I trying to understand Lorentz transformation derivation, and confuse on a simple statement: If i have 2 frame of reference, and the second moves relative to the first with speed $V$, so relative to second frame of reference the first have velocity $-V$. Why? It is obviously in Newtonian mechanics, when the time is absolute, but how to prove it in special relativity? This statement used in lorentz transformation derivation.

Perhaps, this follows from the principle of relativity, but i don't know how, for me principle of relativity means just that equations of some physical processes don't change with changing inertial frame of system, and if i put the same initial conditions then the process will proceed identically in different inertial frames of reference.