apply Nat.zero_lt_succ _
case h.hx
a b y x : ℕ
⊢ x + 1 > 0

case h.a
a b y x : ℕ
⊢ a ≤ a + b

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

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