∀ {𝕜 : Type u_3} [inst : NontriviallyNormedField 𝕜] {E : Type u_1} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {F : Type u_4} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {G : Type u_2}
  [inst_5 : NormedAddCommGroup G] [inst_6 : NormedSpace 𝕜 G] {n : ℕ} (c : OrderedFinpartition n)
  (f : ContinuousMultilinearMap 𝕜 (fun i => F) G) (p : (i : Fin c.length) → ContinuousMultilinearMap 𝕜 (fun i => E) F)
  (m : Fin c.length) (q q' : ContinuousMultilinearMap 𝕜 (fun i => E) F),
  (fun p => c.compAlongOrderedFinpartition f p) (Function.update p m (q + q')) =
    (fun p => c.compAlongOrderedFinpartition f p) (Function.update p m q) +
      (fun p => c.compAlongOrderedFinpartition f p) (Function.update p m q')