Theorems · Theorem · order theory

GaloisConnection.upperBounds_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), upperBounds (l '' s) = u ⁻¹' upperBounds s

Defined in

Mathlib.Order.GaloisConnection.Basic

Cited by

2 results in Mathlib

Foundations

Depth 7 from the axioms · uses propext, Quot.sound

Assumes

PreorderPreorder