$P(X > s + t | X > s) = P(X > t)$ for all $s, t \ge 0$

$P(X > s + t) = P(X > s) + P(X > t)$

$P(X > s | X > t) = P(X > s)$ for $s > t$

$E[X|X>s] = E[X]$