Theorems · Theorem · logic and foundations
Set.to_countable
∀ {α : Type u} (s : Set α) [Countable ↑s], s.CountableProve Set.Countable from a Countable instance on the subtype.
- Defined in
- Mathlib.Data.Set.Countable
- Cited by
- 46 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- Countable
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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 and proof · cited by 7,166
- Countablestatement and proof · cited by 633
- Set.Countablestatement · cited by 545
Cited by46
Results whose statement or proof uses this declaration.
- Set.Finite.countableproof · cited by 30
- MeasurableSet.univ_piproof · cited by 19
- Set.countable_emptyproof · cited by 14
- Set.countable_singletonproof · cited by 13
- Set.countable_univproof · cited by 7
- MeasureTheory.measurableSet_exists_tendstoproof · cited by 4
- MeasurableSet.measurableAtom_of_countableproof · cited by 3
- measurable_of_countableproof · cited by 3
- Measurable.liminfproof · cited by 2
- volume_iUnion_setOfPred_liouvilleWithproof · cited by 2
- MeasureTheory.hahn_decompositionproof · cited by 2
- Filter.atTop_countable_basisproof · cited by 2