Theorems · Definition · order theory

StrictMonoOn.orderIso

{α : Type u_4} →
  {β : Type u_5} →
    [inst : LinearOrder α] → [inst_1 : Preorder β] → (f : α → β) → (s : Set α) → StrictMonoOn f s → ↑s ≃o ↑(f '' s)

If a function f is strictly monotone on a set s, then it defines an order isomorphism between s and its image.

Defined in

Mathlib.Order.Hom.Set

Cited by

2 results in Mathlib

Foundations

Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderPreorder