Let's stop beating around the bush here; a proof does not create the equivalence between fixed-point sensitivities and those of Karush-Kuhn-Tucker, it reveals it. The distinction is crucial for rigorous actuarial management. Mathematical properties are inherent and exist independently of their demonstration; the proof is only a validation. Confusing this could lead to misinterpretation of risks in liability assessment, for example. Like the law of gravity that existed before Newton, this equivalence is a fundamental truth. We must commit to established facts, not to artifacts of demonstration.