apply le_of_eq_of_le
case a.h₁
b n : ℕ
hb : 1 < b
hn : 1 ≤ n
⊢ b ≤ b * n

case a.h₂
b n : ℕ
hb : 1 < b
hn : 1 ≤ n
⊢ log b (b * n / b) + 1 ≤ log b n + 1

case a
b n : ℕ
hb : 1 < b
hn : 1 ≤ n
⊢ log b n + 1 ≤ log b (b * n)
case a.h₁.h₁
b n : ℕ
hb : 1 < b
hn : 1 ≤ n
⊢ b = ?a.h₁.b✝

case a.h₁.h₂
b n : ℕ
hb : 1 < b
hn : 1 ≤ n
⊢ ?a.h₁.b✝ ≤ b * n

case a.h₁.b
b n : ℕ
hb : 1 < b
hn : 1 ≤ n
⊢ ℕ

case a.h₂
b n : ℕ
hb : 1 < b
hn : 1 ≤ n
⊢ log b (b * n / b) + 1 ≤ log b n + 1

case a
b n : ℕ
hb : 1 < b
hn : 1 ≤ n
⊢ log b n + 1 ≤ log b (b * n)