English
Repeated: the unit closed ball scales to any closed ball by a nonzero scalar: c • closedBall(0,1) = closedBall(0, ||c||).
Русский
Единичный замкнутый шар масштабируется до любого замкнутого шара через скаляры: c • closedBall(0,1) = closedBall(0, ||c||).
LaTeX
$$$c \\cdot \\overline{B}(0,1) = \\overline{B}(0, \\|c\\|)$$$
Lean4
theorem norm_zsmul (n : ℤ) (x : E) : ‖n • x‖ = ‖(n : 𝕜)‖ * ‖x‖ := by
rw [← norm_smul, ← Int.smul_one_eq_cast, smul_assoc, one_smul]