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



fn f1_replace_last_element(first: &Vec<i32>, second: &Vec<i32>) -> (replaced_list: Vec<i32>)
    requires
        first.len() > 0,
{
    let mut replaced_list = Vec::new();
    let first_end = first.len() - 1;
    let mut index = 0;

    while index < first_end
    {
        replaced_list.push(first[index]);
        index += 1;
    }
    index = 0;
    while index < second.len()
    {
        replaced_list.push(second[index]);
        index += 1;
    }
    replaced_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
}





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 f3_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 f3_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 f3_count_frequency(&arr, arr[index]) == 1 {
            unique_arr.push(arr[index]);
        }
        index += 1;
    }
    unique_arr
}



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

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: usize) -> bool {
    (count_frequency_rcr(inp, p3_key) == outp)
}

fn chain_driver(first: &Vec<i32>, second: &Vec<i32>, p2_elem: i32, p3_key: i32) -> (r_final: usize)
    requires
        first.len() > 0,
    ensures
        exists|v1: Seq<i32>, v2: Seq<i32>| #[trigger] step1(first@, second@, v1) && #[trigger] step2(v1, p2_elem, v2) && step3(v2, p3_key, r_final),
{
    let x1 = f1_replace_last_element(first, second);
    let x2 = f2_insert_before_each(&x1, p2_elem);
    let x3 = f3_count_frequency(&x2, p3_key);
    proof {
        assert(step1(first@, second@, x1@));
        assert(step2(x1@, p2_elem, x2@));
        assert(step3(x2@, p3_key, x3));
    }
    x3
}

} // verus!