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



fn f1_element_wise_module(arr1: &Vec<u32>, arr2: &Vec<u32>) -> (result: Vec<u32>)
    requires
        arr1.len() == arr2.len(),
        forall|i: int| 0 <= i < arr2.len() ==> arr2[i] != 0,
        forall|i: int|
            (0 <= i < arr1.len()) ==> (i32::MIN <= #[trigger] (arr1[i] % arr2[i]) <= i32::MAX),
{
    let mut output_arr = Vec::with_capacity(arr1.len());
    let mut index = 0;
    while index < arr1.len()
    {
        output_arr.push((arr1[index] % arr2[index]));
        index += 1;
    }
    output_arr
}





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
}



spec fn step1(__hp0: Seq<u32>, __hp1: Seq<u32>, outp: Seq<u32>) -> bool {
    (outp.len() == __hp0.len())
    && (forall|i: int|
            0 <= i < outp.len() ==> #[trigger] outp[i] == #[trigger] (__hp0[i] % __hp1[i]))
}

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

fn chain_driver(arr1: &Vec<u32>, arr2: &Vec<u32>) -> (r_final: Vec<u32>)
    requires
        arr1.len() == arr2.len(),
        forall|i: int| 0 <= i < arr2.len() ==> arr2[i] != 0,
        forall|i: int|
            (0 <= i < arr1.len()) ==> (i32::MIN <= #[trigger] (arr1[i] % arr2[i]) <= i32::MAX),
    ensures
        exists|v1: Seq<u32>| #[trigger] step1(arr1@, arr2@, v1) && step2(v1, r_final@),
{
    let x1 = f1_element_wise_module(arr1, arr2);
    let x2 = f2_find_odd_numbers(&x1);
    proof {
        assert(step1(arr1@, arr2@, x1@));
        assert(step2(x1@, x2@));
    }
    x2
}

} // verus!