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



fn f1_max_length_list(seq: &Vec<Vec<i32>>) -> (max_list: &Vec<i32>)
    requires
        seq.len() > 0,
{
    let mut max_list = &seq[0];
    let mut index = 1;

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





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
}





fn f3_is_greater(arr: &Vec<i32>, number: i32) -> (result: bool)
{
    let mut i = 0;
    while i < arr.len()
    {
        if number <= arr[i] {
            return false;
        }
        i += 1;
    }
    true
}



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_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>, p3_number: i32, outp: bool) -> bool {
    (outp == (forall|i: int| 0 <= i < inp.len() ==> p3_number > inp[i]))
}

fn chain_driver(seq: &Vec<Vec<i32>>, p2_elem: i32, p3_number: i32) -> (r_final: bool)
    requires
        seq.len() > 0,
    ensures
        exists|v1: Seq<i32>, v2: Seq<i32>| #[trigger] step1(seq@, v1) && #[trigger] step2(v1, p2_elem, v2) && step3(v2, p3_number, r_final),
{
    let x1 = f1_max_length_list(seq);
    let x2 = f2_insert_before_each(x1, p2_elem);
    let x3 = f3_is_greater(&x2, p3_number);
    proof {
        assert(step1(seq@, x1@));
        assert(step2(x1@, p2_elem, x2@));
        assert(step3(x2@, p3_number, x3));
    }
    x3
}

} // verus!