theorem extracted_formal_statement_54 {n m : ℕ+} {b : Fin ↑m → ℝ} {A : Matrix (Fin ↑m) (Fin ↑n) ℝ}
  (x : EuclideanSpace ℝ (Fin ↑n)) (ε : ℝ) (εpos : ε > 0) (y : EuclideanSpace ℝ (Fin ↑n)) (a : ‖x - y‖ ≤ ε) :
  0 ≤ ‖x - y‖ := sorry

State before:
case right.hb
n m : ℕ+
b : Fin ↑m → ℝ
A : Matrix (Fin ↑m) (Fin ↑n) ℝ
x : EuclideanSpace ℝ (Fin ↑n)
ε : ℝ
εpos : ε > 0
y : EuclideanSpace ℝ (Fin ↑n)
a✝ : ‖x - y‖ ≤ ε
⊢ 0 ≤ ‖x - y‖

Tactic: apply norm_nonneg

State after:

Relevant lemmas:
norm_nonneg : ∀ {E : Type u_5} [inst : SeminormedAddGroup E] (a : E), 0 ≤ ‖a‖