Theorems · Theorem · real analysis
BoxIntegral.Prepartition.biUnion_le_iff
∀ {ι : Type u_1} {I : BoxIntegral.Box ι} (π : BoxIntegral.Prepartition I)
{πi : (J : BoxIntegral.Box ι) → BoxIntegral.Prepartition J} {π' : BoxIntegral.Prepartition I},
π.biUnion πi ≤ π' ↔ ∀ J ∈ π, πi J ≤ π'.restrict J- Cited by
- 1 results in Mathlib
- Foundations
- Depth 135 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LE.le.transproof · cited by 3,151
- WithBot.someproof · cited by 541
- BoxIntegral.Boxstatement and proof · cited by 464
- inf_le_rightproof · cited by 238
- BoxIntegral.Prepartitionstatement and proof · cited by 199
- Eq.trans_leproof · cited by 155
- WithBot.coe_le_coeproof · cited by 76
- BoxIntegral.Prepartition.biUnionstatement and proof · cited by 24
- BoxIntegral.Prepartition.restrictstatement and proof · cited by 16
- BoxIntegral.Prepartition.mem_biUnionproof · cited by 9
- BoxIntegral.Prepartition.restrict_monoproof · cited by 3
- BoxIntegral.Prepartition.mem_restrictproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- BoxIntegral.Prepartition.eventually_splitMany_inf_eq_filterproof · cited by 3