theorem extracted_formal_statement_191 {n m : ℕ+} {A : Matrix (Fin ↑m) (Fin ↑n) ℝ} {b : Fin ↑m → ℝ} {μ : ℝ} {μpos : 0 < μ}
  {Ane0 : A ≠ 0} {x₀ : EuclideanSpace ℝ (Fin ↑n)} (p : LASSO A b μ μpos Ane0 x₀) (h_original_goal : ↑p.L > 0) :
  ↑‖(toEuclideanLin ≪≫ₗ LinearMap.toContinuousLinearMap) (Aᵀ * A)‖₊ > 0 := sorry

State before:
n m : ℕ+
A : Matrix (Fin ↑m) (Fin ↑n) ℝ
b : Fin ↑m → ℝ
μ : ℝ
μpos : 0 < μ
Ane0 : A ≠ 0
x₀ : EuclideanSpace ℝ (Fin ↑n)
p : LASSO A b μ μpos Ane0 x₀
⊢ ↑p.L > 0

Tactic: rw [p.Leq]

State after:
[n m : ℕ+
 A : Matrix (Fin ↑m) (Fin ↑n) ℝ
 b : Fin ↑m → ℝ
 μ : ℝ
 μpos : 0 < μ
 Ane0 : A ≠ 0
 x₀ : EuclideanSpace ℝ (Fin ↑n)
 p : LASSO A b μ μpos Ane0 x₀
 ⊢ ↑‖(toEuclideanLin ≪≫ₗ LinearMap.toContinuousLinearMap) (Aᵀ * A)‖₊ > 0]

Relevant lemmas: