theorem extracted_formal_statement_0.{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) : Differentiable ℝ H := 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
⊢ Differentiable ℝ H

Tactic: apply Differentiable.comp h
    apply IsBoundedLinearMap.differentiable
    exact instIsBoundedLinearMapL2equiv

State after:

Relevant lemmas:
instIsBoundedLinearMapL2equiv : ∀ {E : Type u_1} {F : Type u_2} [inst : NormedAddCommGroup E]
  [inst_4 : InnerProductSpace ℝ E] [inst_5 : NormedAddCommGroup F] [inst_6 : InnerProductSpace ℝ F],
  IsBoundedLinearMap ℝ id
Differentiable.comp : ∀ {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] {f : E → F} {g : F → G},
  Differentiable 𝕜 g → Differentiable 𝕜 f → Differentiable 𝕜 (g ∘ f)
IsBoundedLinearMap.differentiable : ∀ {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] {f : E → F}, IsBoundedLinearMap 𝕜 f → Differentiable 𝕜 f