no goals
ι : Type ?u.999131
α : Type u
β : Type v
γ : Type w
inst✝² : PseudoEMetricSpace α
inst✝¹ : PseudoEMetricSpace β
inst✝ : PseudoEMetricSpace γ
e : α ≃ᵢ β
⊢ CompleteSpace α ↔ CompleteSpace β
simp only [completeSpace_iff_isComplete_univ, ← e.range_eq_univ, ← image_univ,
  isComplete_image_iff e.isometry.uniformInducing]