have h3 : (Nat.digits 10 y).length ≤ m := by
  have h4 := lemma2 h1
  exact Nat.le_of_lt_succ h4
case succ
m y : ℕ
h1 : y < 10 ^ m
x : ℕ
⊢ (Nat.digits 10 ((x + 1) * 10 ^ m + y)).sum = (Nat.digits 10 ((x + 1) * 10 ^ m)).sum + (Nat.digits 10 y).sum
case succ
m y : ℕ
h1 : y < 10 ^ m
x : ℕ
h3 : (Nat.digits 10 y).length ≤ m
⊢ (Nat.digits 10 ((x + 1) * 10 ^ m + y)).sum = (Nat.digits 10 ((x + 1) * 10 ^ m)).sum + (Nat.digits 10 y).sum