apply Nat.pow_le_pow_right
a b y x : ℕ
⊢ (x + 1 + y) ^ a ≤ (x + 1 + y) ^ (a + b)

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

case h
a b y x : ℕ
⊢ (x + 1) ^ a ≤ (x + 1 + y) ^ a
case hx
a b y x : ℕ
⊢ x + 1 + y > 0

case a
a b y x : ℕ
⊢ a ≤ a + b

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

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