Theorems · Theorem · logic and foundations
Set.countable_coe_iff
∀ {α : Type u} {s : Set α}, Countable ↑s ↔ s.Countable- Defined in
- Mathlib.Data.Set.Countable
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
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 · cited by 7,166
- Countablestatement · cited by 633
- Set.Countablestatement · cited by 545
Cited by15
Results whose statement or proof uses this declaration.
- Set.Countable.to_subtypeproof · cited by 33
- Set.countable_univ_iffproof · cited by 5
- Countable.to_setproof · cited by 3
- Set.countable_ofPred_nonempty_of_disjointproof · cited by 2
- Measurable.liminf'proof · cited by 2
- MeasureTheory.setIntegral_countableproof · cited by 2
- MeasureTheory.exists_subset_real_measurableEquivproof · cited by 1
- MeasureTheory.Measure.MeasureDense.of_generateFrom_isSetAlgebra_finiteproof · cited by 1
- IsLindelof.countableproof · cited by 1
- MeasureTheory.countable_generateSetAlgebraproof · cited by 1
- MeasureTheory.exists_accPt_of_nullSingletonClassproof · cited by 1
- isSigmaCompact_biUnionproof · cited by 0