∀ {R : Type u_3} {A : Type u_1} {B : Type u_2} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A]
  [inst_3 : Semiring B] [inst_4 : Algebra R B] (x : R), ((algebraMap R (A × B)) x).1 = ((algebraMap R (A × B)) x).1