Theorems · Theorem · logic and foundations
Cardinal.lt_aleph0_iff_set_finite
∀ {α : Type u} {S : Set α}, Cardinal.mk ↑S < Cardinal.aleph0 ↔ S.Finite- Defined in
- Mathlib.SetTheory.Cardinal.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.Elemstatement · cited by 7,166
- Cardinalstatement · cited by 2,598
- Set.Finitestatement · cited by 1,814
- Cardinal.mkstatement · cited by 942
- Cardinal.aleph0statement · cited by 521
- Set.finite_coe_iffproof · cited by 21
- Cardinal.lt_aleph0_iff_finiteproof · cited by 8
Cited by7
Results whose statement or proof uses this declaration.
- Submodule.FG.finite_generatorsproof · cited by 6
- finTrdeg_iff_trdegproof · cited by 4
- Set.Finite.lt_aleph0proof · cited by 4
- Cardinal.lt_aleph0_iff_subtype_finiteproof · cited by 2
- IsNoetherian.iff_rank_lt_aleph0proof · cited by 2
- LinearIndependent.setFiniteproof · cited by 2
- Cardinal.mk_set_eq_nat_iff_finsetproof · cited by 2