Theorems · Theorem · order theory

surjOn_Ioo_of_monotone_surjective

∀ {α : Type u_1} {β : Type u_2} [inst : LinearOrder α] [inst_1 : PartialOrder β] {f : α → β},
  Monotone f → Function.Surjective f → ∀ (a b : α), Set.SurjOn f (Set.Ioo a b) (Set.Ioo (f a) (f b))

Defined in

Mathlib.Order.Interval.Set.SurjOn

Cited by

2 results in Mathlib

Foundations

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

Assumes

LinearOrderPartialOrder