Theorems · Theorem · order theory

StrictAntiOn.mapsTo_Ioc

∀ {α : Type u_1} {β : Type u_2} {f : α → β} [inst : PartialOrder α] [inst_1 : Preorder β] {a b : α},
  StrictAntiOn f (Set.Icc a b) → Set.MapsTo f (Set.Ioc a b) (Set.Ico (f b) (f a))

Defined in

Mathlib.Order.Interval.Set.Image

Cited by

2 results in Mathlib

Foundations

Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PartialOrderPreorder