Theorems · Theorem · order theory

GaloisConnection.l_le

∀ {α : Type u} {β : Type v} [inst : Preorder α] [inst_1 : Preorder β] {l : α → β} {u : β → α},
  GaloisConnection l u → ∀ {a : α} {b : β}, a ≤ u b → l a ≤ b

Defined in

Mathlib.Order.GaloisConnection.Defs

Cited by

28 results in Mathlib

Foundations

Depth 3 from the axioms · uses no axioms

Assumes

PreorderPreorder