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



fn f1_interleave(s1: &Vec<i32>, s2: &Vec<i32>, s3: &Vec<i32>) -> (res: Vec<i32>)
    requires
        s1@.len() == s2@.len() && s2@.len() == s3@.len(),
        0 <= (s1@.len() * 3) <= i32::MAX,
{
    let new_seq_len = s1.len() * 3;
    let mut output_seq = Vec::with_capacity(new_seq_len);
    let mut index = 0;

    while index < s1.len()
    {
        output_seq.push(s1[index]);
        output_seq.push(s2[index]);
        output_seq.push(s3[index]);
        index += 1;
    }
    output_seq
}





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>, __hp1: Seq<i32>, __hp2: Seq<i32>, outp: Seq<i32>) -> bool {
    (outp.len() == __hp0.len() * 3)
    && (forall|i: int|
            0 <= i < __hp0.len() ==> (outp[3 * i] == __hp0[i] && outp[3 * i + 1] == __hp1[i] && outp[3 * i + 2]
                == __hp2[i]))
}

spec fn step2(inp: Seq<i32>, p2_key: i32, outp: usize) -> bool {
    (count_frequency_rcr(inp, p2_key) == outp)
}

fn chain_driver(s1: &Vec<i32>, s2: &Vec<i32>, s3: &Vec<i32>, p2_key: i32) -> (r_final: usize)
    requires
        s1@.len() == s2@.len() && s2@.len() == s3@.len(),
        0 <= (s1@.len() * 3) <= i32::MAX,
    ensures
        exists|v1: Seq<i32>| #[trigger] step1(s1@, s2@, s3@, v1) && step2(v1, p2_key, r_final),
{
    let x1 = f1_interleave(s1, s2, s3);
    let x2 = f2_count_frequency(&x1, p2_key);
    proof {
        assert(step1(s1@, s2@, s3@, x1@));
        assert(step2(x1@, p2_key, x2));
    }
    x2
}

} // verus!