It is time to set the standard: a proof does not create an equivalence; it demonstrates it fully.
The equivalence between sensitivities at fixed points and KKT is an intrinsic property, not a fabrication.
For our actuarial commitments, we must rely on existing properties, not on a creation.
For example, the law of gravity was not created by Newton, but explained by his theory; similarly, this proof clarifies a pre-existing relationship.