∀ {R : Type u_1} {M : Type u_2} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] [CharZero R]
  [IsDomain R] [Module.IsTorsionFree R M] {x : M} {Φ : Set M},
  Φ.Finite →
    Submodule.span R Φ = ⊤ →
      ∀ {f g : Module.Dual R M},
        f x = 2 →
          Set.MapsTo (⇑(Module.preReflection x f)) Φ Φ → g x = 2 → Set.MapsTo (⇑(Module.preReflection x g)) Φ Φ → f = g