A formal type of proof most frequently encountered in elementary geometry courses in which known or derived statements
are written in the left column, and the reason that each statement is known or valid
is written next to it in the right column. The proof then proceeds from the known
facts to the theorem to be demonstrated. This form of
proof can therefore be pedagogically useful by teaching logical thinking, since steps
incrementally build of previous results and each step can be made only if it can
be explicitly justified.

However, this form of proof is virtually never used by practicing mathematicians because its confining and verbose format render it of very limited utility to any but the most simple of theorems.