theorem extracted_formal_statement_4 {m : ℕ+} (x : EuclideanSpace ℝ (Fin ↑m)) (h_original_goal : 0 ≤ ∑ i, ‖x i‖ ^ 2)
  (i : Fin ↑m) : i ∈ Finset.univ → 0 ≤ ‖x i‖ ^ 2 := sorry

State before:
m : ℕ+
x : EuclideanSpace ℝ (Fin ↑m)
⊢ 0 ≤ ∑ i, ‖x i‖ ^ 2

Tactic: apply sum_nonneg

State after:
[case h
 m : ℕ+
 x : EuclideanSpace ℝ (Fin ↑m)
 ⊢ ∀ i ∈ Finset.univ, 0 ≤ ‖x i‖ ^ 2]

Relevant lemmas:
Finset.sum_nonneg : ∀ {ι : Type u_1} {N : Type u_5} [inst : OrderedAddCommMonoid N] {f : ι → N} {s : Finset ι},
  (∀ i ∈ s, 0 ≤ f i) → 0 ≤ ∑ i ∈ s, f i