∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {Ω : TopologicalSpace.Opens E} {F : Type u_2}
  [inst_2 : AddCommGroup F] [inst_3 : Module ℝ F] [inst_4 : TopologicalSpace F] {F' : Type u_3}
  [inst_5 : AddCommGroup F'] [inst_6 : Module ℝ F'] [inst_7 : TopologicalSpace F'] {n : ℕ∞}
  [inst_8 : IsTopologicalAddGroup F] [inst_9 : ContinuousSMul ℝ F] [inst_10 : IsTopologicalAddGroup F']
  [inst_11 : ContinuousSMul ℝ F'] {A : F →L[ℝ] F'} {T : Distribution Ω F n} {f : TestFunction Ω ℝ n},
  ((Distribution.mapCLM A) T) f = A (T f)