use vstd::prelude::*;
fn main() {}
verus!{



fn f1_split_and_append(list: &Vec<i32>, n: usize) -> (new_list: Vec<i32>)
    requires
        list@.len() > 0,
        0 < n < list@.len(),
{
    let mut new_list = Vec::new();
    let mut index = n;
    while index < list.len()
    {
        new_list.push(list[index]);
        index += 1;
    }
    let mut index = 0;
    while index < n
    {
        new_list.push(list[index]);
        index += 1;
    }
    new_list
}





fn f2_find_negative_numbers(arr: &Vec<i32>) -> (negative_list: Vec<i32>)
{
    let mut negative_list: Vec<i32> = Vec::new();
    let input_len = arr.len();

    let mut index = 0;
    while index < arr.len()
    {
        if (arr[index] < 0) {
            negative_list.push(arr[index]);
        }
        index += 1;
    }
    negative_list
}





fn f3_has_only_one_distinct_element(arr: &Vec<i32>) -> (result: bool)
{
    if arr.len() <= 1 {
        return true;
    }
    let mut index = 1;
    while index < arr.len()
    {
        if arr[0] != arr[index] {
            return false;
        }
        index += 1;
    }
    true
}



spec fn step1(__hp0: Seq<i32>, __hp1: usize, outp: Seq<i32>) -> bool {
    (outp == __hp0.subrange(__hp1 as int, __hp0.len() as int).add(__hp0.subrange(0, __hp1 as int)))
}

spec fn step2(inp: Seq<i32>, outp: Seq<i32>) -> bool {
    (outp == inp.filter(|x: i32| x < 0))
}

spec fn step3(inp: Seq<i32>, outp: bool) -> bool {
    (outp == (forall|i: int| 1 <= i < inp.len() ==> inp[0] == #[trigger] inp[i]))
}

fn chain_driver(list: &Vec<i32>, n: usize) -> (r_final: bool)
    requires
        list@.len() > 0,
        0 < n < list@.len(),
    ensures
        exists|v1: Seq<i32>, v2: Seq<i32>| #[trigger] step1(list@, n, v1) && #[trigger] step2(v1, v2) && step3(v2, r_final),
{
    let x1 = f1_split_and_append(list, n);
    let x2 = f2_find_negative_numbers(&x1);
    let x3 = f3_has_only_one_distinct_element(&x2);
    proof {
        assert(step1(list@, n, x1@));
        assert(step2(x1@, x2@));
        assert(step3(x2@, x3));
    }
    x3
}

} // verus!