I have been doing some thinking about the Einstein Equivalence Principle (EEP) and its formulation, namely:
The outcome of any local non-gravitational experiment in a freely falling laboratory isindependent of the velocity of the laboratory and its location in spacetime.
After some time it came to mind the following idea: isn't this formulation just a consequence of the weak equivalence principle plus the covariance principle?
A consequence of the WEP because a freely falling laboratory is equivalent to one in the absence of a gravitational field. But also a consequence of the covariance principle because in the absence of gravity the outcome of the experiment is velocity and position independent.
Any insight is welcome!