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Do Einstein's two postulates of relativity emerge from the Minkowski spacetime metric?

Suppose we begin with Minkowski spacetime and the Minkoswki metric.

https://simple.wikipedia.org/wiki/Minkowski_spacetime

Can we then derive Einstein's two postulates of relativity?

1. First postulate (principle of relativity)

The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems of coordinates in uniform translatory motion. OR: The laws of physics are the same in all inertial frames of reference.

2. Second postulate (invariance of c)

As measured in any inertial frame of reference, light is always propagated in empty space with a definite velocity c that is independent of the state of motion of the emitting body. OR: The speed of light in free space has the same value c in all inertial frames of reference.

Thanks! :)