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Theorems · Theorem · order theory

Monotone.Iio

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

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

Antitone.Ioo · cited by 1Antitone.IooiUnion_Ioo_of_mono_of_isGLB_of_isLUB · cited by 1iUnion_Ioo_of_mono_of_isG…Antitone.Ico · cited by 1Antitone.IcoSet · cited by 53352SetPreorder · cited by 7952PreorderMonotone · cited by 1397MonotoneSet.Iio · cited by 1166Set.IioMonotone.comp · cited by 67Monotone.compmonotone_Iio · cited by 4monotone_IioMonotone.IioCITED BYCITES

Cites6

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Cited by3

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