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Theorems · Theorem · order theory

Set.iUnion_true

∀ {α : Type u_1} {s : True → Set α}, Set.iUnion s = s trivial
Defined in
Mathlib.Data.Set.Lattice
Cited by
42 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_iUnion_fintype_le · cited by 3MeasureTheory.measure_iUn…AddMonoidHom.isOpenQuotientMap_of_isQuotientMap · cited by 3AddMonoidHom.isOpenQuotie…AddSubgroup.leftCoset_cover_filter_FiniteIndex_aux · cited by 3AddSubgroup.leftCoset_cov…Subgroup.leftCoset_cover_filter_FiniteIndex_aux · cited by 3Subgroup.leftCoset_cover_…Topology.RelCWComplex.skeletonLT_top · cited by 2RelCWComplex.skeletonLT_t…SimpleGraph.coe_finsetWalkLength_eq · cited by 2SimpleGraph.coe_finsetWal…Module.Finite.of_isLocalized_maximal · cited by 2Finite.of_isLocalized_max…ProbabilityTheory.Kernel.densityProcess_fst_univ_ae · cited by 2Kernel.densityProcess_fst…MeasureTheory.addContent_iUnion · cited by 2MeasureTheory.addContent_…Submodule.span_attach_biUnion · cited by 2Submodule.span_attach_biU…Algebra.adjoin_attach_biUnion · cited by 1Algebra.adjoin_attach_biU…StieltjesFunction.length_subadditive_Icc_Ioo · cited by 1StieltjesFunction.length_…Topology.RelCWComplex.union_iUnion_openCell_eq_complex · cited by 1RelCWComplex.union_iUnion…MeasureTheory.VectorMeasure.setIntegral_iUnion_fintype · cited by 1VectorMeasure.setIntegral…MonoidHom.isOpenQuotientMap_of_isQuotientMap · cited by 1MonoidHom.isOpenQuotientM…Set · cited by 53352SetSet.iUnion · cited by 2483Set.iUnioniSup_true · cited by 2iSup_trueSet.iUnion_trueCITED BYCITES

Cites3

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Cited by42

Results whose statement or proof uses this declaration.