Theorems · Theorem · logic and foundations
Set.Countable.image
∀ {α : Type u} {β : Type v} {s : Set α}, s.Countable → ∀ (f : α → β), (f '' s).Countable- Defined in
- Mathlib.Data.Set.Countable
- Cited by
- 47 results in Mathlib
- Foundations
- Depth 14 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.Elemproof · cited by 7,166
- Set.imagestatement · cited by 5,609
- Countableproof · cited by 633
- Set.Countablestatement and proof · cited by 545
- Set.image_eq_rangeproof · cited by 57
- Set.Countable.to_subtypeproof · cited by 33
- Set.countable_rangeproof · cited by 31
Cited by47
Results whose statement or proof uses this declaration.
- TopologicalSpace.exists_countable_basisproof · cited by 9
- MeasurableSet.image_of_monotoneOnproof · cited by 4
- TopologicalSpace.countable_cover_nhdsWithinproof · cited by 3
- IsLindelof.elim_nhds_subcoverproof · cited by 3
- isMeagre_iff_countable_union_isNowhereDenseproof · cited by 3
- TopologicalSpace.IsSeparable.imageproof · cited by 3
- MeasureTheory.lintegral_image_eq_lintegral_deriv_mul_of_monotoneOnproof · cited by 3
- Dense.exists_countable_dense_subsetproof · cited by 2
- MeasureTheory.integral_image_eq_integral_deriv_smul_of_monotoneOnproof · cited by 2
- stronglyMeasurable_derivWithin_Iciproof · cited by 2
- TopologicalSpace.isOpen_biUnion_countableproof · cited by 2