Theorems · Theorem · real analysis
BoxIntegral.Prepartition.IsPartition.le_iff
∀ {ι : Type u_1} {I : BoxIntegral.Box ι} {π₁ π₂ : BoxIntegral.Prepartition I},
π₂.IsPartition → (π₁ ≤ π₂ ↔ ∀ J ∈ π₁, ∀ J' ∈ π₂, (↑J ∩ ↑J').Nonempty → J ≤ J')- Cited by
- 0 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement · cited by 25,697
- Set.Nonemptystatement · cited by 2,627
- BoxIntegral.Boxstatement and proof · cited by 464
- BoxIntegral.Prepartitionstatement and proof · cited by 199
- BoxIntegral.Box.toSetstatement · cited by 121
- BoxIntegral.Prepartition.IsPartitionstatement and proof · cited by 30
- BoxIntegral.Prepartition.IsPartition.iUnion_subsetproof · cited by 2
- BoxIntegral.Prepartition.le_iff_nonempty_imp_le_and_iUnion_subsetproof · cited by 2
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