∀ {α : Type u_2} {β : Type u_3} {γ : Type u_4} [inst : Preorder α] [inst_1 : Preorder β] [inst_2 : Preorder γ]
  (g : β → γ) (f : α → β) (hg : Monotone g) (hf : Monotone f),
  { toFun := g, monotone' := hg }.comp { toFun := f, monotone' := hf } = { toFun := g ∘ f, monotone' := ⋯ }