Theorems · Theorem · logic and foundations
Set.Countable.preimage
∀ {α : Type u} {β : Type v} {s : Set β}, s.Countable → ∀ {f : α → β}, Function.Injective f → (f ⁻¹' s).Countable- Defined in
- Mathlib.Data.Set.Countable
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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.preimagestatement · cited by 4,946
- Set.Countablestatement and proof · cited by 545
- Function.Injective.injOnproof · cited by 280
- Set.Countable.preimage_of_injOnproof · cited by 1
Cited by7
Results whose statement or proof uses this declaration.
- Complex.integral_boundary_rect_of_hasFDerivAt_real_off_countableproof · cited by 3
- MeasureTheory.integral_divergence_of_hasFDerivAt_off_countable_of_equivproof · cited by 2
- IsOpenMap.separableSpace_of_injectiveproof · cited by 1
- FirstOrder.Language.Substructure.CG.of_map_embeddingproof · cited by 1
- Set.Countable.preimage_circleMapproof · cited by 1