Let $L \in BPP$ be decided by a poly-time $TM M (x, u)$ using certificates ofpoly-length $p(n)$.Then for every $n \in \mathbb{N}$  there exists a certificate $u_n$ s.t. for all $x$ with $|x| = n$:$$x \in L \iff M(x, un) = 1$$Can someone gives a intuitive reasont why above theorem is true?
$BPP$ class and theorem
complexity theory;probability theory