apply factors_unique_prod'
f g : Multiset (ℤ√(-3))
hf : ∀ (x : ℤ√(-3)), x ∈ f → OddPrimeOrFour (Zsqrtd.norm x)
hg : ∀ (x : ℤ√(-3)), x ∈ g → OddPrimeOrFour (Zsqrtd.norm x)
hassoc : Associated (Zsqrtd.norm (Multiset.prod f)) (Zsqrtd.norm (Multiset.prod g))
⊢ Multiset.Rel Associated (Multiset.map Zsqrtd.norm f) (Multiset.map Zsqrtd.norm g)
case a
f g : Multiset (ℤ√(-3))
hf : ∀ (x : ℤ√(-3)), x ∈ f → OddPrimeOrFour (Zsqrtd.norm x)
hg : ∀ (x : ℤ√(-3)), x ∈ g → OddPrimeOrFour (Zsqrtd.norm x)
hassoc : Associated (Zsqrtd.norm (Multiset.prod f)) (Zsqrtd.norm (Multiset.prod g))
⊢ ∀ (x : ℤ), x ∈ Multiset.map Zsqrtd.norm f → OddPrimeOrFour x

case a
f g : Multiset (ℤ√(-3))
hf : ∀ (x : ℤ√(-3)), x ∈ f → OddPrimeOrFour (Zsqrtd.norm x)
hg : ∀ (x : ℤ√(-3)), x ∈ g → OddPrimeOrFour (Zsqrtd.norm x)
hassoc : Associated (Zsqrtd.norm (Multiset.prod f)) (Zsqrtd.norm (Multiset.prod g))
⊢ ∀ (x : ℤ), x ∈ Multiset.map Zsqrtd.norm g → OddPrimeOrFour x

case a
f g : Multiset (ℤ√(-3))
hf : ∀ (x : ℤ√(-3)), x ∈ f → OddPrimeOrFour (Zsqrtd.norm x)
hg : ∀ (x : ℤ√(-3)), x ∈ g → OddPrimeOrFour (Zsqrtd.norm x)
hassoc : Associated (Zsqrtd.norm (Multiset.prod f)) (Zsqrtd.norm (Multiset.prod g))
⊢ Associated (Multiset.prod (Multiset.map Zsqrtd.norm f)) (Multiset.prod (Multiset.map Zsqrtd.norm g))