rw [abs_eq <| zero_le_one' ℤ] at hv2
case intro.intro.intro
x A : ℤ√(-3)
hx : x.re = 0
u : (ℤ√(-3))ˣ
hu : x * ↑u = A
v : ℤ
hv1 : ↑u = ↑v
hv2 : |v| = 1
hA : A.re = 0
⊢ x = A ∨ x = star A
case intro.intro.intro
x A : ℤ√(-3)
hx : x.re = 0
u : (ℤ√(-3))ˣ
hu : x * ↑u = A
v : ℤ
hv1 : ↑u = ↑v
hv2 : v = 1 ∨ v = -1
hA : A.re = 0
⊢ x = A ∨ x = star A