| use vstd::prelude::*; |
| fn main() {} |
| verus!{ |
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| 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 |
| } |
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| fn f2_insert_before_each(arr: &Vec<i32>, elem: i32) -> (result: Vec<i32>) |
| { |
| let mut result: Vec<i32> = Vec::new(); |
| let mut index = 0; |
|
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| while index < arr.len() |
| { |
| result.push(elem); |
| result.push(arr[index]); |
| index += 1; |
| } |
| result |
| } |
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| 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 |
| } |
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| 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]) |
| } |
|
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| 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]) |
| } |
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| spec fn step3(inp: Seq<i32>, outp: bool) -> bool { |
| (outp == (forall|i: int| 1 <= i < inp.len() ==> inp[0] == #[trigger] inp[i])) |
| } |
|
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| fn chain_driver(nums: &Vec<i32>, p2_elem: 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>, v2: Seq<i32>| #[trigger] step1(nums@, v1) && #[trigger] step2(v1, p2_elem, v2) && step3(v2, r_final), |
| { |
| let x1 = f1_cube_element(nums); |
| let x2 = f2_insert_before_each(&x1, p2_elem); |
| let x3 = f3_has_only_one_distinct_element(&x2); |
| proof { |
| assert(step1(nums@, x1@)); |
| assert(step2(x1@, p2_elem, x2@)); |
| assert(step3(x2@, x3)); |
| } |
| x3 |
| } |
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| } |
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|
