calc
  _ ≃ p               := eqv_refl
  _ ≃ p * 1           := eqv_symm mul_identR
  _ ≃ p * sgn (1 : ℚ) := mul_substR (from_integer_subst (Rel.symm sgn_one))
  _ ≤ p * sgn p       := mul_sgn_self_max
  _ ≃ abs p           := eqv_symm abs_sgn
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 ≤ abs p
no goals