Theorem: ℤω.im_of_coe (Mordell4/Eisenstein.lean)

State before:
a b c : ℤω
⊢ (OneHom.toFun (↑↑inclusion) a).im = ↑a.y * rt3 / 2
Tactic:
change (toℂ a).im = a.y * rt3 / 2
State after:
a b c : ℤω
⊢ (toℂ a).im = ↑a.y * rt3 / 2

State before:
a b c : ℤω
⊢ (toℂ a).im = ↑a.y * rt3 / 2
Tactic:
unfold toℂ
State after:
a b c : ℤω
⊢ (↑a.x + ↑a.y * complexω).im = ↑a.y * rt3 / 2

State before:
a b c : ℤω
⊢ (↑a.x + ↑a.y * complexω).im = ↑a.y * rt3 / 2
Tactic:
unfold complexω
State after:
a b c : ℤω
⊢ (↑a.x + ↑a.y * { re := -1 / 2, im := rt3 / 2 }).im = ↑a.y * rt3 / 2

State before:
a b c : ℤω
⊢ (↑a.x + ↑a.y * { re := -1 / 2, im := rt3 / 2 }).im = ↑a.y * rt3 / 2
Tactic:
simp only [add_im, int_cast_im, mul_im, int_cast_re, MulZeroClass.zero_mul, add_zero, zero_add]
State after:
a b c : ℤω
⊢ ↑a.y * (rt3 / 2) = ↑a.y * rt3 / 2

State before:
a b c : ℤω
⊢ ↑a.y * (rt3 / 2) = ↑a.y * rt3 / 2
Tactic:
ring
State after:
no goals