∀ (β : Type u_2) (γ : Type u_1) [inst : ConditionallyCompleteLinearOrderedField β]
  [inst_1 : ConditionallyCompleteLinearOrderedField γ] (x y : β),
  (↑↑(LinearOrderedField.inducedOrderRingHom β γ).toRingHom).toFun (x + y) =
    (↑↑(LinearOrderedField.inducedOrderRingHom β γ).toRingHom).toFun x +
      (↑↑(LinearOrderedField.inducedOrderRingHom β γ).toRingHom).toFun y