| use vstd::prelude::*; |
| fn main() {} |
| verus!{ |
|
|
|
|
|
|
| fn f1_cube_element(nums: &Vec<i32>) -> (cubed: Vec<i32>) |
| requires |
| forall|k: int| |
| 0 <= k < nums.len() ==> (i32::MIN <= #[trigger] nums[k] * #[trigger] nums[k] |
| <= i32::MAX), |
| forall|k: int| |
| 0 <= k < nums.len() ==> (i32::MIN <= #[trigger] nums[k] * #[trigger] nums[k] |
| * #[trigger] nums[k] <= i32::MAX), |
| { |
| let mut cubed_array: Vec<i32> = Vec::new(); |
| let mut i = 0; |
| while i < nums.len() |
| { |
| cubed_array.push(nums[i] * nums[i] * nums[i]); |
| i += 1; |
| } |
| cubed_array |
| } |
|
|
|
|
|
|
|
|
|
|
| proof fn f2_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 f2_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 f2_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 (!f2_contains(arr2, arr1[index])) { |
| |
| output_str.push(arr1[index]); |
| } |
| index += 1; |
| } |
| output_str |
| } |
|
|
|
|
|
|
| spec fn step1(__hp0: Seq<i32>, outp: Seq<i32>) -> bool { |
| (forall|i: int| |
| 0 <= i < __hp0.len() ==> outp[i] == #[trigger] __hp0[i] * #[trigger] __hp0[i] |
| * #[trigger] __hp0[i]) |
| } |
|
|
| spec fn step2(inp: Seq<i32>, p2_key: i32, outp: bool) -> bool { |
| (outp <==> (exists|i: int| 0 <= i < inp.len() && (inp[i] == p2_key))) |
| } |
|
|
| fn chain_driver(nums: &Vec<i32>, p2_key: i32) -> (r_final: bool) |
| requires |
| forall|k: int| |
| 0 <= k < nums.len() ==> (i32::MIN <= #[trigger] nums[k] * #[trigger] nums[k] |
| <= i32::MAX), |
| forall|k: int| |
| 0 <= k < nums.len() ==> (i32::MIN <= #[trigger] nums[k] * #[trigger] nums[k] |
| * #[trigger] nums[k] <= i32::MAX), |
| ensures |
| exists|v1: Seq<i32>| #[trigger] step1(nums@, v1) && step2(v1, p2_key, r_final), |
| { |
| let x1 = f1_cube_element(nums); |
| let x2 = f2_contains(&x1, p2_key); |
| proof { |
| assert(step1(nums@, x1@)); |
| assert(step2(x1@, p2_key, x2)); |
| } |
| x2 |
| } |
|
|
| } |
|
|
