Theorems · Theorem · order theory
Set.iUnion_of_empty
∀ {α : Type u_1} {ι : Sort u_5} [IsEmpty ι] (s : ι → Set α), ⋃ i, s i = ∅- Defined in
- Mathlib.Data.Set.Lattice
- Cited by
- 68 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- IsEmpty
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 and proof · cited by 53,352
- Set.iUnionstatement · cited by 2,483
- IsEmptystatement and proof · cited by 759
- iSup_of_emptyproof · cited by 5
Cited by68
Results whose statement or proof uses this declaration.
- MeasurableSet.iUnionproof · cited by 81
- Monotone.measure_iUnionproof · cited by 10
- MeasureTheory.Measure.haar.index_posproof · cited by 5
- IsCompactOpenCovered.iff_of_uniqueproof · cited by 5
- MeasureTheory.IsSetRing.biUnion_memproof · cited by 5
- MeasureTheory.Measure.haar.addIndex_posproof · cited by 5
- AddSubgroup.leftCoset_cover_filter_FiniteIndex_auxproof · cited by 3
- MeasureTheory.integral_biUnion_finsetproof · cited by 3
- Metric.AreSeparated.finite_iUnion_left_iffproof · cited by 3
- Subgroup.leftCoset_cover_filter_FiniteIndex_auxproof · cited by 3
- IsClosedMap.isEvenlyCovered_of_openPartialHomeomorphproof · cited by 2
- isSigmaCompact_iUnion_of_isCompactproof · cited by 2