case mp =>
  intro (_ : p ⊢0⊣ q)
  show p ≃ q
  have : dist p q ≤ 0 := close_dist.mp ‹p ⊢0⊣ q›
  have : dist p q ≥ 0 := dist_nonneg
  have : dist p q ≃ 0 := le_antisymm ‹dist p q ≤ 0› ‹dist p q ≥ 0›
  have : p ≃ q := dist_zero.mp 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 ⊢0⊣ q → p ≃ q
no goals