Theorems · Theorem · order theory

GaloisConnection.isLUB_l_image

∀ {α : Type u} {β : Type v} [inst : Preorder α] [inst_1 : Preorder β] {l : α → β} {u : β → α},
  GaloisConnection l u → ∀ {s : Set α} {a : α}, IsLUB s a → IsLUB (l '' s) (l a)

Defined in

Mathlib.Order.GaloisConnection.Basic

Cited by

5 results in Mathlib

Foundations

Depth 11 from the axioms · uses propext, Quot.sound

Assumes

PreorderPreorder