Theorems · Theorem · order theory
Set.monotone_accumulate
∀ {α : Type u_1} {β : Type u_2} {s : α → Set β} [inst : Preorder α], Monotone (Set.accumulate s)- Defined in
- Mathlib.Order.SetAccumulate
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 63 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.
Cites6
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
- Monotonestatement · cited by 1,397
- le_transproof · cited by 985
- Set.accumulatestatement · cited by 32
- Set.biUnion_subset_biUnion_leftproof · cited by 18
Cited by10
Results whose statement or proof uses this declaration.
- MeasureTheory.monotone_spanningSetsproof · cited by 8
- MeasureTheory.exists_measure_symmDiff_lt_of_generateFrom_isSetRingproof · cited by 2
- MeasureTheory.addContent_iUnion_eq_sum_of_tendsto_zeroproof · cited by 2
- Set.accumulate_subset_accumulateproof · cited by 1
- MeasureTheory.measure_iUnion_eq_iSup_accumulateproof · cited by 1
- compactCovering_subsetproof · cited by 1
- Set.directed_accumulateproof · cited by 0
- MeasureTheory.Measure.InnerRegularWRT.isCompact_isClosedproof · cited by 0
- MeasureTheory.addContent_iUnion_eq_tsum_of_addContent_iUnion_eq_iSupproof · cited by 0
- Set.biUnion_accumulateproof · cited by 0