The basic format of structured proofs is surprisingly similar to how middle-school math typically teaches students to write proofs, the &quot;two-column proof&quot; structure. A proof is a sequence of numbered statements in the left column, each of which has to be justified by reasons noted in the right column, which are either appeals to a previous numbered statement, or to a named theorem&#x2F;lemma already introduced in the textbook. Instead of using the second column, Lamport instead writes &quot;PROOF: ...&quot; and gives the justification below each numbered statement, but it otherwise seems quite similar.