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Theorems · Theorem · order theory

Antitone.Iio

∀ {α : Type u_1} {β : Type u_2} [inst : Preorder α] [inst_1 : Preorder β] {f : α → β},
  Antitone f → Antitone fun x => Set.Iio (f x)
Defined in
Mathlib.Order.Interval.Set.Monotone
Cited by
2 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.

Monotone.Ioo · cited by 0Monotone.IooMonotone.Ico · cited by 0Monotone.IcoSet · cited by 53352SetPreorder · cited by 7952PreorderSet.Iio · cited by 1166Set.IioAntitone · cited by 563AntitoneMonotone.comp_antitone · cited by 16Monotone.comp_antitonemonotone_Iio · cited by 4monotone_IioAntitone.IioCITED BYCITES

Cites6

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Cited by2

Results whose statement or proof uses this declaration.