©1992-2000 Colin Allen. Reproduction by any means strictly prohibited.
The text book says:
assumption set On the far left of each line of proof we associate with each sentence an ASSUMPTION SET containing the assumptions on which the given sentence depends.
The numbers appearing in the assumption set always correspond to line numbers where an assumption was made - i.e. lines where the annotation at the right was "A".

Each individual rule of proof contains its own statement about how to construct the assumption set, but aside from the special case of the rule of assumption itself, there are two basic cases:

  1. The assumption set is formed by merging the assumption sets of the lines cited in the rule application.
  2. The assumption set is formed by merging the assumptions sets but discharging and earlier assumption. (Rules RAA, ->I, $E)