∀ {α : Type u_1} {β : Type u_2} {R : Type u_3} [inst : CommSemiring R] (S : Type u_8) [inst_1 : Semiring S]
  [inst_2 : Algebra R S] (x : α ⊕ β → S),
  (AlgEquiv.sumArrowEquivProdArrow α β R S) x = (Equiv.sumArrowEquivProdArrow α β S) x