Theorems · Theorem · order theory
Set.preimage_eq_empty
∀ {α : Type u_1} {β : Type u_2} {f : α → β} {s : Set β}, Disjoint s (Set.range f) → f ⁻¹' s = ∅- Defined in
- Mathlib.Data.Set.Image
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 58 from the axioms · uses propext, Classical.choice, 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 and proof · cited by 53,352
- Set.preimagestatement and proof · cited by 4,946
- Set.rangestatement and proof · cited by 4,705
- Disjointstatement and proof · cited by 2,201
- Set.preimage_rangeproof · cited by 38
- Disjoint.preimageproof · cited by 22
Cited by3
Results whose statement or proof uses this declaration.
- MeasureTheory.SimpleFunc.integral_eq_sum_of_subsetproof · cited by 3
- Set.preimage_eq_empty_iffproof · cited by 1
- MeasureTheory.SimpleFunc.setToSimpleFunc_eq_sum_of_subsetproof · cited by 1