Theorems · Theorem · logic and foundations
Set.countable_iff_exists_subset_range
∀ {α : Type u} [Nonempty α] {s : Set α}, s.Countable ↔ ∃ f, s ⊆ Set.range f- Defined in
- Mathlib.Data.Set.Countable
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Nonempty
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.
- Setstatement and proof · cited by 53,352
- Set.rangestatement and proof · cited by 4,705
- Set.Countablestatement and proof · cited by 545
- Set.Countable.monoproof · cited by 34
- Set.countable_rangeproof · cited by 31
- Set.enumerateCountableproof · cited by 15
- Set.subset_range_enumerateproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- TopologicalSpace.exists_dense_seqproof · cited by 5
- KuratowskiEmbedding.exists_isometric_embeddingproof · cited by 2
- MeasureTheory.isSeparable_of_sigmaFiniteproof · cited by 0