theorem extracted_formal_statement_2.{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) : IsBoundedLinearMap ℝ fun x => x := sorry

State before:
case h
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
⊢ IsBoundedLinearMap ℝ fun x => x

Tactic: 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