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



fn f1_reverse_to_k(list: &Vec<i32>, n: usize) -> (reversed_list: Vec<i32>)
    requires
        list@.len() > 0,
        0 < n < list@.len(),
{
    let mut reversed_list = Vec::new();
    let mut index = 0;
    while index < n
    {
        reversed_list.push(list[n - 1 - index]);
        index += 1;
    }
    index = n;
    while index < list.len()
    {
        reversed_list.push(list[index]);
        index += 1;
    }
    reversed_list
}





fn f2_insert_before_each(arr: &Vec<i32>, elem: i32) -> (result: Vec<i32>)
{
    let mut result: Vec<i32> = Vec::new();
    let mut index = 0;

    while index < arr.len()
    {
        result.push(elem);
        result.push(arr[index]);
        index += 1;
    }
    result
}





fn f3_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 f3_intersection(arr1: &Vec<i32>, arr2: &Vec<i32>) -> (result: Vec<i32>)
{
    let mut output_arr = Vec::new();

    let mut index = 0;
    while index < arr1.len()
    {
        if (f3_contains(arr2, arr1[index]) && !f3_contains(&output_arr, arr1[index])) {
            output_arr.push(arr1[index]);
            
        }
        index += 1;
    }
    output_arr
}



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

spec fn step2(inp: Seq<i32>, p2_elem: i32, outp: Seq<i32>) -> bool {
    (outp.len() == (2 * inp.len()))
    && (forall|k: int| 0 <= k < inp.len() ==> #[trigger] outp[2 * k] == p2_elem)
    && (forall|k: int| 0 <= k < inp.len() ==> #[trigger] outp[2 * k + 1] == inp[k])
}

spec fn step3(inp: Seq<i32>, p3_key: i32, outp: bool) -> bool {
    (outp == (exists|i: int| 0 <= i < inp.len() && (inp[i] == p3_key)))
}

fn chain_driver(list: &Vec<i32>, n: usize, p2_elem: i32, p3_key: i32) -> (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, p2_elem, v2) && step3(v2, p3_key, r_final),
{
    let x1 = f1_reverse_to_k(list, n);
    let x2 = f2_insert_before_each(&x1, p2_elem);
    let x3 = f3_contains(&x2, p3_key);
    proof {
        assert(step1(list@, n, x1@));
        assert(step2(x1@, p2_elem, x2@));
        assert(step3(x2@, p3_key, x3));
    }
    x3
}

} // verus!