rw [show 2 * (e.a1 * pth_root (-(e.a3 ^ 2) - e.a6) + e.a3)
    + e.a1 * pth_root (- (e.a3 ^ 2) - e.a6) + e.a3 = 3 * ((e.a1 * pth_root (-(e.a3 ^ 2) - e.a6)) + e.a3) by ring]
case pos.h_2.refine_3
K : Type u
inst✝¹ : Field K
inst✝ : ECTate.PerfectRing K
e : Model K
h : discr e = 0
hc4 : c4 e = 0
hc6 : c6 e = 0
x✝ : ℕ
heq✝ : ringChar K = 3
hchar : ringChar K = 3
hcharne : ringChar K ≠ 0
hchar' : ↑(ringChar K) = 3
hchar'' : 3 = 0
hb2 : e.a1 * e.a1 + 4 * e.a2 = 0
hb4 : e.a1 * e.a3 + 2 * e.a4 = 0
⊢ 2 * (e.a1 * pth_root (-e.a3 ^ 2 - e.a6) + e.a3) + e.a1 * pth_root (-e.a3 ^ 2 - e.a6) + e.a3 = 0
case pos.h_2.refine_3
K : Type u
inst✝¹ : Field K
inst✝ : ECTate.PerfectRing K
e : Model K
h : discr e = 0
hc4 : c4 e = 0
hc6 : c6 e = 0
x✝ : ℕ
heq✝ : ringChar K = 3
hchar : ringChar K = 3
hcharne : ringChar K ≠ 0
hchar' : ↑(ringChar K) = 3
hchar'' : 3 = 0
hb2 : e.a1 * e.a1 + 4 * e.a2 = 0
hb4 : e.a1 * e.a3 + 2 * e.a4 = 0
⊢ 3 * (e.a1 * pth_root (-e.a3 ^ 2 - e.a6) + e.a3) = 0