rw [← Nat.sub_add_comm, add_comm, Nat.sub_add_comm]
case h
a b x : ℕ
⊢ (x + 1) ^ (a + b) - (x + 1) ^ a + (x + 1 + 1) ^ a ≤ (x + 1 + 1) ^ (a + b)
case h
a b x : ℕ
⊢ (x + 1 + 1) ^ a - (x + 1) ^ a + (x + 1) ^ (a + b) ≤ (x + 1 + 1) ^ (a + b)

case h
a b x : ℕ
⊢ (x + 1) ^ a ≤ (x + 1 + 1) ^ a

case h
a b x : ℕ
⊢ (x + 1) ^ a ≤ (x + 1) ^ (a + b)