rw [div_add_mul_self, div_eq_zero_of_lt] <;> simp [hie.lt_iff_len_le.mpr hS₁, hie.range_pos]
case e_a.e_a
M : Type u_1
inst✝⁵ : Zero M
inst✝⁴ : One M
inst✝³ : Add M
inst✝² : Mul M
inst✝¹ : LT M
inst✝ : M ⊧ₘ* 𝐈𝚫₀ + 𝛀₁
L I i j S₁ S₂ : M
hij : i + j ≤ ‖I‖
hS₁ : ‖S₁‖ ≤ i * ‖L‖
hie : Exponential (i * ‖L‖) (bexp (I # L) (i * ‖L‖))
⊢ (S₁ + S₂ * bexp (I # L) (i * ‖L‖)) / bexp (I # L) (i * ‖L‖) = S₂
no goals