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Theorems · Theorem · logic and foundations

Set.inter_union_distrib_left

∀ {α : Type u} (s t u : Set α), s ∩ (t ∪ u) = s ∩ t ∪ s ∩ u
Defined in
Mathlib.Data.Set.Basic
Cited by
39 results in Mathlib
Foundations
Depth 21 from the axioms · uses propext, Quot.sound
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Dashed lines are statement dependencies; solid lines are citations in proofs.

frontier_inter_subset · cited by 4frontier_inter_subsetMeasureTheory.IsStoppingTime.measurableSpace_min · cited by 4IsStoppingTime.measurable…Convex.sdiff_singleton_eventually_mem_nhds · cited by 3Convex.sdiff_singleton_ev…MeasureTheory.Measure.restrict_union_le · cited by 3Measure.restrict_union_leContinuousOn.if' · cited by 3ContinuousOn.if'Topology.RelCWComplex.skeletonLT_inter_closedCell_eq_skeletonLT_inter_cellFrontier · cited by 2RelCWComplex.skeletonLT_i…measure_eq_measure_preimage_add_measure_tsum_Ico_zpow · cited by 2measure_eq_measure_preima…eVariationOn.Icc_add_Icc · cited by 2eVariationOn.Icc_add_IccSet.sep_or · cited by 2Set.sep_orTopologicalSpace.vietoris.isTopologicalBasis · cited by 2vietoris.isTopologicalBas…Topology.RelCWComplex.isClosed_inter_cellFrontier_succ_of_le_isClosed_inter_closedCell · cited by 2RelCWComplex.isClosed_int…Topology.RelCWComplex.isClosed_of_isClosed_inter_openCell_or_isClosed_inter_closedCell · cited by 2RelCWComplex.isClosed_of_…Convex.nhdsWithin_sdiff_eq_nhdsGT · cited by 2Convex.nhdsWithin_sdiff_e…Convex.nhdsWithin_sdiff_eq_nhdsLT · cited by 2Convex.nhdsWithin_sdiff_e…Convex.nhdsWithin_sdiff_eq_nhdsNE · cited by 2Convex.nhdsWithin_sdiff_e…Set · cited by 53352Setinf_sup_left · cited by 28inf_sup_leftSet.inter_union_distrib_leftCITED BYCITES

Cites2

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Cited by39

Results whose statement or proof uses this declaration.