calc
  i ≤ log (a + b) := le_trans (le_log_of_mem hi) (log_monotone (by simp))
  _ < log (2 * (a + b)) := by simp [log_two_mul_of_pos (show 0 < a + b from by simp [pos_of_nonempty hi])]
  _ ≤ log (2 * (a + b) + 1) := log_monotone (by simp)
case inl
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
a b i : M
hi : i ∈ a
⊢ i < log (2 * (a + b) + 1)
no goals