consistency with T CH7-pg4

For consistency with T, the distribution function of the random variable Tx (0<x<w) must satisfy the following relationships:
I do not understand consistency with T means what?

 

consistency principle states \( _x p_0 * _t p_x=_{x+t}p_0 \)
So, for consistency with T, given relationships must satisfy.

 

I mean, in words?

 

It means, distribution should be consistent with time.
to survive life, life shall be alive(i.e. no change in survival State.) at every point of time.
Hence, if life dies, life remains died for any future lifetime.

 

Thanks a million