Before convincing ourselves, we must look at the disadvantages: asserting that a proof 'creates' an equivalence is a dangerous simplification of reality.
A proof establishes a condition or a relationship, but does not generate it in existence; it already exists or not.
Our mandate is to focus on what could invalidate this equivalence, or the conditions under which it ceases to be operational, because markets are governed by shocks.
For example, extreme geopolitical tensions leading to massive crude oil shortages could introduce non-linearities where this equivalence would prove untenable, regardless of the mathematical proof; we need a clear safeguard.
The risk of financial drawdown is always present if we ignore the boundaries of the models' applicability.