∀ {A : Type u_1} [inst : NonUnitalCStarAlgebra A] [inst_1 : PartialOrder A] {E : Type u_2} {F : Type u_3}
  [inst_2 : NormedAddCommGroup E] [inst_3 : Module ℂ E] [inst_4 : SMul A E] [inst_5 : NormedAddCommGroup F]
  [inst_6 : Module ℂ F] [inst_7 : SMul A F] [inst_8 : CStarModule A E] [inst_9 : CStarModule A F]
  (x y : WithCStarModule A (E × F)), star (inner A x.1 y.1 + inner A x.2 y.2) = inner A y.1 x.1 + inner A y.2 x.2