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



fn f1_min_sublist(seq: &Vec<Vec<i32>>) -> (min_list: &Vec<i32>)
    requires
        seq.len() > 0,
{
    let mut min_list = &seq[0];
    let mut index = 1;

    while index < seq.len()
    {
        if ((seq[index]).len() < min_list.len()) {
            min_list = &seq[index];
        }
        index += 1;
    }
    min_list
}





fn f2_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 f2_any_value_exists(arr1: &Vec<i32>, arr2: &Vec<i32>) -> (result: bool)
{
    let mut index = 0;
    while index < arr1.len()
    {
        if (f2_contains(arr2, arr1[index])) {
            return true;
        }
        index += 1;
    }
    false
}



spec fn step1(__hp0: Seq<Vec<i32>>, outp: Seq<i32>) -> bool {
    (forall|k: int| 0 <= k < __hp0.len() ==> outp.len() <= #[trigger] (__hp0[k]).len())
    && (exists|k: int| 0 <= k < __hp0.len() && outp =~= #[trigger] (__hp0[k]@))
}

spec fn step2(inp: Seq<i32>, p2_key: i32, outp: bool) -> bool {
    (outp == (exists|i: int| 0 <= i < inp.len() && (inp[i] == p2_key)))
}

fn chain_driver(seq: &Vec<Vec<i32>>, p2_key: i32) -> (r_final: bool)
    requires
        seq.len() > 0,
    ensures
        exists|v1: Seq<i32>| #[trigger] step1(seq@, v1) && step2(v1, p2_key, r_final),
{
    let x1 = f1_min_sublist(seq);
    let x2 = f2_contains(x1, p2_key);
    proof {
        assert(step1(seq@, x1@));
        assert(step2(x1@, p2_key, x2));
    }
    x2
}

} // verus!