Theorems · Definition · real analysis
BoxIntegral.Prepartition.compl
{ι : Type u_1} → {I : BoxIntegral.Box ι} → [Finite ι] → BoxIntegral.Prepartition I → BoxIntegral.Prepartition IIf π is a prepartition of I, then π.compl is a prepartition of I
such that π.compl.iUnion = I \ π.iUnion.
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 144 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Finite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finitestatement and proof · cited by 3,029
- BoxIntegral.Boxstatement and proof · cited by 464
- BoxIntegral.Prepartitionstatement and proof · cited by 199
- BoxIntegral.Prepartition.exists_iUnion_eq_sdiffproof · cited by 3
Cited by12
Results whose statement or proof uses this declaration.
- BoxIntegral.Prepartition.iUnion_complstatement · cited by 5
- BoxIntegral.IntegrationParams.exists_memBaseSet_le_iUnion_eqstatement and proof · cited by 2
- BoxIntegral.IntegrationParams.tendsto_embedBox_toFilteriUnion_topproof · cited by 1
- BoxIntegral.IntegrationParams.biUnionTagged_memBaseSetstatement and proof · cited by 1
- BoxIntegral.Prepartition.compl_congrstatement · cited by 1
- BoxIntegral.Prepartition.compl_topstatement · cited by 1
- BoxIntegral.IntegrationParams.exists_memBaseSet_isPartitionproof · cited by 1
- BoxIntegral.Prepartition.IsPartition.compl_eq_botstatement · cited by 1
- BoxIntegral.IntegrationParams.MemBaseSet.exists_common_complproof · cited by 1
- BoxIntegral.Prepartition.compl.congr_simpstatement and proof · cited by 0
- BoxIntegral.IntegrationParams.toFilterDistortioniUnion_neBotstatement and proof · cited by 0