∀ {M : Type u_1} [inst : CommMonoidWithZero M] [IsCancelMulZero M] {N : Type u_2} [inst_2 : CommMonoidWithZero N]
  [UniqueFactorizationMonoid N] [inst_4 : UniqueFactorizationMonoid M] {m p : Associates M} {n : Associates N},
  n ≠ 0 →
    ∀ (hp : p ∈ UniqueFactorizationMonoid.normalizedFactors m) (d : ↑(Set.Iic m) ≃o ↑(Set.Iic n)), Prime ↑(d ⟨p, ⋯⟩)