theorem extracted_formal_statement_6.{u_2, u_1} {E : Type u_1} {F : Type u_2} [inst : NormedAddCommGroup E]
  [inst_1 : InnerProductSpace ℝ E] [inst_2 : NormedAddCommGroup F] [inst_3 : InnerProductSpace ℝ F]
  {H : WithLp 2 (E × F) → ℝ} (h : Differentiable ℝ H) (x : E) : Differentiable ℝ (Prod.mk x) := sorry

State before:
E : Type u_1
F : Type u_2
inst✝³ : NormedAddCommGroup E
inst✝² : InnerProductSpace ℝ E
inst✝¹ : NormedAddCommGroup F
inst✝ : InnerProductSpace ℝ F
H : WithLp 2 (E × F) → ℝ
h : Differentiable ℝ H
x : E
⊢ Differentiable ℝ (Prod.mk x)

Tactic: exact Differentiable.prodMk (differentiable_const x) differentiable_id'

State after:

Relevant lemmas:
differentiable_id' : ∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_4 : NormedAddCommGroup E]
  [inst_5 : NormedSpace 𝕜 E], Differentiable 𝕜 fun x => x
Differentiable.prodMk : ∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2}
  [inst_4 : NormedAddCommGroup E] [inst_5 : NormedSpace 𝕜 E] {F : Type u_3} [inst_6 : NormedAddCommGroup F]
  [inst_7 : NormedSpace 𝕜 F] {G : Type u_4} [inst_8 : NormedAddCommGroup G] [inst_9 : NormedSpace 𝕜 G] {f₁ : E → F}
  {f₂ : E → G}, Differentiable 𝕜 f₁ → Differentiable 𝕜 f₂ → Differentiable 𝕜 fun x => (f₁ x, f₂ x)
differentiable_const : ∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2}
  [inst_4 : NormedAddCommGroup E] [inst_5 : NormedSpace 𝕜 E] {F : Type u_3} [inst_6 : NormedAddCommGroup F]
  [inst_7 : NormedSpace 𝕜 F] (c : F), Differentiable 𝕜 fun x => c