Theorems · Theorem · real analysis
BoxIntegral.Box.mem_splitCenterBox
∀ {ι : Type u_1} {I : BoxIntegral.Box ι} {s : Set ι} {y : ι → ℝ},
y ∈ I.splitCenterBox s ↔ y ∈ I ∧ ∀ (i : ι), (I.lower i + I.upper i) / 2 < y i ↔ i ∈ s- Cited by
- 3 results in Mathlib
- Foundations
- Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- Realstatement and proof · cited by 25,697
- LE.le.transproof · cited by 3,151
- LT.lt.leproof · cited by 2,189
- Set.Iocproof · cited by 971
- BoxIntegral.Boxstatement and proof · cited by 464
- LT.lt.transproof · cited by 370
- Set.piecewiseproof · cited by 136
- BoxIntegral.Box.upperstatement and proof · cited by 70
- BoxIntegral.Box.lowerstatement and proof · cited by 65
- BoxIntegral.Box.lower_lt_upperproof · cited by 13
- BoxIntegral.Box.splitCenterBoxstatement · cited by 12
Cited by3
Results whose statement or proof uses this declaration.
- BoxIntegral.Box.splitCenterBox_leproof · cited by 2
- BoxIntegral.Box.disjoint_splitCenterBoxproof · cited by 1
- BoxIntegral.Box.exists_mem_splitCenterBoxproof · cited by 0