∀ {E : Type u_5} [inst : Norm E] [inst_1 : AddCommGroup E] [inst_2 : MetricSpace E] (h₁ : ∀ (x : E), ‖x‖ = dist 0 x)
  (h₂ : ∀ (x y z : E), dist x y ≤ dist (z + x) (z + y)),
  NormedAddCommGroup.ofAddDist h₁ h₂ =
    { toNorm := (NormedAddGroup.ofAddDist h₁ h₂).toNorm, toAddGroup := (NormedAddGroup.ofAddDist h₁ h₂).toAddGroup,
      add_comm := ⋯, toMetricSpace := (NormedAddGroup.ofAddDist h₁ h₂).toMetricSpace, dist_eq := ⋯ }