\begin{definition}[Definition:Pool of Assumptions]
The '''pool of assumptions''', for a formula deduced in a particular proof by natural deduction, is the collection of all the assumptions upon which the formula depends.
These consist of premises and possibly some intermediate assumptions.
The assumptions in this pool are called, naturally enough, the '''pooled assumptions'''.
The '''pooled assumptions''' at the end of a proof (its conclusion) are thus seen to be the premises.
\end{definition}