no goals
𝓕 : Type ?u.999913
𝕜 : Type ?u.999916
α : Type ?u.999919
ι : Type ?u.999922
κ : Type ?u.999925
E : Type u_1
F : Type ?u.999931
G : Type ?u.999934
inst✝¹ : SeminormedCommGroup E
inst✝ : SeminormedCommGroup F
a a₁ a₂ b b₁ b₂ : E
r r₁ r₂ : ℝ
c : E
⊢ a * c ∈ closedBall (b * c) r ↔ a ∈ closedBall b r
simp only [mem_closedBall, dist_eq_norm_div, mul_div_mul_right_eq_div]