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File size: 2,707 Bytes
c62beea | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 | 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: &Vec<i32>, key: i32) -> (result: bool)
{
let mut i = 0;
while i < str.len()
{
if (str[i] == key) {
return true;
}
i += 1;
}
false
}
fn f1_remove_elements(arr1: &Vec<i32>, arr2: &Vec<i32>) -> (result: Vec<i32>)
{
let mut output_str = Vec::new();
let mut index: usize = 0;
while index < arr1.len()
{
if (!f1_contains(arr2, arr1[index])) {
output_str.push(arr1[index]);
}
index += 1;
}
output_str
}
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_contains_k(arr: &Vec<i32>, k: i32) -> (result: bool)
{
let mut index = 0;
while index < arr.len()
{
if (arr[index] == k) {
return true;
}
index += 1;
}
false
}
spec fn step1(__hp0: Seq<i32>, __hp1: Seq<i32>, outp: Seq<i32>) -> 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<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_k: i32, outp: bool) -> bool {
(outp == (exists|i: int| 0 <= i < inp.len() && (inp[i] == p3_k)))
}
fn chain_driver(arr1: &Vec<i32>, arr2: &Vec<i32>, p2_elem: i32, p3_k: i32) -> (r_final: bool)
ensures
exists|v1: Seq<i32>, v2: Seq<i32>| #[trigger] step1(arr1@, arr2@, v1) && #[trigger] step2(v1, p2_elem, v2) && step3(v2, p3_k, r_final),
{
let x1 = f1_remove_elements(arr1, arr2);
let x2 = f2_insert_before_each(&x1, p2_elem);
let x3 = f3_contains_k(&x2, p3_k);
proof {
assert(step1(arr1@, arr2@, x1@));
assert(step2(x1@, p2_elem, x2@));
assert(step3(x2@, p3_k, x3));
}
x3
}
} // verus!
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