Abstract: According to the principle of relativity and the principle of invariance of light speed, not only Lorentz transformation can be derived, but also the relativity of motion, that is, the Einstein condition is true. It is also shown that under the condition of the principle of relativity, the principle of invariance of light speed, interval invariance and Lorentz transformation relationship are equivalent.

Key words: the principle of relativity, the principle of invariance of light speed, relativity of motion, Lorentz transformation