level_2/41.rs

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



proof fn f1_lemma_vec_push<T>(vec: Seq<T>, i: T, l: usize)
    requires
        l == vec.len(),
    ensures
        forall|k: int| 0 <= k < vec.len() ==> #[trigger] vec[k] == vec.push(i)[k],
        vec.push(i).index(l as int) == i,
{
}

fn f1_contains(str: &[u8], key: u8) -> (result: bool)
{
    let mut i = 0;
    while i < str.len()
    {
        if (str[i] == key) {
            return true;
        }
        i += 1;
    }
    false
}

fn f1_remove_chars(str1: &[u8], str2: &[u8]) -> (result: Vec<u8>)
{
    let mut output_str = Vec::new();
    let mut index: usize = 0;

    while index < str1.len()
    {
        if (!f1_contains(str2, str1[index])) {
            
            output_str.push(str1[index]);
        }
        index += 1;
    }
    output_str
}





fn f2_contains_z(text: &[u8]) -> (result: bool)
{
    let mut index = 0;
    while index < text.len()
    {
        if text[index] == 90 || text[index] == 122 {
            return true;
        }
        index += 1;
    }
    false
}



spec fn step1(__hp0: Seq<u8>, __hp1: Seq<u8>, outp: Seq<u8>) -> bool {
    (forall|i: int|
            0 <= i < outp.len() ==> (__hp0.contains(#[trigger] outp[i]) && !__hp1.contains(
                #[trigger] outp[i],
            )))
    && (forall|i: int|
            0 <= i < __hp0.len() ==> (__hp1.contains(#[trigger] __hp0[i]) || outp.contains(
                #[trigger] __hp0[i],
            )))
}

spec fn step2(inp: Seq<u8>, outp: bool) -> bool {
    (outp == (exists|i: int| 0 <= i < inp.len() && (inp[i] == 90 || inp[i] == 122)))
}

fn chain_driver(str1: &[u8], str2: &[u8]) -> (r_final: bool)
    ensures
        exists|v1: Seq<u8>| #[trigger] step1(str1@, str2@, v1) && step2(v1, r_final),
{
    let x1 = f1_remove_chars(str1, str2);
    let x2 = f2_contains_z(x1.as_slice());
    proof {
        assert(step1(str1@, str2@, x1@));
        assert(step2(x1@, x2));
    }
    x2
}

} // verus!