Analyze the prove exchange lemma: swapping preserves feasibility.
Examples
Input:"proof_case_1"
Output:true
Input:"proof_case_2"
Output:true
Hints
Consider how swapping two elements affects the overall feasibility of the solution, and whether this operation can be used to transform any feasible solution into another.
Explore the properties of the feasibility condition—does it depend on the order of elements, or is it invariant under certain transformations like swaps?
Formalize the proof by induction or contradiction: assume swapping breaks feasibility, then derive a contradiction by analyzing the impact on the feasibility condition.