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



fn f1_interleave(s1: &Vec<i32>, s2: &Vec<i32>, s3: &Vec<i32>) -> (res: Vec<i32>)
    requires
        s1@.len() == s2@.len() && s2@.len() == s3@.len(),
        0 <= (s1@.len() * 3) <= i32::MAX,
{
    let new_seq_len = s1.len() * 3;
    let mut output_seq = Vec::with_capacity(new_seq_len);
    let mut index = 0;

    while index < s1.len()
    {
        output_seq.push(s1[index]);
        output_seq.push(s2[index]);
        output_seq.push(s3[index]);
        index += 1;
    }
    output_seq
}





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
}





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

fn f3_remove_elements(arr1: &Vec<i32>, arr2: &Vec<i32>) -> (result: Vec<i32>)
{
    let mut output_str = Vec::new();
    let mut index: usize = 0;

    while index < arr1.len()
    {
        if (!f3_contains(arr2, arr1[index])) {
            
            output_str.push(arr1[index]);
        }
        index += 1;
    }
    output_str
}



spec fn step1(__hp0: Seq<i32>, __hp1: Seq<i32>, __hp2: Seq<i32>, outp: Seq<i32>) -> bool {
    (outp.len() == __hp0.len() * 3)
    && (forall|i: int|
            0 <= i < __hp0.len() ==> (outp[3 * i] == __hp0[i] && outp[3 * i + 1] == __hp1[i] && outp[3 * i + 2]
                == __hp2[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: bool) -> bool {
    (outp <==> (exists|i: int| 0 <= i < inp.len() && (inp[i] == p3_key)))
}

fn chain_driver(s1: &Vec<i32>, s2: &Vec<i32>, s3: &Vec<i32>, p3_key: i32) -> (r_final: bool)
    requires
        s1@.len() == s2@.len() && s2@.len() == s3@.len(),
        0 <= (s1@.len() * 3) <= i32::MAX,
    ensures
        exists|v1: Seq<i32>, v2: Seq<i32>| #[trigger] step1(s1@, s2@, s3@, v1) && #[trigger] step2(v1, v2) && step3(v2, p3_key, r_final),
{
    let x1 = f1_interleave(s1, s2, s3);
    let x2 = f2_find_negative_numbers(&x1);
    let x3 = f3_contains(&x2, p3_key);
    proof {
        assert(step1(s1@, s2@, s3@, x1@));
        assert(step2(x1@, x2@));
        assert(step3(x2@, p3_key, x3));
    }
    x3
}

} // verus!