calc
  _ ≃ dist p q    := eqv_refl
  _ ≃ abs (p - q) := dist_abs
  _ ≃ abs 0       := abs_subst (sub_eqv_zero_iff_eqv.mpr ‹p ≃ q›)
  _ ≃ 0           := abs_zero.mpr eqv_refl
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
x✝ : p ≃ q
⊢ dist p q ≃ 0
no goals