theorem extracted_formal_statement_17 {n : ℕ+} (h_original_goal : ConvexOn ℝ Set.univ fun x => ∑ i, ‖x i‖)
  ⦃x : EuclideanSpace ℝ (Fin ↑n)⦄ :
  x ∈ Set.univ →
    ∀ ⦃y : EuclideanSpace ℝ (Fin ↑n)⦄,
      y ∈ Set.univ →
        ∀ ⦃a b : ℝ⦄, 0 ≤ a → 0 ≤ b → a + b = 1 → ∑ i, ‖(a • x + b • y) i‖ ≤ a • ∑ i, ‖x i‖ + b • ∑ i, ‖y i‖ := sorry

State before:
n : ℕ+
⊢ ConvexOn ℝ Set.univ fun x => ∑ i, ‖x i‖

Tactic: rw [ConvexOn]
    constructor
    use convex_univ

State after:
[case right
 n : ℕ+
 ⊢ ∀ ⦃x : EuclideanSpace ℝ (Fin ↑n)⦄,
     x ∈ Set.univ →
       ∀ ⦃y : EuclideanSpace ℝ (Fin ↑n)⦄,
         y ∈ Set.univ →
           ∀ ⦃a b : ℝ⦄, 0 ≤ a → 0 ≤ b → a + b = 1 → ∑ i, ‖(a • x + b • y) i‖ ≤ a • ∑ i, ‖x i‖ + b • ∑ i, ‖y i‖]

Relevant lemmas:
convex_univ : ∀ {𝕜 : Type u_1} {E : Type u_2} [inst : OrderedSemiring 𝕜] [inst_1 : AddCommMonoid E] [inst_2 : SMul 𝕜 E],
  Convex 𝕜 Set.univ