have hki : i = x.start + k := by
  rw [Nat.add_comm, Nat.sub_add_cancel ge_start]
case zero
α : Type u
lt : α → α → Bool
x✝ : Subarray α
n : Nat
y : Array α
i : Nat
x : Subarray α
ge_start : x.start ≤ i
lt_stop : i < x.stop
k : Nat := i - x.start
⊢ ∃ k hk, x.as[i] = x[k]
case zero
α : Type u
lt : α → α → Bool
x✝ : Subarray α
n : Nat
y : Array α
i : Nat
x : Subarray α
ge_start : x.start ≤ i
lt_stop : i < x.stop
k : Nat := i - x.start
hki : i = x.start + k
⊢ ∃ k hk, x.as[i] = x[k]