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Theorems · Theorem · order theory

Monotone.Iic

∀ {α : Type u_1} {β : Type u_2} [inst : Preorder α] [inst_1 : Preorder β] {f : α → β},
  Monotone f → Monotone fun x => Set.Iic (f x)
Defined in
Mathlib.Order.Interval.Set.Monotone
Cited by
6 results in Mathlib
Foundations
Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PreorderPreorder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Filter.HasBasis.nhds · cited by 4HasBasis.nhdsMeasureTheory.Measure.tendsto_IicSnd_atTop · cited by 1Measure.tendsto_IicSnd_at…Filter.sInter_nhds · cited by 1Filter.sInter_nhdsAntitone.Ioc · cited by 0Antitone.IocFilter.nhds_bot · cited by 0Filter.nhds_botAntitone.Icc · cited by 0Antitone.IccSet · cited by 53352SetPreorder · cited by 7952PreorderMonotone · cited by 1397MonotoneSet.Iic · cited by 1111Set.IicMonotone.comp · cited by 67Monotone.compmonotone_Iic · cited by 5monotone_IicMonotone.IicCITED BYCITES

Cites6

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Cited by6

Results whose statement or proof uses this declaration.