case mpr =>
  intro (_ : sgn p ≄ -1)
  show p ≥ 0
  have : sgn p ≃ sgn (p - 0) := sgn_subst (eqv_symm sub_zero)
  have : sgn (p - 0) ≄ -1 := AA.neqv_substL this ‹sgn p ≄ -1›
  have : p ≥ 0 := ge_sgn.mpr this
  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
⊢ sgn p ≄ -1 → p ≥ 0
no goals