Theorems · Theorem · order theory
iUnion_disjointed
∀ {α : Type u_1} {ι : Type u_2} [inst : PartialOrder ι] [inst_1 : LocallyFiniteOrderBot ι] {f : ι → Set α},
⋃ i, disjointed f i = ⋃ i, f i- Defined in
- Mathlib.Order.Disjointed
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- PartialOrderstatement and proof · cited by 6,410
- Set.iUnionstatement · cited by 2,483
- LocallyFiniteOrderBotstatement and proof · cited by 286
- disjointedstatement · cited by 64
- iSup_disjointedproof · cited by 2
Cited by16
Results whose statement or proof uses this declaration.
- MeasureTheory.measure_iUnion_leproof · cited by 39
- exists_partition_approximatesLinearOn_of_hasFDerivWithinAtproof · cited by 5
- Directed.measure_iUnionproof · cited by 5
- MeasureTheory.VectorMeasure.tendsto_vectorMeasure_iUnion_atTop_natproof · cited by 3
- MeasureTheory.VectorMeasure.restrict_le_restrict_iUnionproof · cited by 3
- MeasureTheory.extend_iUnion_le_tsum_natproof · cited by 1
- MeasureTheory.lintegral_abs_det_fderiv_le_addHaar_imageproof · cited by 1
- MeasureTheory.OuterMeasure.isCaratheodory_iUnionproof · cited by 1
- MeasureTheory.Measure.measure_isHaarMeasure_eq_smul_of_isEverywherePosproof · cited by 1
- MeasureTheory.Measure.measure_toMeasurable_inter_of_coverproof · cited by 1
- MeasureTheory.SeparableSpace.exists_measurable_partition_diam_leproof · cited by 1