Theorems · Theorem · real analysis
BoxIntegral.BoxAdditiveMap.map_split_add
∀ {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 → ∀ (i : ι) (x : ℝ), Option.elim' 0 (⇑f) (I.splitLower i x) + Option.elim' 0 (⇑f) (I.splitUpper i x) = f I- Cited by
- 0 results in Mathlib
- Foundations
- Depth 134 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoid
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- AddCommMonoidstatement and proof · cited by 12,281
- WithTopstatement and proof · cited by 3,754
- WithTop.somestatement and proof · cited by 1,128
- BoxIntegral.Boxstatement and proof · cited by 464
- BoxIntegral.BoxAdditiveMapstatement and proof · cited by 92
- Option.elim'statement and proof · cited by 30
- BoxIntegral.Box.splitLowerstatement and proof · cited by 11
- BoxIntegral.Box.splitUpperstatement and proof · cited by 11
- BoxIntegral.BoxAdditiveMap.sum_partition_boxesproof · cited by 5
- BoxIntegral.Prepartition.isPartitionSplitproof · cited by 3
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