calc
  _ ≃ abs p     := eqv_refl
  _ ≃ p * sgn p := abs_sgn
  _ ≃ p * 1     := mul_substR (from_integer_subst ‹sgn p ≃ 1›)
  _ ≃ p         := mul_identR
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
x✝ : sgn p ≃ 1
⊢ abs p ≃ p
no goals