Theorems · Theorem · order theory
Set.preimage_singleton_eq_empty
∀ {α : Type u_1} {β : Type u_2} {f : α → β} {y : β}, f ⁻¹' {y} = ∅ ↔ y ∉ Set.range f- Defined in
- Mathlib.Data.Set.Image
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.preimagestatement · cited by 4,946
- Set.rangestatement · cited by 4,705
- Iff.notproof · cited by 489
- Set.not_nonempty_iff_eq_emptyproof · cited by 56
- Set.preimage_singleton_nonemptyproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- measurable_to_countableproof · cited by 6
- MeasureTheory.setToFun_of_le_map_of_stronglyMeasurableproof · cited by 2
- MeasureTheory.SimpleFunc.preimage_eq_empty_iffproof · cited by 0
- MvPowerSeries.coeff_rename_eq_zeroproof · cited by 0
- Filter.TendstoCofinite.mapDomain_eq_zeroproof · cited by 0