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



fn f1_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
}





fn f2_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 f2_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 (f2_contains(arr2, arr1[index]) && !f2_contains(&output_arr, arr1[index])) {
            output_arr.push(arr1[index]);
            
        }
        index += 1;
    }
    output_arr
}



spec fn step1(__hp0: Seq<i32>, outp: Seq<i32>) -> bool {
    (outp == __hp0.filter(|x: i32| x < 0))
}

spec fn step2(inp: Seq<i32>, p2_key: i32, outp: bool) -> bool {
    (outp == (exists|i: int| 0 <= i < inp.len() && (inp[i] == p2_key)))
}

fn chain_driver(arr: &Vec<i32>, p2_key: i32) -> (r_final: bool)
    ensures
        exists|v1: Seq<i32>| #[trigger] step1(arr@, v1) && step2(v1, p2_key, r_final),
{
    let x1 = f1_find_negative_numbers(arr);
    let x2 = f2_contains(&x1, p2_key);
    proof {
        assert(step1(arr@, x1@));
        assert(step2(x1@, p2_key, x2));
    }
    x2
}

} // verus!