theorem extracted_formal_statement_48.{u_5, u_4} {α : Type u_4} {β : Type u_5} [inst : NormedAddCommGroup α]
  [inst_1 : InnerProductSpace ℝ α] [inst_2 : NormedAddCommGroup β] [inst_3 : InnerProductSpace ℝ β] (A : α →L[ℝ] β)
  (a₁ a₂ : α) : ‖-(A a₂ - A a₁)‖ = ‖A a₂ - A a₁‖ := sorry

State before:
α : Type u_4
β : Type u_5
inst✝³ : NormedAddCommGroup α
inst✝² : InnerProductSpace ℝ α
inst✝¹ : NormedAddCommGroup β
inst✝ : InnerProductSpace ℝ β
A : α →L[ℝ] β
a₁ a₂ : α
⊢ ‖-(A a₂ - A a₁)‖ = ‖A a₂ - A a₁‖

Tactic: apply norm_neg

State after:

Relevant lemmas:
norm_neg : ∀ {E : Type u_5} [inst : SeminormedAddGroup E] (a : E), ‖-a‖ = ‖a‖