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



proof fn f1_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 f1_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 f1_difference(arr1: &Vec<i32>, arr2: &Vec<i32>) -> (result: Vec<i32>)
{
    let mut result = Vec::new();

    let mut index = 0;
    while index < arr1.len()
    {
        if (!f1_contains(arr2, arr1[index]) && !f1_contains(&result, arr1[index])) {
            
            result.push(arr1[index]);
        }
        index += 1;
    }
    index = 0;
    while index < arr2.len()
    {
        if (!f1_contains(arr1, arr2[index]) && !f1_contains(&result, arr2[index])) {
            
            result.push(arr2[index]);
        }
        index += 1;
    }
    result
}





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
}



spec fn step1(__hp0: Seq<i32>, __hp1: Seq<i32>, outp: Seq<i32>) -> bool {
    (forall|i: int|
            0 <= i < __hp0.len() ==> (!__hp1.contains(#[trigger] __hp0[i]) ==> outp.contains(
                __hp0[i],
            )))
    && (forall|i: int|
            0 <= i < __hp1.len() ==> (!__hp0.contains(#[trigger] __hp1[i]) ==> outp.contains(
                __hp1[i],
            )))
    && (forall|i: int, j: int|
            0 <= i < j < outp.len() ==> #[trigger] outp[i] != #[trigger] outp[j])
}

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

fn chain_driver(arr1: &Vec<i32>, arr2: &Vec<i32>) -> (r_final: Vec<i32>)
    ensures
        exists|v1: Seq<i32>| #[trigger] step1(arr1@, arr2@, v1) && step2(v1, r_final@),
{
    let x1 = f1_difference(arr1, arr2);
    let x2 = f2_find_negative_numbers(&x1);
    proof {
        assert(step1(arr1@, arr2@, x1@));
        assert(step2(x1@, x2@));
    }
    x2
}

} // verus!