have : Positive (a * sgn a) := sgn_positive.mpr ‹sgn (a * sgn a) ≃ 1›
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 : ℤ
x✝ : Nonzero a
this✝¹ : Sqrt1 (sgn a)
this✝ : sgn a * sgn a ≃ 1
this : sgn (a * sgn a) ≃ 1
⊢ Positive (a * sgn a)
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 : ℤ
x✝ : Nonzero a
this✝² : Sqrt1 (sgn a)
this✝¹ : sgn a * sgn a ≃ 1
this✝ : sgn (a * sgn a) ≃ 1
this : Positive (a * sgn a)
⊢ Positive (a * sgn a)