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



fn f1_get_first_elements(arr: &Vec<Vec<i32>>) -> (result: Vec<i32>)
    requires
        forall|i: int| 0 <= i < arr.len() ==> #[trigger] arr[i].len() > 0,
{
    let mut first_elem_arr: Vec<i32> = Vec::new();
    let mut index = 0;
    while index < arr.len()
    {
        let seq = &arr[index];
        first_elem_arr.push(seq[0]);
        index += 1;
    }
    first_elem_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
}



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

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

fn chain_driver(arr: &Vec<Vec<i32>>) -> (r_final: Vec<i32>)
    requires
        forall|i: int| 0 <= i < arr.len() ==> #[trigger] arr[i].len() > 0,
    ensures
        exists|v1: Seq<i32>| #[trigger] step1(arr@, v1) && step2(v1, r_final@),
{
    let x1 = f1_get_first_elements(arr);
    let x2 = f2_find_negative_numbers(&x1);
    proof {
        assert(step1(arr@, x1@));
        assert(step2(x1@, x2@));
    }
    x2
}

} // verus!