Definition:Pool of Assumptions

Definition
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.

The assumptions in this pool are called, naturally enough, the pooled assumptions.

In constructing a proof, there is no essential distinction between assumptions and premises.

Thus, in a particular sequent $p_1, \ldots, p_n \vdash p$, the collection $\left\{{p_1, \ldots, p_n}\right\}$ is also called the pool of assumptions.