apply Nat.succ_le_succ
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.a
b n : ℕ
hb : 1 < b
hn : 1 ≤ n
⊢ log b (b * n / b) ≤ log b n

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