Theorems · Theorem · real analysis
BoxIntegral.BoxAdditiveMap.sum_partition_boxes
∀ {ι : Type u_1} {M : Type u_2} [inst : AddCommMonoid M] {I₀ : WithTop (BoxIntegral.Box ι)} {I : BoxIntegral.Box ι}
(f : BoxIntegral.BoxAdditiveMap ι M I₀),
↑I ≤ I₀ → ∀ {π : BoxIntegral.Prepartition I}, π.IsPartition → ∑ J ∈ π.boxes, f J = f I- Cited by
- 5 results in Mathlib
- Foundations
- Depth 127 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoid
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.
- DFunLike.coestatement · cited by 62,936
- AddCommMonoidstatement and proof · cited by 12,281
- Finset.sumstatement · cited by 5,195
- WithTopstatement and proof · cited by 3,754
- WithTop.somestatement and proof · cited by 1,128
- BoxIntegral.Boxstatement and proof · cited by 464
- BoxIntegral.Prepartitionstatement and proof · cited by 199
- BoxIntegral.BoxAdditiveMapstatement and proof · cited by 92
- BoxIntegral.Prepartition.boxesstatement · cited by 77
- BoxIntegral.Prepartition.IsPartitionstatement and proof · cited by 30
- BoxIntegral.BoxAdditiveMap.sum_partition_boxes'proof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- BoxIntegral.hasIntegral_constproof · cited by 3
- BoxIntegral.HasIntegral.of_bRiemann_eq_false_of_forall_isLittleOproof · cited by 2
- BoxIntegral.integralSum_biUnion_partitionproof · cited by 1
- BoxIntegral.BoxAdditiveMap.map_split_addproof · cited by 0
- BoxIntegral.BoxAdditiveMap.sum_boxes_congrproof · cited by 0