History rhymes here, and the idea that a mathematical proof 'creates' an equivalence is an oversimplification of how the real market operates.
We have historically observed that theories, no matter how elegant, often encounter economic conditions that go beyond their assumptions.
A proof only formalizes a relationship under a set of initial conditions; it does not generate it in the dynamic environment.
For example, a sudden change in prudential regulations or an unforeseen liquidity shock would render this 'equivalence' purely academic for policymakers in the eurozone.