Theorems · Theorem · order theory

MonotoneOn.mapsTo_uIcc

∀ {α : Type u_1} {β : Type u_2} [inst : LinearOrder α] [inst_1 : Lattice β] {f : α → β} {a b : α},
  MonotoneOn f (Set.uIcc a b) → Set.MapsTo f (Set.uIcc a b) (Set.uIcc (f a) (f b))

Defined in

Mathlib.Order.Interval.Set.UnorderedInterval

Cited by

2 results in Mathlib

Foundations

Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderLattice