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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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 | 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(arr: &Vec<i32>, key: i32) -> (result: bool)
{
let mut index = 0;
while index < arr.len()
{
if (arr[index] == key) {
return true;
}
index += 1;
}
false
}
fn f1_find_dissimilar(arr1: &Vec<i32>, arr2: &Vec<i32>) -> (result: Vec<i32>)
{
let mut result = Vec::new();
let mut index = 0;
while index < arr1.len()
{
if (!f1_contains(arr2, arr1[index]) && !f1_contains(&result, arr1[index])) {
result.push(arr1[index]);
}
index += 1;
}
let mut index = 0;
while index < arr2.len()
{
if (!f1_contains(arr1, arr2[index]) && !f1_contains(&result, arr2[index])) {
result.push(arr2[index]);
}
index += 1;
}
result
}
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_has_only_one_distinct_element(arr: &Vec<i32>) -> (result: bool)
{
if arr.len() <= 1 {
return true;
}
let mut index = 1;
while index < arr.len()
{
if arr[0] != arr[index] {
return false;
}
index += 1;
}
true
}
spec fn step1(__hp0: Seq<i32>, __hp1: Seq<i32>, outp: Seq<i32>) -> bool {
(forall|i: int|
0 <= i < __hp0.len() ==> (!__hp1.contains(#[trigger] __hp0[i]) ==> outp.contains(
__hp0[i],
)))
&& (forall|i: int|
0 <= i < __hp1.len() ==> (!__hp0.contains(#[trigger] __hp1[i]) ==> outp.contains(
__hp1[i],
)))
&& (forall|i: int, j: int|
0 <= i < j < outp.len() ==> #[trigger] outp[i] != #[trigger] outp[j])
}
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>, outp: bool) -> bool {
(outp == (forall|i: int| 1 <= i < inp.len() ==> inp[0] == #[trigger] inp[i]))
}
fn chain_driver(arr1: &Vec<i32>, arr2: &Vec<i32>, p2_elem: 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, r_final),
{
let x1 = f1_find_dissimilar(arr1, arr2);
let x2 = f2_insert_before_each(&x1, p2_elem);
let x3 = f3_has_only_one_distinct_element(&x2);
proof {
assert(step1(arr1@, arr2@, x1@));
assert(step2(x1@, p2_elem, x2@));
assert(step3(x2@, x3));
}
x3
}
} // verus!
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