theorem extracted_formal_statement_75 {n : ℕ+} (h_original_goal : ConvexOn ℝ Set.univ fun x => ∑ i, ‖x i‖) :
  Convex ℝ Set.univ ∧
    ∀ ⦃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]

State after:
[n : ℕ+
 ⊢ Convex ℝ Set.univ ∧
     ∀ ⦃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: