Theorems · Theorem · logic and foundations
Cardinal.lift_lt_aleph0
∀ {c : Cardinal.{u}}, Cardinal.lift.{v, u} c < Cardinal.aleph0 ↔ c < Cardinal.aleph0- Defined in
- Mathlib.SetTheory.Cardinal.Order
- 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.
Cites5
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
- Cardinal.liftstatement and proof · cited by 583
- Cardinal.aleph0statement and proof · cited by 521
- Cardinal.lift_aleph0proof · cited by 41
- Cardinal.lift_ltproof · cited by 39
Cited by10
Results whose statement or proof uses this declaration.
- Cardinal.ord_aleph0proof · cited by 9
- Module.finrank_le_finrank_of_rank_le_rankproof · cited by 7
- Subfield.cardinalMk_closure_le_maxproof · cited by 3
- Module.Basis.nonempty_fintype_index_of_rank_lt_aleph0proof · cited by 2
- card_algHom_le_finrankproof · cited by 1
- finite_of_isTranscendenceBasisproof · cited by 1
- FinTrdeg.of_isTranscendenceBasisproof · cited by 0
- FinTrdeg.transproof · cited by 0
- finite_of_algebraicIndependentproof · cited by 0
- cardinal_lt_aleph0_of_finiteDimensionalproof · cited by 0