Theorems · Theorem · order theory

OrderEmbedding.image_Ioo

∀ {α : Type u_1} {β : Type u_2} [inst : Preorder α] [inst_1 : Preorder β] (e : α ↪o β),
  (Set.range ⇑e).OrdConnected → ∀ (x y : α), ⇑e '' Set.Ioo x y = Set.Ioo (e x) (e y)

Defined in

Mathlib.Order.Interval.Set.OrdConnected

Cited by

2 results in Mathlib

Foundations

Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PreorderPreorder