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



fn f1_remove_kth_element(list: &Vec<i32>, k: usize) -> (new_list: Vec<i32>)
    requires
        list.len() > 0,
        0 < k < list@.len(),
{
    let mut new_list = Vec::new();
    let mut index = 0;
    while index < (k - 1)
    {
        new_list.push(list[index]);
        index += 1;
    }
    let mut index = k;
    while index < list.len()
    {
        new_list.push(list[index]);
        index += 1;
    }
    new_list
}





fn f2_contains(arr: &Vec<i32>, key: i32) -> (result: bool)
{
    let mut i = 0;
    while i < arr.len()
    {
        if (arr[i] == key) {
            return true;
        }
        i += 1;
    }
    false
}

fn f2_any_value_exists(arr1: &Vec<i32>, arr2: &Vec<i32>) -> (result: bool)
{
    let mut index = 0;
    while index < arr1.len()
    {
        if (f2_contains(arr2, arr1[index])) {
            return true;
        }
        index += 1;
    }
    false
}



spec fn step1(__hp0: Seq<i32>, __hp1: usize, outp: Seq<i32>) -> bool {
    (outp == __hp0.subrange(0, __hp1 - 1 as int).add(
            __hp0.subrange(__hp1 as int, __hp0.len() as int),
        ))
}

spec fn step2(inp: Seq<i32>, p2_key: i32, outp: bool) -> bool {
    (outp == (exists|i: int| 0 <= i < inp.len() && (inp[i] == p2_key)))
}

fn chain_driver(list: &Vec<i32>, k: usize, p2_key: i32) -> (r_final: bool)
    requires
        list.len() > 0,
        0 < k < list@.len(),
    ensures
        exists|v1: Seq<i32>| #[trigger] step1(list@, k, v1) && step2(v1, p2_key, r_final),
{
    let x1 = f1_remove_kth_element(list, k);
    let x2 = f2_contains(&x1, p2_key);
    proof {
        assert(step1(list@, k, x1@));
        assert(step2(x1@, p2_key, x2));
    }
    x2
}

} // verus!