case mp =>
  intro (_ : p > 0)
  show sgn p ≃ 1
  have : sgn (p - 0) ≃ 1 := gt_sgn.mp ‹p > 0›
  calc
    _ ≃ sgn p       := Rel.refl
    _ ≃ sgn (p - 0) := sgn_subst (eqv_symm sub_zero)
    _ ≃ 1           := ‹sgn (p - 0) ≃ 1›
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