no goals
𝕜 : Type ?u.285162
E : Type u_1
F : Type ?u.285168
inst✝¹ : SeminormedAddCommGroup E
inst✝ : NormedSpace ℝ E
s : Set E
r : ℝ
x✝ x : E
⊢ gauge (Metric.ball 0 1) x = ‖x‖
rw [← ball_normSeminorm ℝ, Seminorm.gauge_ball, coe_normSeminorm]