rw [Multiset.prod_cons, Multiset.prod_cons, ← mul_assoc, ← Zsqrtd.norm_eq_mul_conj] at hcoprime
case neg.intro.intro
p : ℤ√(-3)
him : ¬p.im = 0
this✝ : star p ≠ p
t2 : Multiset (ℤ√(-3))
hcoprime : IsCoprime (Multiset.prod (p ::ₘ star p ::ₘ t2)).re (Multiset.prod (p ::ₘ star p ::ₘ t2)).im
h1 : p ∈ p ::ₘ star p ::ₘ t2
h2 : star p ∈ p ::ₘ star p ::ₘ t2
this : star p ∈ star p ::ₘ t2
⊢ IsUnit p
case neg.intro.intro
p : ℤ√(-3)
him : ¬p.im = 0
this✝ : star p ≠ p
t2 : Multiset (ℤ√(-3))
hcoprime : IsCoprime (↑(Zsqrtd.norm p) * Multiset.prod t2).re (↑(Zsqrtd.norm p) * Multiset.prod t2).im
h1 : p ∈ p ::ₘ star p ::ₘ t2
h2 : star p ∈ p ::ₘ star p ::ₘ t2
this : star p ∈ star p ::ₘ t2
⊢ IsUnit p