case mpr =>
  intro (_ : p ≃ q)
  show p ⊢0⊣ q
  have : dist p q ≃ 0 := dist_zero.mpr ‹p ≃ q›
  have : dist p q ≤ 0 := le_cases.mpr (Or.inr this)
  have : p ⊢0⊣ q := close_dist.mpr this
  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 → p ⊢0⊣ q
no goals