Theorems · Theorem · measure theory
MeasureTheory.IsSetSemiring.sUnion_union_sUnion_disjointOfDiffUnion_of_subset
∀ {α : Type u_1} {C : Set (Set α)} {s : Set α} {I : Finset (Set α)} (hC : MeasureTheory.IsSetSemiring C) (hs : s ∈ C)
(hI : ↑I ⊆ C), (∀ t ∈ I, t ⊆ s) → ⋃₀ ↑I ∪ ⋃₀ ↑(hC.disjointOfDiffUnion hs hI) = s- Defined in
- Mathlib.MeasureTheory.SetSemiring
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Finsetstatement and proof · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- Set.sUnionstatement and proof · cited by 392
- MeasureTheory.IsSetSemiringstatement and proof · cited by 78
- Set.union_sdiff_cancelproof · cited by 16
- MeasureTheory.IsSetSemiring.disjointOfDiffUnionstatement and proof · cited by 16
- Set.sUnion_subsetproof · cited by 9
- MeasureTheory.IsSetSemiring.sdiff_sUnion_eq_sUnion_disjointOfDiffUnionproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.IsSetSemiring.sUnion_union_disjointOfDiffUnion_of_subsetproof · cited by 1