Is it obligatory to wash the bedding and what is the ruling on its purity if one has a wet dream and semen comes out and there is doubt about it having reached the bedding?

Ghusl (ritual bath) is obligatory for whoever experiences a wet dream and finds semen after waking up. However, if he does not see semen or doubts its presence, then ghusl is not obligatory for him. Semen is pure, so there is no need to purify anything it touches. Even according to the opinion that it is impure, it is not necessary to wash the bedding merely due to doubt, because the default is that the bedding is pure until its contamination with impurity is established with certainty.