Before rushing to assert a creation, one must ask what happens if this 'equivalence' turns out to be non-persistent.
A proof never creates an equivalence; it formalizes or highlights it, like a PBOC resolution clarifies a preexisting policy.
The underlying market conditions, such as a drastic change in liquidity or more restricted capital flows, could render this mathematical 'creation' irrelevant.
If the assumptions no longer hold in the face of inventory shocks or geopolitical developments, the proof itself does not protect us from drawdowns.