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



spec fn f1_is_ascii_digit_spec(c: char) -> bool {
    c == '0' || c == '1' || c == '2' || c == '3' || c == '4' || c == '5' || c == '6' || c == '7'
        || c == '8' || c == '9'
}

fn f1_is_ascii_digit(c: char) -> (r: bool)
{
    c == '0' || c == '1' || c == '2' || c == '3' || c == '4' || c == '5' || c == '6' || c == '7'
        || c == '8' || c == '9'
}

spec fn f1_all_digits_spec(s: Seq<char>) -> bool {
    forall|i: nat| #![auto] i < s.len() ==> f1_is_ascii_digit_spec(s[i as int])
}

fn f1_all_digits(s: String) -> (result: bool)
    requires
        s.is_ascii(),
{
    let mut i = 0;
    while i < s.as_str().unicode_len()
    {
        if !f1_is_ascii_digit(s.as_str().get_char(i)) {
            return false;
        }
        i = i + 1;
    }
    true
}



spec fn step1(__hp0: String, outp: bool) -> bool {
    (f1_all_digits_spec(__hp0@) == outp)
}

fn chain_driver(s: String) -> (r_final: bool)
    requires
        s.is_ascii(),
    ensures
        step1(s, r_final),
{
    let x1 = f1_all_digits(s);
    proof {
        assert(step1(s, x1));
    }
    x1
}

} // verus!