𝓕 : Type ?u.499976
𝕜 : Type ?u.499979
α : Type ?u.499982
ι : Type ?u.499985
κ : Type ?u.499988
E : Type u_1
F : Type ?u.499994
G : Type ?u.499997
inst✝³ : SeminormedGroup E
inst✝² : SeminormedGroup F
inst✝¹ : SeminormedGroup G
s : Set E
a✝ a₁ a₂ b b₁ b₂ : E
r r₁ r₂ : ℝ
inst✝ : T0Space E
a : E
this : NormedGroup E :=
  let src := inst✝³;
  NormedGroup.mk
⊢ ‖a‖ ≤ 0 ↔ a = 1
𝓕 : Type ?u.499976
𝕜 : Type ?u.499979
α : Type ?u.499982
ι : Type ?u.499985
κ : Type ?u.499988
E : Type u_1
F : Type ?u.499994
G : Type ?u.499997
inst✝³ : SeminormedGroup E
inst✝² : SeminormedGroup F
inst✝¹ : SeminormedGroup G
s : Set E
a✝ a₁ a₂ b b₁ b₂ : E
r r₁ r₂ : ℝ
inst✝ : T0Space E
a : E
⊢ ‖a‖ ≤ 0 ↔ a = 1
letI : NormedGroup E :=
  { ‹SeminormedGroup E› with toMetricSpace := MetricSpace.ofT0PseudoMetricSpace E }
no goals
𝓕 : Type ?u.499976
𝕜 : Type ?u.499979
α : Type ?u.499982
ι : Type ?u.499985
κ : Type ?u.499988
E : Type u_1
F : Type ?u.499994
G : Type ?u.499997
inst✝³ : SeminormedGroup E
inst✝² : SeminormedGroup F
inst✝¹ : SeminormedGroup G
s : Set E
a✝ a₁ a₂ b b₁ b₂ : E
r r₁ r₂ : ℝ
inst✝ : T0Space E
a : E
this : NormedGroup E :=
  let src := inst✝³;
  NormedGroup.mk
⊢ ‖a‖ ≤ 0 ↔ a = 1
rw [← dist_one_right, dist_le_zero]