∀ {R : Type u_3} {A : Type u_1} {C : Type u_2} [inst : CommSemiring R] [inst_1 : NonUnitalNonAssocRing A]
  [inst_2 : Module R A] [inst_3 : SMulCommClass R A A] [inst_4 : IsScalarTower R A A] [inst_5 : AddCommMonoid C]
  [inst_6 : Module R C] [inst_7 : CoalgebraStruct R C] (a : WithConv (C →ₗ[R] A)), 0 * a = 0