case mp =>
  intro (_ : p ≥ 0)
  show sgn p ≄ -1
  have : sgn (p - 0) ≄ -1 := ge_sgn.mp ‹p ≥ 0›
  have : sgn (p - 0) ≃ sgn p := sgn_subst sub_zero
  have : sgn p ≄ -1 := AA.neqv_substL this ‹sgn (p - 0) ≄ -1›
  exact this
ℕ ℤ ℚ : Type
inst✝¹⁰ : Natural ℕ
inst✝⁹ : Integer ℤ
inst✝⁸ : Core ℚ
inst✝⁷ : Addition ℚ
inst✝⁶ : Multiplication ℚ
inst✝⁵ : Negation ℚ
inst✝⁴ : Sign ℚ
inst✝³ : Subtraction ℚ
inst✝² : Reciprocation ℚ
inst✝¹ : Division ℚ
inst✝ : Order ℚ
p : ℚ
⊢ p ≥ 0 → sgn p ≄ -1
no goals