How to prove the memoryless property?
Memoryless Property: Suppose $X \sim~ \mathrm{Exp}(\lambda)$. Then $\Pr(X>s+t|X>s)=\Pr(X>t)$ for $s,t\in\mathbb{R}$?
Attempts: $\Pr(X>s+t|X>s)=\frac{\Pr(X>s+t,X>s)}{P(X>s)}$ and I claim that $\Pr(X>s+t,X>s)=\Pr(X>s+t)$ but don't know whether that claim is correct or not.