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predicate exist1(a: array<int>, x:int)
reads a;
{
multiset(a[..])[x] == 1
}
predicate exist2(a: array<int>, x:int)
reads a;
{
multiset(a[..])[x] >= 2
}
predicate tail(a: array<int>)
reads a;
{
forall i : int :: 0 <= i < a.Length ==>
(a[i] != 0 || multiset(a[i..])[0] == a.Length - i)
}
method test1()
{
var a := new int[3][1, 2, 2];
assert a[..] == [1, 2, 2];
assert !exist1(a, 0);
assert exist1(a, 1);
assert !exist1(a, 2);
}
method test2()
{
var a := new int[6][1, 2, 2, 3, 3, 3];
assert a[..] == [1, 2, 2, 3, 3, 3];
assert !exist2(a, 0);
assert !exist2(a, 1);
assert exist2(a, 2);
assert exist2(a, 3);
}
method test3()
{
var a := new int[4][1, 2, 3, 0];
assert a[..] == [1, 2, 3, 0];
assert tail(a);
// "no zeros is vacuously true"
var b := new int[4][1, 2, 3, 4];
assert b[..] == [1, 2, 3, 4];
assert tail(b);
var c := new int[6][1, 2, 3, 0, 5, 6];
assert c[..] == [1, 2, 3, 0, 5, 6];
assert c[3..] == [0, 5, 6];
assert !tail(c);
var d := new int[6][1, 2, 0, 0, 5, 0];
assert d[..] == [1, 2, 0, 0, 5, 0];
assert d[2..] == [0, 0, 5, 0];
assert !tail(d);
}
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