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method FindZero(a: array<int>) returns (r: int)
requires a != null && forall i :: 0 <= i && i < a.Length ==> 0 <= a[i];
requires forall i :: 0 <= i && i+1 < a.Length ==> a[i]-1 <= a[i+1];
ensures 0 <= r ==> r < a.Length && a[r] == 0;
ensures r < 0 ==> forall i :: 0 <= i && i < a.Length ==> a[i] != 0;
{
var n := 0;
while (n < a.Length)
invariant forall i :: 0 <= i && i < n && i < a.Length ==> a[i] != 0;
{
if (a[n] == 0) { r := n; return; }
Lemma(a, n, a[n]);
n := n + a[n];
}
r := -1;
}
ghost method Lemma(a: array<int>, k: int, m: int)
requires a != null && forall i :: 0 <= i && i < a.Length ==> 0 <= a[i];
requires forall i :: 0 <= i && i+1 < a.Length ==> a[i]-1 <= a[i+1];
requires 0 <= k;
requires k < a.Length ==> m <= a[k];
ensures forall i :: k <= i && i < k+m && i < a.Length ==> a[i] != 0;
decreases m;
{
if (0 < m && k < a.Length) {
assert a[k] != 0;
Lemma(a, k+1, m-1);
}
}
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