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Theorems · Theorem · order theory

Set.iUnion_empty

∀ {α : Type u_1} {ι : Sort u_5}, ⋃ x, ∅ = ∅
Defined in
Mathlib.Data.Set.Lattice
Cited by
68 results in Mathlib
Foundations
Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MeasureTheory.Measure.haar.index_pos · cited by 5haar.index_posIsCompactOpenCovered.iff_of_unique · cited by 5IsCompactOpenCovered.iff_…MeasureTheory.IsSetRing.biUnion_mem · cited by 5IsSetRing.biUnion_memMeasureTheory.Measure.haar.addIndex_pos · cited by 5haar.addIndex_posAddSubgroup.leftCoset_cover_filter_FiniteIndex_aux · cited by 3AddSubgroup.leftCoset_cov…MeasureTheory.integral_biUnion_finset · cited by 3MeasureTheory.integral_bi…Metric.AreSeparated.finite_iUnion_left_iff · cited by 3AreSeparated.finite_iUnio…Subgroup.leftCoset_cover_filter_FiniteIndex_aux · cited by 3Subgroup.leftCoset_cover_…nhdsWithin_biUnion · cited by 2nhdsWithin_biUnionEncodable.iUnion_decode₂_cases · cited by 2Encodable.iUnion_decode₂_…AlgebraicGeometry.Scheme.zeroLocus_biInf · cited by 2Scheme.zeroLocus_biInfIsCompact.uniform_oscillationWithin · cited by 2IsCompact.uniform_oscilla…Metric.ediam_iUnion_mem_option · cited by 2Metric.ediam_iUnion_mem_o…Besicovitch.exist_disjoint_covering_families · cited by 2Besicovitch.exist_disjoin…IsLindelof.indexed_countable_subcover · cited by 2IsLindelof.indexed_counta…Set · cited by 53352SetSet.iUnion · cited by 2483Set.iUnioniSup_bot · cited by 29iSup_botSet.iUnion_emptyCITED BYCITES

Cites3

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by68

Results whose statement or proof uses this declaration.