Theorems · Theorem · real analysis
BoxIntegral.Prepartition.le_iff_nonempty_imp_le_and_iUnion_subset
∀ {ι : Type u_1} {I : BoxIntegral.Box ι} {π₁ π₂ : BoxIntegral.Prepartition I},
π₁ ≤ π₂ ↔ (∀ J ∈ π₁, ∀ J' ∈ π₂, (↑J ∩ ↑J').Nonempty → J ≤ J') ∧ π₁.iUnion ⊆ π₂.iUnion- Cited by
- 2 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- Set.Nonemptystatement and proof · cited by 2,627
- BoxIntegral.Boxstatement and proof · cited by 464
- BoxIntegral.Prepartitionstatement and proof · cited by 199
- BoxIntegral.Box.toSetstatement and proof · cited by 121
- BoxIntegral.Prepartition.iUnionstatement and proof · cited by 71
- BoxIntegral.Box.upperproof · cited by 70
- BoxIntegral.Box.upper_memproof · cited by 7
- BoxIntegral.Prepartition.eq_of_mem_of_memproof · cited by 6
- BoxIntegral.Prepartition.iUnion_monoproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- BoxIntegral.Prepartition.eq_of_boxes_subset_iUnion_supersetproof · cited by 2
- BoxIntegral.Prepartition.IsPartition.le_iffproof · cited by 0