$\forall$$p$:FinProbSpace, $a$:$\mathbb{Q}$, $f$:($\mathbb{N}\rightarrow\mathbb{N}$), $X$:($n$:$\mathbb{N}\rightarrow$RandomVariable($p$;$f$($n$))).
\\[0ex]rv{-}iid($p$;$n$.$f$($n$);$n$.$X$($n$)) $\Rightarrow$ rv{-}iid($p$;$n$.$f$($n$);$n$.$X$($n$) + $a$)