Theorems · Theorem · logic and foundations
Cardinal.lift_iSup_le_sum
∀ {ι : Type u} [Small.{v, u} ι] (f : ι → Cardinal.{v}), Cardinal.lift.{u, v} (⨆ i, f i) ≤ Cardinal.sum f- Defined in
- Mathlib.SetTheory.Cardinal.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Small
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Cardinalstatement and proof · cited by 2,598
- iSupstatement · cited by 2,415
- Cardinal.liftstatement · cited by 583
- Smallstatement and proof · cited by 369
- Cardinal.sumstatement and proof · cited by 58
- ciSup_le'proof · cited by 39
- Cardinal.bddAbove_of_smallproof · cited by 37
- Cardinal.lift_iSupproof · cited by 16
- Cardinal.lift_le_sumproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Cardinal.sum_eq_lift_iSup_of_lift_mk_le_lift_iSupproof · cited by 2