∀ {α : Type u} {β : Type v} {γ : Type w} [inst : Preorder α] [inst_1 : Preorder β] [inst_2 : Preorder γ]
  {h : α × β → γ}, Monotone h ↔ (∀ (a : α), Monotone fun b => h (a, b)) ∧ ∀ (b : β), Monotone fun a => h (a, b)