∀ (R : Type u_2) {α : Type u_1} {β : Type u_3} [inst : CommSemiring R] (e : α ≃ β) [inst_1 : Semiring β]
  [inst_2 : Algebra R β] (x y : R),
  (↑↑((RingEquiv.symm e.ringEquiv).toRingHom.comp (algebraMap R β))).toFun (x + y) =
    (↑↑((RingEquiv.symm e.ringEquiv).toRingHom.comp (algebraMap R β))).toFun x +
      (↑↑((RingEquiv.symm e.ringEquiv).toRingHom.comp (algebraMap R β))).toFun y