case zero =>
  show abs (p^0) ≃ (abs p)^0
  have : sgn (1:ℚ) ≃ 1 := sgn_one
  have : abs (1:ℚ) ≃ 1 := abs_positive this
  calc
    _ ≃ abs (p^0) := eqv_refl
    _ ≃ abs 1     := abs_subst pow_zero
    _ ≃ 1         := ‹abs (1:ℚ) ≃ 1›
    _ ≃ (abs p)^0 := eqv_symm pow_zero
ℕ ℤ : Type
inst✝¹² : Natural ℕ
inst✝¹¹ : Integer ℤ
ℚ : Type
inst✝¹⁰ : Core ℚ
inst✝⁹ : Addition ℚ
inst✝⁸ : Multiplication ℚ
inst✝⁷ : Negation ℚ
inst✝⁶ : Subtraction ℚ
inst✝⁵ : Reciprocation ℚ
inst✝⁴ : Division ℚ
inst✝³ : Sign ℚ
inst✝² : Order ℚ
inst✝¹ : Metric ℚ
inst✝ : Natural.Exponentiation ℕ fun x x_1 => x * x_1
p : ℚ
n : ℕ
⊢ abs (p ^ 0) ≃ abs p ^ 0
no goals