exact ⟨‖S‖, by simp, rfl, ‖L‖, by simp, rfl, by simp [not_lt.mpr le]⟩
case inl.mp
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
S L i : M
le : ‖S‖ ≤ i * ‖L‖
⊢ ∃ lS ≤ S,
    lS = ‖S‖ ∧
      ∃ lL ≤ L,
        lL = ‖L‖ ∧
          (lS ≤ i * lL → 0 = 0) ∧
            (i * lL < lS →
              ∃ b ≤ S,
                Exponential (i * lL) b ∧ ∃ hL ≤ 2 * L + 1, Exponential lL hL ∧ ∃ divS ≤ S, divS = S / b ∧ 0 = divS % hL)
no goals