[R] Does a survival probability(the probability not experiencing an event) have to be non-increasing?

[Zhiyuan Sun]

My question is related to a cox model with time-dependent variable.
When I think about it more, I get a little confused about
non-increasing assumption for survival probability for an individual.
For example, for a time-dependent ,say x, assuming increasing x
increases the risk of event. Assume,time t1 < t2.  If at x at t1<< x
at t2, obviously, hazard at t1 will less than hazard at t2, assuming
no other covariaates. But is it possible that s(t2|x at t2) > s(t1|x
at t1), since at t2, an individual is at greater risk.  This is kind
of confusing to me.

Thanks for any helpful insights!

Zhiyuan