case mpr =>
  intro (_ : sgn p ≃ 1)
  show p > 0
  have : sgn (p - 0) ≃ 1 := calc
    _ ≃ sgn (p - 0) := Rel.refl
    _ ≃ sgn p       := sgn_subst sub_zero
    _ ≃ 1           := ‹sgn p ≃ 1›
  have : p > 0 := gt_sgn.mpr ‹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
⊢ sgn p ≃ 1 → p > 0
no goals