Theorems · Theorem · logic and foundations
Cardinal.lift_mk_le_lift_mk_of_surjective
∀ {α : Type u} {β : Type v} {f : α → β},
Function.Surjective f → Cardinal.lift.{u, v} (Cardinal.mk β) ≤ Cardinal.lift.{v, u} (Cardinal.mk α)- Defined in
- Mathlib.SetTheory.Cardinal.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Cardinalstatement · cited by 2,598
- Cardinal.mkstatement · cited by 942
- Cardinal.liftstatement · cited by 583
- Function.injective_surjInvproof · cited by 14
- Cardinal.lift_mk_le_lift_mk_of_injectiveproof · cited by 10
Cited by5
Results whose statement or proof uses this declaration.
- Ordinal.lift_card_iSup_le_sum_cardproof · cited by 2
- OreLocalization.cardinalMk_le_maxproof · cited by 1
- AddOreLocalization.cardinalMk_le_maxproof · cited by 1
- OreLocalization.cardinalMk_le_lift_cardinalMk_of_commuteproof · cited by 0
- AddOreLocalization.cardinalMk_le_lift_cardinalMk_of_addCommuteproof · cited by 0