case mpr =>
  intro (_ : p ≃ 0)
  show abs p ≃ 0
  calc
    abs p           ≃ _ := abs_sgn
    p * sgn p       ≃ _ := mul_substL ‹p ≃ 0›
    (0 : ℚ) * sgn p ≃ _ := mul_absorbL
    0               ≃ _ := 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
⊢ p ≃ 0 → abs p ≃ 0
no goals