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



fn f1_element_wise_division(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|m: int|
            0 <= m < arr1.len() ==> (u32::MIN <= #[trigger] arr1[m] / #[trigger] arr2[m]
                <= u32::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_even_numbers(arr: &Vec<u32>) -> (even_numbers: Vec<u32>)
{
    let mut even_numbers: Vec<u32> = Vec::new();
    let input_len = arr.len();

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





fn f3_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 f4_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 f5_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 f6_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
}





fn f7_find_even_numbers(arr: &Vec<u32>) -> (even_numbers: Vec<u32>)
{
    let mut even_numbers: Vec<u32> = Vec::new();
    let input_len = arr.len();

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





fn f8_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
}





fn f9_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
}





spec fn f10_is_even(n: u32) -> bool {
    (n % 2) == 0
}

fn f10_is_product_even(arr: &Vec<u32>) -> (result: bool)
{
    let mut index = 0;
    while index < arr.len()
    {
        if (arr[index] % 2 == 0) {
            return true;
        }
        index += 1;
    }
    false
}



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))
}

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

spec fn step4(inp: Seq<u32>, outp: Seq<u32>) -> bool {
    (outp == inp.filter(|x: u32| x % 2 != 0))
}

spec fn step5(inp: Seq<u32>, outp: Seq<u32>) -> bool {
    (outp == inp.filter(|x: u32| x % 2 != 0))
}

spec fn step6(inp: Seq<u32>, outp: Seq<u32>) -> bool {
    (outp == inp.filter(|x: u32| x % 2 == 0))
}

spec fn step7(inp: Seq<u32>, outp: Seq<u32>) -> bool {
    (outp == inp.filter(|x: u32| x % 2 == 0))
}

spec fn step8(inp: Seq<u32>, outp: Seq<u32>) -> bool {
    (outp == inp.filter(|x: u32| x % 2 == 0))
}

spec fn step9(inp: Seq<u32>, outp: Seq<u32>) -> bool {
    (outp == inp.filter(|x: u32| x % 2 != 0))
}

spec fn step10(inp: Seq<u32>, outp: bool) -> bool {
    (outp <==> (exists|k: int| 0 <= k < inp.len() && f10_is_even(#[trigger] inp[k])))
}

fn chain_driver(arr1: &Vec<u32>, arr2: &Vec<u32>) -> (r_final: bool)
    requires
        arr1.len() == arr2.len(),
        forall|i: int| 0 <= i < arr2.len() ==> arr2[i] != 0,
        forall|m: int|
            0 <= m < arr1.len() ==> (u32::MIN <= #[trigger] arr1[m] / #[trigger] arr2[m]
                <= u32::MAX),
    ensures
        exists|v1: Seq<u32>, v2: Seq<u32>, v3: Seq<u32>, v4: Seq<u32>, v5: Seq<u32>, v6: Seq<u32>, v7: Seq<u32>, v8: Seq<u32>, v9: Seq<u32>| #[trigger] step1(arr1@, arr2@, v1) && #[trigger] step2(v1, v2) && #[trigger] step3(v2, v3) && #[trigger] step4(v3, v4) && #[trigger] step5(v4, v5) && #[trigger] step6(v5, v6) && #[trigger] step7(v6, v7) && #[trigger] step8(v7, v8) && #[trigger] step9(v8, v9) && step10(v9, r_final),
{
    let x1 = f1_element_wise_division(arr1, arr2);
    let x2 = f2_find_even_numbers(&x1);
    let x3 = f3_find_odd_numbers(&x2);
    let x4 = f4_filter_odd_numbers(&x3);
    let x5 = f5_find_odd_numbers(&x4);
    let x6 = f6_remove_odds(&x5);
    let x7 = f7_find_even_numbers(&x6);
    let x8 = f8_remove_odds(&x7);
    let x9 = f9_filter_odd_numbers(&x8);
    let x10 = f10_is_product_even(&x9);
    proof {
        assert(step1(arr1@, arr2@, x1@));
        assert(step2(x1@, x2@));
        assert(step3(x2@, x3@));
        assert(step4(x3@, x4@));
        assert(step5(x4@, x5@));
        assert(step6(x5@, x6@));
        assert(step7(x6@, x7@));
        assert(step8(x7@, x8@));
        assert(step9(x8@, x9@));
        assert(step10(x9@, x10));
    }
    x10
}

} // verus!