∀ (α : Type u_1) (β : Type u_2) [inst : AddMonoid α] [inst_1 : PartialOrder α] [inst_2 : AddMonoid β]
  [inst_3 : Preorder β],
  (Prod.Lex.toLexOrderHom.comp ↑(OrderAddMonoidHom.inr α β)).toFun 0 =
    (Prod.Lex.toLexOrderHom.comp ↑(OrderAddMonoidHom.inr α β)).toFun 0