exact log_eq_of_pos (by simp) (Exponential.exponential_succ_mul_two.mpr H)
  (le_trans (by simpa using hy') le_self_add) (two_mul_add_one_lt_two_mul_of_lt hy)
case intro.intro.intro
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
y : M
pos : 0 < y
y' : M
hy' : y' ≤ y
H : Exponential (log y) y'
hy : y < 2 * y'
⊢ log (2 * y + 1) = log y + 1
no goals