Theorems · Theorem · order theory
Set.preimage_singleton_nonempty
∀ {α : Type u_1} {β : Type u_2} {f : α → β} {y : β}, (f ⁻¹' {y}).Nonempty ↔ y ∈ Set.range f- Defined in
- Mathlib.Data.Set.Image
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 5 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 · cited by 53,352
- Set.preimagestatement · cited by 4,946
- Set.rangestatement · cited by 4,705
- Set.Nonemptystatement · cited by 2,627
Cited by2
Results whose statement or proof uses this declaration.
- Set.preimage_singleton_eq_emptyproof · cited by 5
- MeasureTheory.SimpleFunc.lintegral_eq_of_subsetproof · cited by 3