exact lt_of_le_of_lt (le_trans (le_pair_left i x) (le_log_of_mem hix))
  (by simp [log_two_mul_add_one_of_pos (pos_of_nonempty hix)])
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* 𝐈𝚺₁
s i x : M
hix : ⟪i, x⟫ ∈ s
⊢ i < log (2 * s + 1)
no goals