induction' m with m ih
m : ℕ
⊢ ∀ {y : ℕ}, y < 10 ^ m → (Nat.digits 10 y).length < m + 1
case zero

⊢ ∀ {y : ℕ}, y < 10 ^ 0 → (Nat.digits 10 y).length < 0 + 1

case succ
m : ℕ
ih : ∀ {y : ℕ}, y < 10 ^ m → (Nat.digits 10 y).length < m + 1
⊢ ∀ {y : ℕ}, y < 10 ^ (m + 1) → (Nat.digits 10 y).length < m + 1 + 1