Theorems · Theorem · real analysis

BoxIntegral.TaggedPrepartition.isSubordinate_biUnionTagged

∀ {ι : Type u_1} {I : BoxIntegral.Box ι} {r : (ι → ℝ) → ↑(Set.Ioi 0)} [inst : Fintype ι]
  {π : BoxIntegral.Prepartition I} {πi : (J : BoxIntegral.Box ι) → BoxIntegral.TaggedPrepartition J},
  (π.biUnionTagged πi).IsSubordinate r ↔ ∀ J ∈ π, (πi J).IsSubordinate r

Defined in: Mathlib.Analysis.BoxIntegral.Partition.Tagged
Cited by: 3 results in Mathlib
Foundations: Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Fintype

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Cites13

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

DFunLike.coeproof · cited by 62,936
Realstatement and proof · cited by 25,697
Fintypestatement and proof · cited by 7,736
Set.Elemstatement and proof · cited by 7,166
Set.Ioistatement and proof · cited by 1,463
Metric.closedBallproof · cited by 704
BoxIntegral.Boxstatement and proof · cited by 464
BoxIntegral.Prepartitionstatement and proof · cited by 199
BoxIntegral.TaggedPrepartitionstatement and proof · cited by 126
BoxIntegral.Box.Iccproof · cited by 76
BoxIntegral.TaggedPrepartition.IsSubordinatestatement · cited by 15
BoxIntegral.Prepartition.biUnionTaggedstatement · cited by 13

Cited by3

Results whose statement or proof uses this declaration.

BoxIntegral.Prepartition.exists_tagged_le_isHenstock_isSubordinate_iUnion_eqproof · cited by 6
BoxIntegral.IntegrationParams.biUnionTagged_memBaseSetproof · cited by 1
BoxIntegral.Box.exists_taggedPartition_isHenstock_isSubordinate_homotheticproof · cited by 1