ring
case mk.mk.mk
x✝² y✝² x✝¹ y✝¹ x✝ y✝ : ℤ
⊢ { x := (x✝² + x✝¹) * x✝ - (y✝² + y✝¹) * y✝, y := (x✝² + x✝¹) * y✝ + (y✝² + y✝¹) * x✝ - (y✝² + y✝¹) * y✝ } =
    { x := x✝² * x✝ - y✝² * y✝ + (x✝¹ * x✝ - y✝¹ * y✝),
      y := x✝² * y✝ + y✝² * x✝ - y✝² * y✝ + (x✝¹ * y✝ + y✝¹ * x✝ - y✝¹ * y✝) }
no goals