Theorems · Theorem · order theory
Set.iUnion_accumulate
∀ {α : Type u_1} {β : Type u_2} {s : α → Set β} [inst : Preorder α], ⋃ x, Set.accumulate s x = ⋃ x, s x- Defined in
- Mathlib.Order.SetAccumulate
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Preorderstatement and proof · cited by 7,952
- Set.iUnionstatement · cited by 2,483
- Set.Subset.antisymmproof · cited by 213
- Set.accumulatestatement · cited by 32
- Set.iUnion_monoproof · cited by 21
- Set.subset_accumulateproof · cited by 3
Cited by7
Results whose statement or proof uses this declaration.
- MeasureTheory.iUnion_spanningSetsproof · cited by 19
- iUnion_compactCoveringproof · cited by 5
- MeasureTheory.exists_measure_symmDiff_lt_of_generateFrom_isSetRingproof · cited by 2
- MeasureTheory.addContent_iUnion_eq_sum_of_tendsto_zeroproof · cited by 2
- MeasureTheory.measure_iUnion_eq_iSup_accumulateproof · cited by 1
- MeasureTheory.addContent_iUnion_eq_tsum_of_addContent_iUnion_eq_iSupproof · cited by 0