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



fn f1_square_nums(nums: &Vec<i32>) -> (squared: Vec<i32>)
    requires
        forall|k: int|
            0 <= k < nums.len() ==> (0 <= #[trigger] nums[k] * #[trigger] nums[k] < i32::MAX),
{
    let mut result: Vec<i32> = Vec::new();
    let mut index = 0;

    while index < nums.len()
    {
        result.push(nums[index] * nums[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
}





fn f3_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
}



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

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

spec fn step3(inp: Seq<i32>, p3_elem: i32, outp: Seq<i32>) -> bool {
    (outp.len() == (2 * inp.len()))
    && (forall|k: int| 0 <= k < inp.len() ==> #[trigger] outp[2 * k] == p3_elem)
    && (forall|k: int| 0 <= k < inp.len() ==> #[trigger] outp[2 * k + 1] == inp[k])
}

fn chain_driver(nums: &Vec<i32>, p3_elem: i32) -> (r_final: Vec<i32>)
    requires
        forall|k: int|
            0 <= k < nums.len() ==> (0 <= #[trigger] nums[k] * #[trigger] nums[k] < i32::MAX),
    ensures
        exists|v1: Seq<i32>, v2: Seq<i32>| #[trigger] step1(nums@, v1) && #[trigger] step2(v1, v2) && step3(v2, p3_elem, r_final@),
{
    let x1 = f1_square_nums(nums);
    let x2 = f2_find_negative_numbers(&x1);
    let x3 = f3_insert_before_each(&x2, p3_elem);
    proof {
        assert(step1(nums@, x1@));
        assert(step2(x1@, x2@));
        assert(step3(x2@, p3_elem, x3@));
    }
    x3
}

} // verus!