∀ {A : Type u_1} {G : Type u_2} {V : Type u_3} [inst : CommRing A] [inst_1 : Monoid G] [inst_2 : AddCommMonoid V]
  [inst_3 : Module A V] (ρ : Representation A G V) (a : ρ.IntertwiningMap ρ), a * 0 = 0