Theorems · Definition · real analysis
BoxIntegral.Prepartition.split
{ι : Type u_1} → (I : BoxIntegral.Box ι) → ι → ℝ → BoxIntegral.Prepartition IThe partition of I : Box ι into the boxes I ∩ {y | y ≤ x i} and I ∩ {y | x i < y}.
One of these boxes can be empty, then this partition is just the single-box partition ⊤.
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 131 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.
- Realstatement and proof · cited by 25,697
- BoxIntegral.Boxstatement and proof · cited by 464
- BoxIntegral.Prepartitionstatement · cited by 199
- BoxIntegral.Box.splitLowerproof · cited by 11
- BoxIntegral.Box.splitUpperproof · cited by 11
- BoxIntegral.Prepartition.ofWithBotproof · cited by 7
Cited by15
Results whose statement or proof uses this declaration.
- BoxIntegral.Prepartition.splitManyproof · cited by 13
- BoxIntegral.Prepartition.isPartitionSplitstatement · cited by 3
- BoxIntegral.Prepartition.inf_splitstatement · cited by 2
- BoxIntegral.Prepartition.splitMany_insertstatement and proof · cited by 2
- BoxIntegral.Prepartition.mem_split_iff'statement · cited by 2
- BoxIntegral.Prepartition.iUnion_splitstatement · cited by 1
- BoxIntegral.Prepartition.restrict_splitstatement and proof · cited by 1
- BoxIntegral.Prepartition.inf_splitManyproof · cited by 1
- BoxIntegral.Prepartition.coe_eq_of_mem_split_of_lt_memstatement and proof · cited by 1
- BoxIntegral.Prepartition.coe_eq_of_mem_split_of_mem_lestatement and proof · cited by 1
- BoxIntegral.Prepartition.splitMany_le_splitstatement · cited by 1
- BoxIntegral.Prepartition.sum_split_boxesstatement · cited by 1