ring_nf
case mk.mk
c : ℤω
x✝¹ y✝¹ x✝ y✝ : ℤ
⊢ ↑x✝¹ * ↑x✝ - ↑y✝¹ * ↑y✝ + (↑x✝¹ * ↑y✝ + ↑y✝¹ * ↑x✝ - ↑y✝¹ * ↑y✝) * complexω =
    (↑x✝¹ + ↑y✝¹ * complexω) * (↑x✝ + ↑y✝ * complexω)
case mk.mk
c : ℤω
x✝¹ y✝¹ x✝ y✝ : ℤ
⊢ ↑x✝¹ * ↑x✝ + ↑x✝¹ * ↑y✝ * complexω + ↑x✝ * ↑y✝¹ * complexω + (-(↑y✝¹ * ↑y✝) - ↑y✝¹ * ↑y✝ * complexω) =
    ↑x✝¹ * ↑x✝ + ↑x✝¹ * ↑y✝ * complexω + ↑x✝ * ↑y✝¹ * complexω + ↑y✝¹ * ↑y✝ * complexω ^ 2