∀ (α : Type u_1) (β : Type u_2) [inst : Monoid α] [inst_1 : PartialOrder α] [inst_2 : Monoid β] [inst_3 : Preorder β],
  OrderMonoidHom.inlₗ α β =
    { toFun := (Prod.Lex.toLexOrderHom.comp ↑(OrderMonoidHom.inl α β)).toFun, map_one' := ⋯, map_mul' := ⋯,
      monotone' := ⋯ }