We call $x$ a geometric random variable if $x$ takes values $\{1,2,3,$dots$\}$ and $P[x=x]=p(1-p{)}^{x-1}$

where $m,n,P[xs+t|x>t]=P[xs]0.$ Prove that for any two positive integers $m,n,P[xs+t|x>t]=P[xs]$