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



fn f1_contains(arr: &Vec<i32>, key: i32) -> (result: bool)
{
    let mut i = 0;
    while i < arr.len()
    {
        if (arr[i] == key) {
            return true;
        }
        i += 1;
    }
    false
}

fn f1_shared_elements(list1: &Vec<i32>, list2: &Vec<i32>) -> (shared: Vec<i32>)
{
    let mut shared = Vec::new();

    let mut index = 0;
    while index < list1.len()
    {
        if (f1_contains(list2, list1[index]) && !f1_contains(&shared, list1[index])) {
            shared.push(list1[index]);
            
        }
        index += 1
    }
    shared
}





fn f2_insert_before_each(arr: &Vec<i32>, elem: i32) -> (result: Vec<i32>)
{
    let mut result: Vec<i32> = Vec::new();
    let mut index = 0;

    while index < arr.len()
    {
        result.push(elem);
        result.push(arr[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 f3_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 f3_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 f3_count_frequency(&arr, arr[index]) == 1 {
            unique_arr.push(arr[index]);
        }
        index += 1;
    }
    unique_arr
}



spec fn step1(__hp0: Seq<i32>, __hp1: Seq<i32>, outp: Seq<i32>) -> bool {
    (forall|i: int|
            0 <= i < outp.len() ==> (__hp0.contains(#[trigger] outp[i]) && __hp1.contains(
                #[trigger] outp[i],
            )))
    && (forall|i: int, j: int| 0 <= i < j < outp.len() ==> outp[i] != outp[j])
}

spec fn step2(inp: Seq<i32>, p2_elem: i32, outp: Seq<i32>) -> bool {
    (outp.len() == (2 * inp.len()))
    && (forall|k: int| 0 <= k < inp.len() ==> #[trigger] outp[2 * k] == p2_elem)
    && (forall|k: int| 0 <= k < inp.len() ==> #[trigger] outp[2 * k + 1] == inp[k])
}

spec fn step3(inp: Seq<i32>, outp: Seq<i32>) -> bool {
    (outp == inp.filter(|x: i32| count_frequency_rcr(inp, x) == 1))
}

fn chain_driver(list1: &Vec<i32>, list2: &Vec<i32>, p2_elem: i32) -> (r_final: Vec<i32>)
    ensures
        exists|v1: Seq<i32>, v2: Seq<i32>| #[trigger] step1(list1@, list2@, v1) && #[trigger] step2(v1, p2_elem, v2) && step3(v2, r_final@),
{
    let x1 = f1_shared_elements(list1, list2);
    let x2 = f2_insert_before_each(&x1, p2_elem);
    let x3 = f3_remove_duplicates(&x2);
    proof {
        assert(step1(list1@, list2@, x1@));
        assert(step2(x1@, p2_elem, x2@));
        assert(step3(x2@, x3@));
    }
    x3
}

} // verus!