Theorems · Theorem · order theory
Set.iUnion_singleton_eq_range
∀ {α : Type u_1} {β : Type u_2} (f : α → β), ⋃ x, {f x} = Set.range f- Defined in
- Mathlib.Data.Set.Lattice
- Cited by
- 26 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses propext, Quot.sound
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.rangestatement · cited by 4,705
- Set.iUnionstatement · cited by 2,483
- Set.extproof · cited by 2,266
Cited by26
Results whose statement or proof uses this declaration.
- PrimeSpectrum.iSup_basicOpen_eq_top_iffproof · cited by 6
- Set.iUnion_of_singleton_coeproof · cited by 6
- MeasureTheory.Measure.hausdorffMeasure_zero_singletonproof · cited by 5
- AlgebraicGeometry.IsAffineOpen.iSup_basicOpen_eq_self_iffproof · cited by 2
- range_vecMulLinearproof · cited by 2
- MeasureTheory.measure_preimage_snd_singleton_eq_tsumproof · cited by 1
- Real.isPiSystem_Iic_ratproof · cited by 1
- MeasureTheory.Measure.addHaar_eq_zero_of_disjoint_translates_auxproof · cited by 1
- IsOpenMap.enatCard_connectedComponents_le_encard_preimage_singletonproof · cited by 1
- ProbabilityTheory.eq_condKernel_of_measure_eq_compProd_realproof · cited by 1
- Real.borel_eq_generateFrom_Iic_ratproof · cited by 1
- ENat.measurable_iffproof · cited by 1