Theorems · Theorem · logic and foundations
Cardinal.lift_mk_le_lift_mk_of_injective
∀ {α : Type u} {β : Type v} {f : α → β},
Function.Injective f → Cardinal.lift.{v, u} (Cardinal.mk α) ≤ Cardinal.lift.{u, v} (Cardinal.mk β)- Defined in
- Mathlib.SetTheory.Cardinal.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.rangeproof · cited by 4,705
- Cardinalstatement and proof · cited by 2,598
- Cardinal.mkstatement and proof · cited by 942
- Cardinal.liftstatement and proof · cited by 583
- Cardinal.lift_leproof · cited by 78
- Cardinal.mk_range_eq_of_injectiveproof · cited by 14
- Cardinal.mk_set_leproof · cited by 14
Cited by10
Results whose statement or proof uses this declaration.
- Nat.card_le_card_of_injectiveproof · cited by 19
- Cardinal.lift_mk_le_lift_mk_of_surjectiveproof · cited by 5
- ENat.card_le_card_of_injectiveproof · cited by 3
- Algebra.IsAlgebraic.lift_cardinalMk_le_sigma_polynomialproof · cited by 2
- continuum_le_cardinal_of_nontriviallyNormedFieldproof · cited by 1
- Cardinal.mk_le_of_moduleproof · cited by 1
- Cardinal.not_injective_limitation_setproof · cited by 1
- IntermediateField.rank_sup_leproof · cited by 1
- OreLocalization.cardinalMk_le_lift_cardinalMk_of_commuteproof · cited by 0
- AddOreLocalization.cardinalMk_le_lift_cardinalMk_of_addCommuteproof · cited by 0