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
}





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
}





proof fn f3_lemma_vec_push<T>(vec: Seq<T>, i: T, l: usize)
    requires
        l == vec.len(),
    ensures
        forall|k: int| 0 <= k < vec.len() ==> #[trigger] vec[k] == vec.push(i)[k],
        vec.push(i).index(l as int) == i,
{
}

fn f3_contains(arr: &Vec<i32>, key: i32) -> (result: bool)
{
    let mut index = 0;
    while index < arr.len()
    {
        if (arr[index] == key) {
            return true;
        }
        index += 1;
    }
    false
}

fn f3_difference(arr1: &Vec<i32>, arr2: &Vec<i32>) -> (result: Vec<i32>)
{
    let mut result = Vec::new();

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



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>, outp: Seq<i32>) -> bool {
    (outp == inp.filter(|x: i32| count_frequency_rcr(inp, x) == 1))
}

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>, k: usize, p3_key: i32) -> (r_final: bool)
    requires
        list.len() > 0,
        0 < k < list@.len(),
    ensures
        exists|v1: Seq<i32>, v2: Seq<i32>| #[trigger] step1(list@, k, v1) && #[trigger] step2(v1, v2) && step3(v2, p3_key, r_final),
{
    let x1 = f1_remove_kth_element(list, k);
    let x2 = f2_remove_duplicates(&x1);
    let x3 = f3_contains(&x2, p3_key);
    proof {
        assert(step1(list@, k, x1@));
        assert(step2(x1@, x2@));
        assert(step3(x2@, p3_key, x3));
    }
    x3
}

} // verus!