Things that do not depend on the choice of Cauchy surface

[naima]

A Cauchy surface is a 3d spacelike slice of spacetime.
Could you read the definition (17) p18
the author says that "one can proove that $\sigma$ does not depend on the choice of the Cauchy surface because the functions obey the law of motion."
Could you elaborate?
Thanks

Could anyone add "h" in the title (choice)?

 

[naima]

Sorry
I found the proof several lines below!