Theorems · Theorem · order theory

GaloisConnection.isGLB_u_image

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

Defined in

Mathlib.Order.GaloisConnection.Basic

Cited by

4 results in Mathlib

Foundations

Depth 10 from the axioms · uses propext, Quot.sound

Assumes

PreorderPreorder