theorem extracted_formal_statement_155 {n m : ℕ+} {A : Matrix (Fin ↑m) (Fin ↑n) ℝ} {Ane0 : A ≠ 0}
  (x y : EuclideanSpace ℝ (Fin ↑n)) :
  ‖(Aᵀ * A) *ᵥ (x - y)‖ ≤ ‖LinearMap.toContinuousLinearMap (toEuclideanLin (Aᵀ * A))‖ * ‖x - y‖ := 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
x y : EuclideanSpace ℝ (Fin ↑n)
⊢ ‖(Aᵀ * A) *ᵥ (x - y)‖ ≤ ‖LinearMap.toContinuousLinearMap (toEuclideanLin (Aᵀ * A))‖ * ‖x - y‖

Tactic: apply Matrix.l2_opNorm_mulVec (Aᵀ * A)

State after:

Relevant lemmas:
Matrix.l2_opNorm_mulVec : ∀ {𝕜 : Type u_1} {m : Type u_2} {n : Type u_3} [inst : RCLike 𝕜] [inst_1 : Fintype m]
  [inst_2 : Fintype n] [inst_3 : DecidableEq n] (A : Matrix m n 𝕜) (x : EuclideanSpace 𝕜 n),
  ‖(EuclideanSpace.equiv m 𝕜).symm (A *ᵥ x)‖ ≤ ‖A‖ * ‖x‖