apply mul_le_mul (le_refl _) hn (zero_le _) (zero_le _)
case a.h₁.h₂
b n : ℕ
hb : 1 < b
hn : 1 ≤ n
⊢ b * 1 ≤ 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.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)