Theorems · Theorem · logic and foundations
Set.countable_iUnion
∀ {α : Type u} {ι : Sort x} {t : ι → Set α} [Countable ι], (∀ (i : ι), (t i).Countable) → (⋃ i, t i).Countable- Defined in
- Mathlib.Data.Set.Countable
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Countable
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.Elemproof · cited by 7,166
- Set.iUnionstatement · cited by 2,483
- Countablestatement and proof · cited by 633
- Set.Countablestatement and proof · cited by 545
- Set.Countable.to_subtypeproof · cited by 33
- Set.countable_rangeproof · cited by 31
- Set.iUnion_eq_range_psigmaproof · cited by 1
Cited by22
Results whose statement or proof uses this declaration.
- TopologicalSpace.IsSeparable.iUnionproof · cited by 7
- IsGδ.iInterproof · cited by 5
- UniformSpace.subset_countable_closure_of_almost_dense_setproof · cited by 4
- MeasureTheory.Measure.countable_meas_pos_of_disjoint_iUnion₀proof · cited by 2
- MeasureTheory.MeasurableSet.eq_preimage_restrict_countableproof · cited by 2
- MeasureTheory.Measure.ext_of_Ico'proof · cited by 2
- Besicovitch.exists_disjoint_closedBall_covering_ae_of_finiteMeasure_auxproof · cited by 1
- MeasureTheory.piContent_tendsto_zeroproof · cited by 1
- Complex.countable_preimage_expproof · cited by 1
- Set.nonempty_finiteExhaustion_iffproof · cited by 1
- FirstOrder.Language.DirectLimit.cgproof · cited by 1