simp only [add_re, int_cast_re, mul_re, int_cast_im, MulZeroClass.zero_mul, tsub_zero]
case a
a b c : ℤω
x y : ℤ
⊢ (↑x + ↑y * { re := -1 / 2, im := rt3 / 2 }).re = { re := ↑x - ↑y / 2, im := ↑y * rt3 / 2 }.re
case a
a b c : ℤω
x y : ℤ
⊢ ↑x + ↑y * (-1 / 2) = ↑x - ↑y / 2