Theorem: ℤα.re_of_coe (Mordell4/Rt7Ring.lean)

State before:
a b c : ℤα
⊢ (OneHom.toFun (↑↑inclusion) a).re = ↑a.z + ↑a.w / 2
Tactic:
change (toℂ a).re = a.z + a.w / 2
State after:
a b c : ℤα
⊢ (toℂ a).re = ↑a.z + ↑a.w / 2

State before:
a b c : ℤα
⊢ (toℂ a).re = ↑a.z + ↑a.w / 2
Tactic:
unfold toℂ
State after:
a b c : ℤα
⊢ (↑a.z + ↑a.w * complexα).re = ↑a.z + ↑a.w / 2

State before:
a b c : ℤα
⊢ (↑a.z + ↑a.w * complexα).re = ↑a.z + ↑a.w / 2
Tactic:
unfold complexα
State after:
a b c : ℤα
⊢ (↑a.z + ↑a.w * { re := 1 / 2, im := rt7 / 2 }).re = ↑a.z + ↑a.w / 2

State before:
a b c : ℤα
⊢ (↑a.z + ↑a.w * { re := 1 / 2, im := rt7 / 2 }).re = ↑a.z + ↑a.w / 2
Tactic:
simp only [add_re, int_cast_re, mul_re, int_cast_im, MulZeroClass.zero_mul, tsub_zero]
State after:
a b c : ℤα
⊢ ↑a.z + ↑a.w * (1 / 2) = ↑a.z + ↑a.w / 2

State before:
a b c : ℤα
⊢ ↑a.z + ↑a.w * (1 / 2) = ↑a.z + ↑a.w / 2
Tactic:
ring
State after:
no goals