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
}





pub open spec fn count_frequency_rcr(seq: Seq<i32>, key: i32) -> int
    decreases seq.len(),
{
    if seq.len() == 0 {
        0
    } else {
        count_frequency_rcr(seq.drop_last(), key) + if (seq.last() == key) {
            1 as int
        } else {
            0 as int
        }
    }
}

fn f2_count_frequency(arr: &Vec<i32>, key: i32) -> (frequency: usize)
{
    let mut index = 0;
    let mut counter = 0;
    while index < arr.len()
    {
        if (arr[index] == key) {
            counter += 1;
        }
        index += 1;
    }
    counter
}

fn f2_remove_duplicates(arr: &Vec<i32>) -> (unique_arr: Vec<i32>)
{
    let mut unique_arr: Vec<i32> = Vec::new();
    let input_len = arr.len();


    let mut index = 0;
    while index < arr.len()
    {
        if f2_count_frequency(&arr, arr[index]) == 1 {
            unique_arr.push(arr[index]);
        }
        index += 1;
    }
    unique_arr
}



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| count_frequency_rcr(inp, x) == 1))
}

fn chain_driver(nums: &Vec<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>| #[trigger] step1(nums@, v1) && step2(v1, r_final@),
{
    let x1 = f1_square_nums(nums);
    let x2 = f2_remove_duplicates(&x1);
    proof {
        assert(step1(nums@, x1@));
        assert(step2(x1@, x2@));
    }
    x2
}

} // verus!