match this with
| Or.inl (_ : Positive (a * b)) =>
  have : sgn a ≃ sgn b := positive_mul_iff_sgn_eqv.mp ‹Positive (a * b)›
  have : Sqrt1 (sgn b) ∧ sgn a ≃ sgn b := And.intro ‹Sqrt1 (sgn b)› this
  calc
    sgn (a * b)   ≃ _ := sgn_positive.mp ‹Positive (a * b)›
    1             ≃ _ := Rel.symm (mul_sqrt1_eqv.mpr this)
    sgn a * sgn b ≃ _ := Rel.refl
| Or.inr (_ : Negative (a * b)) =>
  have : sgn a ≄ sgn b := negative_mul_iff_sgn_neqv.mp ‹Negative (a * b)›
  calc
    sgn (a * b)   ≃ _ := sgn_negative.mp ‹Negative (a * b)›
    (-1)          ≃ _ := Rel.symm (mul_sqrt1_neqv.mpr ‹sgn a ≄ sgn b›)
    sgn a * sgn b ≃ _ := Rel.refl
ℕ : Type
inst✝⁵ : Natural ℕ
ℤ : Type
inst✝⁴ : Core ℤ
inst✝³ : Addition ℤ
inst✝² : Multiplication ℤ
inst✝¹ : Negation ℤ
inst✝ : Sign ℤ
a b : ℤ
this✝ : a * b ≃ 0 ∨ Nonzero (a * b)
h✝ : Nonzero (a * b)
left✝ : Sqrt1 (sgn a)
right✝ : Sqrt1 (sgn b)
this : Positive (a * b) ∨ Negative (a * b)
⊢ sgn (a * b) ≃ sgn a * sgn b
no goals