case mpr =>
  intro (_ : p ≃ q) (ε : ℚ) (_ : ε > 0)
  show p ⊢ε⊣ q
  have : dist p q ≤ ε := calc
    _ ≃ dist p q := eqv_refl
    _ ≃ 0        := dist_zero.mpr ‹p ≃ q›
    _ ≤ ε        := le_cases.mpr (Or.inl ‹ε > 0›)
  have : p ⊢ε⊣ q := close_dist.mpr ‹dist p q ≤ ε›
  exact this
ℕ ℤ ℚ : Type
inst✝¹² : Natural ℕ
inst✝¹¹ : Integer ℤ
inst✝¹⁰ : Core ℚ
inst✝⁹ : Addition ℚ
inst✝⁸ : Negation ℚ
inst✝⁷ : Subtraction ℚ
inst✝⁶ : Multiplication ℚ
inst✝⁵ : Reciprocation ℚ
inst✝⁴ : Division ℚ
inst✝³ : Sign ℚ
inst✝² : Order ℚ
inst✝¹ : MinMax ℚ
inst✝ : Metric ℚ
p q : ℚ
⊢ p ≃ q → ∀ {ε : ℚ}, ε > 0 → p ⊢ε⊣ q
no goals