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



fn f1_filter_odd_numbers(arr: &Vec<u32>) -> (odd_list: Vec<u32>)
{
    let mut odd_list: Vec<u32> = Vec::new();
    let input_len = arr.len();

    let mut index = 0;
    while index < arr.len()
    {
        if (arr[index] % 2 != 0) {
            odd_list.push(arr[index]);
        }
        index += 1;
    }
    odd_list
}





fn f2_find_odd_numbers(arr: &Vec<u32>) -> (odd_numbers: Vec<u32>)
{
    let mut odd_numbers: Vec<u32> = Vec::new();
    let input_len = arr.len();

    let mut index = 0;
    while index < arr.len()
    {
        if (arr[index] % 2 != 0) {
            odd_numbers.push(arr[index]);
        }
        index += 1;
    }
    odd_numbers
}





fn f3_remove_odds(arr: &Vec<u32>) -> (even_list: Vec<u32>)
{
    let mut even_list: Vec<u32> = Vec::new();
    let input_len = arr.len();

    let mut index = 0;
    while index < arr.len()
    {
        if (arr[index] % 2 == 0) {
            even_list.push(arr[index]);
        }
        index += 1;
    }
    even_list
}



spec fn step1(__hp0: Seq<u32>, outp: Seq<u32>) -> bool {
    (outp == __hp0.filter(|x: u32| x % 2 != 0))
}

spec fn step2(inp: Seq<u32>, outp: Seq<u32>) -> bool {
    (outp == inp.filter(|x: u32| x % 2 != 0))
}

spec fn step3(inp: Seq<u32>, outp: Seq<u32>) -> bool {
    (outp == inp.filter(|x: u32| x % 2 == 0))
}

fn chain_driver(arr: &Vec<u32>) -> (r_final: Vec<u32>)
    ensures
        exists|v1: Seq<u32>, v2: Seq<u32>| #[trigger] step1(arr@, v1) && #[trigger] step2(v1, v2) && step3(v2, r_final@),
{
    let x1 = f1_filter_odd_numbers(arr);
    let x2 = f2_find_odd_numbers(&x1);
    let x3 = f3_remove_odds(&x2);
    proof {
        assert(step1(arr@, x1@));
        assert(step2(x1@, x2@));
        assert(step3(x2@, x3@));
    }
    x3
}

} // verus!