subproof
An indented stretch of a proof that begins with an assumption.
A subproof is a part of a formal proof that starts with an assumption and is marked by an indented bar. Its lines may cite lines above it that are still available, but once it closes, its individual lines may not be cited again; only the subproof as a whole may be cited, by a rule such as →I.
Examples
In a proof of P → Q, the subproof runs from the assumption P to the line Q.