theorem extracted_formal_statement_13 {n m : ℕ+} {A : Matrix (Fin ↑m) (Fin ↑n) ℝ} (hA : ¬A = 0) :
  let normA := ‖(toEuclideanLin ≪≫ₗ LinearMap.toContinuousLinearMap) A‖;
  ∀ (x : EuclideanSpace ℝ (Fin ↑n)), ‖A *ᵥ x‖ ≤ normA * ‖x‖ := sorry

State before:
n m : ℕ+
A : Matrix (Fin ↑m) (Fin ↑n) ℝ
hA : ¬A = 0
x✝ : EuclideanSpace ℝ (Fin ↑n)
ε : ℝ
εpos : ε > 0
normA : ℝ := ‖(toEuclideanLin ≪≫ₗ LinearMap.toContinuousLinearMap) A‖
x : EuclideanSpace ℝ (Fin ↑n)
⊢ ‖A *ᵥ x‖ ≤ normA * ‖x‖

Tactic: apply Matrix.l2_opNorm_mulVec 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‖