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



fn f1_add_list(arr1: &Vec<i32>, arr2: &Vec<i32>) -> (result: Vec<i32>)
    requires
        arr1.len() == arr2.len(),
        forall|i: int|
            (0 <= i < arr1.len()) ==> (i32::MIN <= #[trigger] (arr1[i] + arr2[i]) <= i32::MAX),
{
    let mut output_arr = Vec::with_capacity(arr1.len());
    let mut index = 0;
    while index < arr1.len()
    {
        output_arr.push((arr1[index] + arr2[index]));
        index += 1;
    }
    output_arr
}





fn f2_find_negative_numbers(arr: &Vec<i32>) -> (negative_list: Vec<i32>)
{
    let mut negative_list: Vec<i32> = Vec::new();
    let input_len = arr.len();

    let mut index = 0;
    while index < arr.len()
    {
        if (arr[index] < 0) {
            negative_list.push(arr[index]);
        }
        index += 1;
    }
    negative_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 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.len() == __hp0.len())
    && (forall|i: int|
            0 <= i < outp.len() ==> #[trigger] outp[i] == #[trigger] (__hp0[i] + __hp1[i]))
}

spec fn step2(inp: Seq<i32>, outp: Seq<i32>) -> bool {
    (outp == inp.filter(|x: i32| x < 0))
}

spec fn step3(inp: Seq<i32>, p3_key: i32, outp: usize) -> bool {
    (count_frequency_rcr(inp, p3_key) == outp)
}

fn chain_driver(arr1: &Vec<i32>, arr2: &Vec<i32>, p3_key: i32) -> (r_final: usize)
    requires
        arr1.len() == arr2.len(),
        forall|i: int|
            (0 <= i < arr1.len()) ==> (i32::MIN <= #[trigger] (arr1[i] + arr2[i]) <= i32::MAX),
    ensures
        exists|v1: Seq<i32>, v2: Seq<i32>| #[trigger] step1(arr1@, arr2@, v1) && #[trigger] step2(v1, v2) && step3(v2, p3_key, r_final),
{
    let x1 = f1_add_list(arr1, arr2);
    let x2 = f2_find_negative_numbers(&x1);
    let x3 = f3_count_frequency(&x2, p3_key);
    proof {
        assert(step1(arr1@, arr2@, x1@));
        assert(step2(x1@, x2@));
        assert(step3(x2@, p3_key, x3));
    }
    x3
}

} // verus!