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
}





pub open spec fn count_frequency_rcr(seq: Seq<i32>, key: i32) -> int
    decreases seq.len(),
{
    if seq.len() == 0 {
        0
    } else {
        count_frequency_rcr(seq.drop_last(), key) + if (seq.last() == key) {
            1 as int
        } else {
            0 as int
        }
    }
}

fn f2_count_frequency(arr: &Vec<i32>, key: i32) -> (frequency: usize)
{
    let mut index = 0;
    let mut counter = 0;
    while index < arr.len()
    {
        if (arr[index] == key) {
            counter += 1;
        }
        index += 1;
    }
    counter
}

fn f2_remove_duplicates(arr: &Vec<i32>) -> (unique_arr: Vec<i32>)
{
    let mut unique_arr: Vec<i32> = Vec::new();
    let input_len = arr.len();


    let mut index = 0;
    while index < arr.len()
    {
        if f2_count_frequency(&arr, arr[index]) == 1 {
            unique_arr.push(arr[index]);
        }
        index += 1;
    }
    unique_arr
}



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>, p2_key: i32, outp: usize) -> bool {
    (count_frequency_rcr(inp, p2_key) == outp)
}

fn chain_driver(list: &Vec<i32>, n: usize, p2_key: i32) -> (r_final: usize)
    requires
        list@.len() > 0,
        0 < n < list@.len(),
    ensures
        exists|v1: Seq<i32>| #[trigger] step1(list@, n, v1) && step2(v1, p2_key, r_final),
{
    let x1 = f1_split_and_append(list, n);
    let x2 = f2_count_frequency(&x1, p2_key);
    proof {
        assert(step1(list@, n, x1@));
        assert(step2(x1@, p2_key, x2));
    }
    x2
}

} // verus!