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Theorems · Definition · real analysis

BoxIntegral.Prepartition.splitMany

{ι : Type u_1} → (I : BoxIntegral.Box ι) → Finset (ι × ℝ) → BoxIntegral.Prepartition I

Split a box along many hyperplanes {y | y i = x}; each hyperplane is given by the pair (i x).

Defined in
Mathlib.Analysis.BoxIntegral.Partition.Split
Cited by
13 results in Mathlib
Foundations
Depth 138 from the axioms · uses propext, Classical.choice, Quot.sound

Around this declaration

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

BoxIntegral.Prepartition.eventually_splitMany_inf_eq_filter · cited by 3Prepartition.eventually_s…BoxIntegral.Prepartition.exists_iUnion_eq_sdiff · cited by 3Prepartition.exists_iUnio…BoxIntegral.Prepartition.splitMany_insert · cited by 2Prepartition.splitMany_in…BoxIntegral.Prepartition.isPartition_splitMany · cited by 2Prepartition.isPartition_…BoxIntegral.Prepartition.iUnion_splitMany · cited by 1Prepartition.iUnion_split…BoxIntegral.Prepartition.inf_splitMany · cited by 1Prepartition.inf_splitManyBoxIntegral.Prepartition.splitMany_le_split · cited by 1Prepartition.splitMany_le…BoxIntegral.Prepartition.eventually_not_disjoint_imp_le_of_mem_splitMany · cited by 1Prepartition.eventually_n…BoxIntegral.Prepartition.exists_splitMany_inf_eq_filter_of_finite · cited by 1Prepartition.exists_split…BoxIntegral.Prepartition.not_disjoint_imp_le_of_subset_of_mem_splitMany · cited by 1Prepartition.not_disjoint…BoxIntegral.Prepartition.splitMany_empty · cited by 0Prepartition.splitMany_em…BoxIntegral.BoxAdditiveMap.sum_boxes_congr · cited by 0BoxAdditiveMap.sum_boxes_…BoxIntegral.Prepartition.IsPartition.exists_splitMany_le · cited by 0IsPartition.exists_splitM…Real · cited by 25697RealFinset · cited by 13712FinsetBoxIntegral.Box · cited by 464BoxIntegral.BoxFinset.inf · cited by 219Finset.infBoxIntegral.Prepartition · cited by 199BoxIntegral.PrepartitionBoxIntegral.Prepartition.split · cited by 14Prepartition.splitPrepartition.splitManyCITED BYCITES

Cites6

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

Cited by13

Results whose statement or proof uses this declaration.