Theorems · Theorem · real analysis
BoxIntegral.IntegrationParams.hasBasis_toFilteriUnion_top
∀ {ι : Type u_1} [inst : Fintype ι] (l : BoxIntegral.IntegrationParams) (I : BoxIntegral.Box ι),
(BoxIntegral.IntegrationParams.toFilteriUnion I ⊤).HasBasis (fun r => ∀ (c : NNReal), l.RCond (r c)) fun r =>
{π | ∃ c, l.MemBaseSet I c (r c) π ∧ π.IsPartition}- Cited by
- 3 results in Mathlib
- Foundations
- Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Top.topstatement and proof · cited by 9,680
- Fintypestatement and proof · cited by 7,736
- Set.Elemstatement and proof · cited by 7,166
- Set.ofPredstatement and proof · cited by 6,101
- NNRealstatement and proof · cited by 4,310
- Set.Ioistatement and proof · cited by 1,463
- Filter.HasBasisstatement and proof · cited by 604
- BoxIntegral.Boxstatement and proof · cited by 464
- BoxIntegral.Prepartitionstatement · cited by 199
- BoxIntegral.TaggedPrepartitionstatement and proof · cited by 126
- BoxIntegral.IntegrationParamsstatement and proof · cited by 101
Cited by3
Results whose statement or proof uses this declaration.
- BoxIntegral.hasIntegral_iffproof · cited by 5
- BoxIntegral.HasIntegral.of_bRiemann_eq_false_of_forall_isLittleOproof · cited by 2
- BoxIntegral.integrable_iff_cauchy_basisproof · cited by 1