Theorems · Theorem · order theory

OrderEmbedding.image_Ici

∀ {α : Type u_1} {β : Type u_2} [inst : Preorder α] [inst_1 : Preorder β] (e : α ↪o β),
  IsUpperSet (Set.range ⇑e) → ∀ (a : α), ⇑e '' Set.Ici a = Set.Ici (e a)

Defined in

Mathlib.Order.UpperLower.Basic

Cited by

1 results in Mathlib

Foundations

Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PreorderPreorder