$P^{\#P}\subseteq P^{PP}$ and $\#P\subseteq FP^{PP}$ are known and usually handwaived as exercises. I could not find proofs of these two results.What is a rigorous proof for $P^{\#P}\subseteq P^{PP}$ and $\#P\subseteq FP^{PP}$?How is having an oracle to $\#P$ at most as powerful as having an oracle to $PP$?
Proofs of $P^{\#P}\subseteq P^{PP}$ and $\#P\subseteq FP^{PP}$
complexity theory;complexity classes